tag:blogger.com,1999:blog-77693454957677431042024-03-18T15:13:26.482-07:00Mathémagique"... Donc, d'après..." et autres sujets mathématiquesMathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.comBlogger82125tag:blogger.com,1999:blog-7769345495767743104.post-74450203140516268712024-02-21T07:03:00.000-08:002024-02-21T07:15:14.587-08:00Une petite pause... et ça repart !<p> </p><p><br /></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="687" data-original-width="1046" height="374" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTUtZi2QLEndb7rivGSE-dgw4dbtUBBaxCgQrSSSrkZStiuRkqpUz53sNIW_KHhiuMHJjepKd1ixYz9rVtrncrhoSr0MRjI8BgY9cXMqi-PgsLq_jSNFpdfTVX12k52E56iHIB2dS6qOkrObPCz24_-EuYwkHDaaqJWhWfy5f3UVIIy4n-uuQy3QzFT5o/w570-h374/Logo-MERCI-bug.jpg" width="570" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Vous cliquez ?</span></span><br /></a></td></tr></tbody></table><br /><p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><i>Mais également merci de votre fidélité à ce blog... et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-46167939611942464112024-02-10T10:09:00.000-08:002024-02-10T10:09:58.858-08:00Les maths comme je les aime /11<p> <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-11.pdf" target="_blank"><span style="font-size: medium;"><span style="font-family: helvetica; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="659" data-original-width="962" height="419" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicEsZapsQMhf5qWiM909S9MfF-vzbYJL4rbIOzdtIfK5q7-Htxl7kFHzza1lhjXr0DNKi6C-k8vnOSV9ZE5Fl1kT8em19xyxngpeCVSuy4B4BSOMw8izSEOgOGL0Z3hDDU_xCH9xZ3Pq7QKP-b11Bq-DQzRV9mylc35wgDBaB_6UUjDcH88sy7dZWCjxQ/w612-h419/bleu-11.jpg" width="612" /></span></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-11.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span><br /></span></a></td></tr></tbody></table></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span></p><p class="ember-view reader-content-blocks__paragraph" id="ember967" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">
... Imaginons donc notre univers de points vu de loin : <br />il ressemble à cette boule </span></span></p><p class="ember-view reader-content-blocks__paragraph" id="ember967"><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE0mPafQEkkGXrWXlDHlBbERFOxAsGHOzD6-CxXxwtwB6F_bP55uBC8yAMvrFm3SVADJZ-TjcpdThLRNn0uvv9ARBmFymjNw7tGHOiEqH_xl78Dx6bou0-MQAcf9ivHNA7JLQIRHDryX3ctGZhL6Xt_znBlVkWrbuJJcfbXQFku2hpifcXb8hK-gRCjmY/s405/univers-BLEU.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="378" data-original-width="405" height="299" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE0mPafQEkkGXrWXlDHlBbERFOxAsGHOzD6-CxXxwtwB6F_bP55uBC8yAMvrFm3SVADJZ-TjcpdThLRNn0uvv9ARBmFymjNw7tGHOiEqH_xl78Dx6bou0-MQAcf9ivHNA7JLQIRHDryX3ctGZhL6Xt_znBlVkWrbuJJcfbXQFku2hpifcXb8hK-gRCjmY/s320/univers-BLEU.jpg" width="320" /></a></span></div><p></p>
<div class="reader-image-block reader-image-block--resize">
<figure class="reader-image-block__figure">
<div class="ivm-image-view-model ">
<div class="ivm-view-attr__img-wrapper display-flex">
<span style="font-size: medium;"><span style="font-family: helvetica;"><img alt="" class="ivm-view-attr__img--centered reader-image-block__img evi-image lazy-image ember-view" id="ember968" src="https://media.licdn.com/dms/image/D4E12AQE8LuOb2hF31A/article-inline_image-shrink_1500_2232/0/1707575943257?e=1712793600&v=beta&t=Iu_L7Vd_1MUMOlgOGiwx5268jXcIiHNkJSsFrMsiEK4" /></span></span>
</div>
</div><span style="font-size: medium;"><span style="font-family: helvetica;">(parce qu’en plus ses points sont bleu : comment et par quoi un
endroit peut-il être coloré ? Ça, c’est le pouvoir de l’imagination !)
</span></span></figure></div>
<p class="ember-view reader-content-blocks__paragraph" id="ember970">
<span style="font-size: medium;"><span class="white-space-pre" style="font-family: helvetica;"> </span><span style="font-family: helvetica;">Et cette boule immense, nous
allons lui infliger trois coupes, la trancher comme un amateur de
pierres semi-précieuses trancherait une géode pour la libérer de sa
gangue et en faire apparaître le quartz ou l’agate qu'elle dissimule.
</span></span></p>
<p class="ember-view reader-content-blocks__paragraph" id="ember971">
<span style="font-size: medium;"><span class="white-space-pre" style="font-family: helvetica;"> </span><span style="font-family: helvetica;">Tranchons donc notre
univers, coupons-le en deux par un de ses plans, et ne gardons que l’un
des deux univers partiels obtenus – par exemple en décolorant les point
de l’autre !
</span></span></p><p></p><p class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><i style="font-family: helvetica;"><span style="color: #1e69ff;"> </span></i></span><span style="font-family: helvetica; font-size: medium;"><b><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph" style="text-align: center;">
<span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-11.pdf" target="_blank"><b>La suite de l'épisode /11 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span>
Mais peut-être prenez-vous le train en route ? Si vous avez raté
les stations précédentes... ou si vous voulez découvrir les suivantes</span></span></p><p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici la progression du voyage</a> 🙂 </span></span></p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><i>Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span style="color: #1e69ff;"> </span></i></span></p><p></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-27571570514602909082024-01-01T06:00:00.000-08:002024-01-18T15:16:37.177-08:00Un "dernier jour" bien arbitraire 🙂 🙂 🙂 <p> <!--[if gte mso 9]><xml>
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</p><h2 align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: x-large;"><b style="font-family: helvetica;"><span style="color: #3737ff;">2024 ?</span></b></span></h2>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Il y a déjà quelques temps que je ne crois plus au
Père Noël,</span><span style="font-family: helvetica;"> <br /></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">et si 2024 ressemble à 2023 </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">croire à la Mère Nouvelan(e), ça va être difficile</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">(avec tout de même une consolation :</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">vous pourrez toujours prétendre ensuite avoir cru à
l’amer nouvel an !)</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Alors au lieu de croire <b>à</b> quelqu’un(e),</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">pourquoi ne pas plutôt croire <b>en</b> quelqu’un(e) –
en quelques-un(e)s ?</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">en celles et ceux qui partagent avec vous </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">même quand vous ne demandez rien ;</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">en celles et ceux qui malgré leur peine restent
ouvert(e)s au monde ;</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">en celles et ceux qui s’expriment au risque de leur
vie ;</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">en celles et ceux qui espèrent (encore) en l’humanité
;</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="color: #3737ff; font-family: helvetica;">en celles et ceux qui vous sourient
lorsque vous leur semblez triste</span><span style="color: #3737ff; font-family: helvetica;"> <br /></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="color: #3737ff; font-family: helvetica;">… ou juste comme ça, <i>gratuitement</i>
:</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="color: #3737ff; font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"><b><i><span style="color: #3737ff;">Je souris à tous ceux que j'aime<br />
<span> </span>Même si je ne les ai vus qu'une
seule fois<br />
<span> </span>Je souris à tous ceux qui
s'aiment<br />
<span> </span>Même si je ne les connais pas</span></i></b></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">(<i><span style="color: #3737ff;">Barbara</span></i>, de
Jacques Prévert… légèrement remanié </span><span style="font-family: helvetica;">🙂<span>)</span><span><br />
<br />
</span><span></span></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Un sourire, donc… </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">non, deux : vous en partagerez bien un avec
quelqu’un(e) ?</span><span> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span> </span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span face=""Segoe UI Emoji", sans-serif">😊</span><span> </span><span face=""Segoe UI Emoji", sans-serif">😊</span></span></p><p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span face=""Segoe UI Emoji", sans-serif"> </span></span></p><p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><i>Merci de votre fidélité à ce blog et peut-être à bientôt ?</i></span></p><p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span><i><br /></i></span></span></p>
Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-27583905481873385052024-01-01T03:00:00.000-08:002024-01-18T15:16:05.644-08:00MERCI à toutes et à tous...<p> </p><p></p><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="823" data-original-width="1252" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyt75i6MfnVYqmGTjwqlMAC7CbXWJ1udZaR2R78G-yxQo-b4GqS-lgZIZmVFon3W3hCqglzwawP2ly_oXPQMteYNpWpHeJ1RenSheHCKXTpht3ixE86WVjuDYC9vUGsMPym_9n6nvFDCIBs-CE6QJG9BQpbEbvnsdlunpJMQIcLUPtT6zxELVI6tkkSIM/w561-h368/Logo-MERCI.jpg" width="561" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Vous cliquez ? 😀</span><br /></span></a></td></tr></tbody></table><p></p><p><br /></p><p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><i>Mais également merci de votre fidélité à ce blog... et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><span style="font-family: helvetica; font-size: medium;"><span><i> </i></span></span></p><p><span style="font-family: helvetica; font-size: medium;"><span><i> </i></span></span></p><p><span style="font-family: helvetica; font-size: medium;"><span><i> </i></span></span></p><p><span style="font-family: helvetica; font-size: medium;"><span><i> </i></span></span></p><p></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-80057937976792230122023-12-13T08:43:00.000-08:002024-01-18T15:17:03.508-08:00Les maths comme je les aime /10<p> </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-10.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="630" data-original-width="922" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJwwlq2yZhk3saSOzp97CYQjczyKAbMxtXBLlOzv2xleP1TFFd5M9ewaxuyAJHIzfbwLcJ04uOzbiM0Dya3EkVEpazha4yqL8s8I7pWcwZ62I3aIQAzpq2XBIETU1n8sZyO9ZzrwltDZoKryPDNqrdMyHYo5XVWEkbXthqq6C4-13kBERtRmK2bWj1-d4/w557-h381/bleu-10.jpg" width="557" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-10.pdf" target="_blank"><span style="font-family: helvetica; font-size: medium;">Cliquez sur l'image</span><br /></a></td></tr></tbody></table><br /><p></p><div style="text-align: left;"> <!--[if gte mso 9]><xml>
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<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Bon, je… (air embarrassé) je n’ai pas été très honnête :
dans les épisodes précédents j’ai « inventé » l’objet ponctuel puis grâce à lui
j’ai pu faire apparaître les premiers éléments de la géométrie : le point, la
ligne, la surface (et ensuite, en m’appuyant sur eux, les nombres – tout au
moins jusqu’aux nombres rationnels) !</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Mais cette géométrie, je l’ai arrêtée, je l’ai <i>cantonnée</i>
au plan, et ça ce n’est <b>pas</b> bien !</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Pourquoi ? Parce que nous ne sommes pas des animaux tout
plats, rampant parmi les points d’un plan ; parce que nous sommes équipés
d’origine d’un système optique stéréo conçu pour fonctionner dans l’espace ;
parce que le contraindre à n’observer l’espace qu’à travers des projections
planes (dessins, photos, vidéos…) ce n’est pas bien !</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span><i style="font-family: helvetica;"><span style="color: #1e69ff;">– Mais pourquoi ce ne
serait pas bien ? Avec tous les logiciels 3D qu’on a maintenant ?</span></i></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span style="color: #1e69ff;"> </span></i><span style="font-family: helvetica;">Euh, parce que ce ne sont PAS des logiciels 3D,
justement, ce sont des logiciels <b>de simulation</b> 3D ! Ils trichent avec
vos yeux… ou plutôt ils trichent avec votre cerveau, ils lui demandent
d’interpréter les informations que vos yeux lui envoient comme du 3D. De <i>déformer</i>
ces informations parce qu’à la base votre cerveau sait très bien que ce n’est
pas du 3D : en 3D vos deux yeux ne verraient pas la même chose !</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span><i style="font-family: helvetica;"><span style="color: #1e69ff;">– D’accord, mais si ces
logiciels nous aident à travailler sur des objets 3D, qu’est-ce que ça peut
faire ?</span></i></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span style="color: #1e69ff;"> </span></i></span><span style="font-family: helvetica; font-size: medium;"><b><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph" style="text-align: center;">
<span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-10.pdf" target="_blank"><b>La suite de l'épisode /10 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span>
Mais peut-être prenez-vous le train en route ? Si vous avez raté
les stations précédentes... ou si vous voulez découvrir les suivantes</span></span></p><p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici la progression du voyage</a> 🙂 </span></span></p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><i>Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span style="color: #1e69ff;"> </span></i></span></p>
</div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-40720598351371138682023-11-21T03:43:00.000-08:002024-01-18T15:17:42.796-08:00Les maths comme je les aime /9<p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-09.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="648" data-original-width="946" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1WjkoGb0hSWpVYVvdxuxK1a6ZYhZyyDdi_uIKlnGzeQLkbIqk2ikRRbFK14gJikCylYNfHtIc7CJCV4Rews165Z9rZgQMmKq7BXrCcCRIwpVMDbZ5c3QrqGyZE0ijLmcIbmOqtGSIcOeQuiHQV3ijiqEpFaWxwssVPHq8FsasXpgDVjLEpmQ62o1NJJU/w578-h396/Bleu-09.jpg" width="578" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-09.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><p></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"> <span>De rien à… un peu plus : chaque nouvel épisode
s'appuie sur les précédents pour <i>raconter</i> un peu plus de maths. </span></span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;"> *** *** *** </span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><b>Multiplier des points ???</b> </span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;">Oui, mais pas n’importe lesquels
: nous travaillons toujours sur les points de la droite <b><i>d</i></b> que
j’ai définie dans les épisodes précédents <span>(cette droite passe par deux points distincts <b>A</b> et <b>B</b> que j’ai
allumés dans un espace tout noir. J’ai appelé le point <b>A</b> « point origine
d’une graduation géométrique de <b><i>d</i></b> », et le point <b>B</b> « point
unité » de cette graduation). </span><span></span></span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> <br /></span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Bon, cette multiplication entre points va <s>peut-être</s>
vraisemblablement vous dérouter.… mais vous le verrez, elle est très sérieuse.
Là je vous la présente, et ensuite on en discute, d’accord ?</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><i><span style="color: #1e69ff;">– Oui, d’accord </span></i><i><span style="color: #1e69ff;">(de toute façon on n’a pas le choix,
c’est vous qui écrivez !)</span><span style="color: #1e69ff;">, mais c’est pas
très rassurant : déjà que votre addition entre points était un peu… bizarre ? </span><span> </span></i></span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Je sais, je sais. Mais rappelez-vous, vous aviez fini par
reconnaître qu’elle tenait la route. <b>On commence ?</b></span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><b><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph" style="text-align: center;">
<span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-09.pdf" target="_blank"><b>L'épisode /9 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span>
Mais peut-être prenez-vous le train en route ? Si vous avez raté
les stations précédentes... ou si vous voulez découvrir les suivantes</span></span></p><p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-family: helvetica; font-size: medium;"><span><a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici la progression du voyage</a> 🙂 </span></span></p>
<p class="reader-text-block__paragraph"><span style="font-family: helvetica; font-size: medium;"><span>
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-family: helvetica; font-size: medium;"><i>Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-91793196559987560812023-11-20T08:34:00.000-08:002024-01-18T15:18:41.986-08:00... le retour !<p> </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="697" data-original-width="1059" height="377" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTrLgvwZXybUWbPAQofnCelc2X45Wgp5Dp1wKIWbmVo8gDR0eZjpJv3yrJ0_yvSK6GKLwY5rf-B1PnZ1jA8Gw1rxPxobI4db83SjwV7oo_QnY91TyKY2_WRz9JpzcOoqWfXAL6sC8TN3C23M3b4KoHytIPTJekG0-I8uWEU05mwp8IXUEL4245r3qvui8/w572-h377/retour-au-vrai-site.jpg" width="572" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image !</span></span><br /></a></td></tr></tbody></table><p></p><h1 style="text-align: center;"><span style="font-family: helvetica;"><span style="font-size: medium;">Et un grand merci également <br />à toutes celles et à tous ceux qui se sont inquiétés <br />de cette pause involontaire !</span></span></h1><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;">À très bientôt maintenant (demain ou après-demain) pour un nouvel épisode.</span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></div><div style="text-align: left;"><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span><i style="font-family: helvetica;">Merci de votre fidélité,</i></span></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></div><div style="text-align: center;"><span style="font-family: helvetica;"><span style="font-size: medium;"> <br /></span></span></div><p> </p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-13256543853609537892023-11-10T08:04:00.002-08:002023-11-11T09:42:42.005-08:00Convalescence<p> </p><p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://mathemagique.eu/" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" data-original-height="631" data-original-width="962" height="372" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9a171Q51oJqhclJqZOk1vOSlng5mVgN0wEEvnJmbgGqlBfz4SizCqwSjgnkiujgoHuvyL4jC9UdqZefBTOqpQrD0002_b78WVBaeAFi9S6keeiJAXTVdfpGp4uo3i92AsJPSODzLd43ARKkIPzyMHshCY_D-LH6mboQgzsavrMV4kadK0Vs2-IgxpVYk/w568-h372/Lk-annonce-site-miroir.jpg" width="568" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: helvetica;"><span style="font-size: medium;">cliquez sur l'image !</span></span><br /></td></tr></tbody></table><p></p><div style="text-align: center;"><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: large;">Ne vous inquiétez pas pour lui, <br />il va revenir en pleine forme !</span><span style="font-size: medium;"><br /></span></span></span></span></span></div><div style="text-align: left;"><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></span></span></span></div><div style="text-align: center;"><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;">Mais ça lui ferait vraiment plaisir que vous cliquiez sur son ami 😁 ... <br />c'est ici : <a href="https://mathemagique.eu/" target="_blank"> https://mathemagique.eu/</a></span></span></span></span></span></div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-84365848212063253502023-11-02T06:04:00.001-07:002024-01-18T15:19:30.244-08:00Les maths comme je les aime /4<p> </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-04.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="657" data-original-width="957" height="382" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCSmzAjxmhbI4WRJ5Zu1_tP6x6Z_-6CHjq1_2hNB4RdZTzpKutdLw35TwM1XFAdIR7a8ZRQO4IfPnWbFlSW9c4PifZaj5IHcrbBb-Ppm1k32LKydgymY-qrm22QFrPdzUIKQH0yZz8PKaH6GyzNcglp1KLPuS0jH6eGwCeWiJL2ZB8WyIpOEoI9532pY/w555-h382/Bleu-04.jpg" width="555" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-04.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span><br /></span></a></td></tr></tbody></table><br /> <span style="font-family: helvetica; font-size: medium;">De rien à… un peu plus : chaque nouvel épisode
s'appuie sur les précédents pour raconter un peu plus de maths. </span><p></p><p><span style="font-family: helvetica; font-size: medium;">[Un épisode /4 <b>après</b> l'épisode /8 🤪 ? Pour plus de fluidité j'ai remanié ma progression... mais je viens seulement d'achever cet épisode intercalaire !] </span>
</p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;"> *** *** *** </span></p><span style="font-size: medium;"><span style="font-family: helvetica;"><b>Incontournable, le plan ? </b><br /></span>
<span style="font-family: helvetica;"><br />
Oui, parce qu’il est l’un des trois éléments de base de la géométrie d’Euclide <br />
(et 22 siècles plus tard de Hilbert) : le point, la droite, le plan ! <br /></span>
<span style="font-family: helvetica;"><br />
Ce que j’ai écrit pour la droite, c’est tout aussi vrai pour lui : sans lui, la géométrie euclidienne n’irait pas bien loin ! <br />(Sans le point non plus, bien sûr mais ça, si après tous les épisodes
précédents vous n’en êtes pas persuadé(e)s, j’abandonne !)
<br /></span>
<span style="font-family: helvetica;"><br />
Mais le plan est incontournable pour une autre raison également… <br />j’y reviendrai bientôt. <br /></span>
<span style="font-family: helvetica;"><br />
Bon, si nous commencions par le commencement ? <br />
Pour inventer le plan, nous allons avoir besoin des droites <br />(ça, c’était l’épisode /3)… et des surfaces.<br /></span>
<span style="font-family: helvetica;"><br />
Je ne vous ai encore rien raconté sur les surfaces et je n’ai pas trop envie d’y consacrer tout un épisode alors vous voulez bien qu’on se contente d’un paragraphe 0 dans cet épisode-ci ? C’est parti !<br /></span>
<span style="font-family: helvetica;"><br /></span>
<span style="color: #1e69ff; font-family: helvetica;">– Eh, pourquoi vous nous demandez notre avis si vous n’attendez même pas notre réponse ?
Mais oui d’accord, nous voulons bien !</span><span style="font-family: helvetica;">
<br /></span>
<span style="font-family: helvetica;"><br />
– Merci… et vous avez raison, j’aurais dû l’attendre ! Je veux toujours aller trop vite !
</span></span><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><b style="font-family: helvetica;"><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-04.pdf" target="_blank"><b>L'épisode /4 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">
Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes... ou si vous voulez découvrir les suivantes</span></span></p><p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici la progression du voyage</a> 🙂 </span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><i style="font-family: helvetica;">Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-55946409111087979042023-10-28T02:47:00.012-07:002024-01-18T15:20:01.678-08:00Rennes 2023 : aux Journées Nationales de l’APMEP<div style="text-align: left;"><span style="font-family: helvetica;"><br /></span></div><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span>Deux jours de présence </span></span></span><br /><span style="font-family: helvetica;"><span style="font-size: medium;"><span>aux stands d’<b>images
des mathématiques</b> et de <b>mathémagique.com</b></span></span></span></div><p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">ce n’est évidemment pas de tout
repos…<br />mais c’est un tel plaisir de vous
voir tous, de bavarder avec vous </span><span style="font-family: helvetica;">😊</span><span style="font-family: helvetica;"></span><span style="font-family: helvetica;"> <br /></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Et un autre plaisir, <b><i><span style="color: #1e69ff;">mon atelier</span></i></b>, où nous avons parlé </span><span style="font-family: helvetica;">de tout et de rien…<br />enfin, plutôt de rien à <s>presque tout</s> un peu
plus ! <br /></span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Le thème en était <span style="color: #0070c0;">: <br /></span></span><span style="font-family: helvetica;"><b><i><span style="color: #1e69ff;">une approche géométrique du nombre (et des structures
numériques)<br /></span></i></b><span style="color: #1e69ff;"></span><span><br />alors bien sûr nous avons parlé</span></span></span></p> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YdpZblitMylTLqzPj6BqAP0kjyaBX7LWwlXvI2ykKBm5fzmOCIdMfhcnp6H5LMFDL6A_eGf7yqWN7iuYx9O52lDPg0OEOrampWOIdZ7tKT2lZiX-eHNTIuyRPGn3YY3s8WSJCBQ65PdeyQNbsi5QpJnp46fYZ_ywg90zu_gw2CSPaWrvNzQnjrQ8G5w/s1310/de-geo-etc.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="949" data-original-width="1310" height="409" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YdpZblitMylTLqzPj6BqAP0kjyaBX7LWwlXvI2ykKBm5fzmOCIdMfhcnp6H5LMFDL6A_eGf7yqWN7iuYx9O52lDPg0OEOrampWOIdZ7tKT2lZiX-eHNTIuyRPGn3YY3s8WSJCBQ65PdeyQNbsi5QpJnp46fYZ_ywg90zu_gw2CSPaWrvNzQnjrQ8G5w/w565-h409/de-geo-etc.jpg" width="565" /> </a></div><div style="text-align: left;"><!--[if gte mso 9]><xml>
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
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<w:LsdException Locked="false" Priority="31" QFormat="true"
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<w:LsdException Locked="false" Priority="32" QFormat="true"
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<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
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<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
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<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
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mso-tstyle-colband-size:0;
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mso-para-margin-left:0cm;
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mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
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mso-font-kerning:1.0pt;
mso-ligatures:standardcontextual;
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<![endif]-->
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<p align="center" class="MsoNoSpacing" style="text-align: center;"><a name="_Hlk149310301"></a><span style="font-family: helvetica;"><span style="font-size: medium;"><b><i><span>MERCI pour vos sourires, vos regards éveillés,
vos interventions </span></i></b><i><span><br /></span></i></span><span style="font-size: small;"><i><span>(et vos applaudissements)</span></i></span><span style="font-size: medium;"><b><i><span> !<br /></span></i></b></span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> <br /></span></span></p></div><p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">Certains épisodes, nous
les avons à peine effleurés <br />(1h30 parfois ça passe vraiment vite),</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">mais si vous cliquez sur le lien juste
en-dessous <br />vous les retrouverez tous au complet</span></span></p>
<p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: small;"><span style="font-family: helvetica;">(ou presque : il me reste encore un peu de travail sur
l'épisode 9 !)</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> :</span></span></p><p align="center" class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://lesmathscommejelesaime.fr/" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="179" data-original-width="841" height="68" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7Ev8M-kD-3DiGRaSxzx4UMSHXvk1ylhCZ2dEzS1g4xo6aNatU-MACHfiNWGcn4S6BV__Y21sKFXz9cm0HybkUSTdYuA2kiIyt9b8-PbsczRn95jBvaKx0bOrz9MsfdPSUvy9mqbMQE_AvdgHEt6gYwgco90NOdHtvHvvnBse95NI4b7kbDEifZp2fh24/s320/logo-et-lien-lmcjla.jpg" width="320" /></a></span></div><span style="font-size: medium;"> </span><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span>
<p></p><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span><i style="font-family: helvetica;">Merci également de votre fidélité et peut-être à bientôt ?</i></span></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p> <br /></div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-55185808397394366212023-10-25T14:07:00.000-07:002024-01-18T15:20:32.619-08:00Les maths comme je les aime /0 Prologue<p> </p><p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-00.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="656" data-original-width="955" height="402" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP_OWl2PwAjn98CpzU6N139DZ6L2YmearXZlSHZpYHZQRNWdlmr5WsIj-YcY6OSdQITpkZMn7MM3_AL0-NF-cFFYQ4OZTA4QIbF4gJ96cDwIkCDRYrPUVmqcAydOJjoRPsx_J0_6xK26VDHssQKXZ-QpUPizY32Y-fjjZ3jIXblQ7_TiDHYmucbX3-qEo/w584-h402/Bleu-00.jpg" width="584" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-00.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><br /><p></p><div style="text-align: left;"> <span style="font-family: helvetica;"><span style="font-size: medium;">
<br /><i>Ce n’était qu’une <b>introduction à la géométrie</b> mais 10 ans plus tard, j’en garde toujours un merveilleux souvenir.
<br /> <br />
</i>Des « quatrièmes » que je ne connaissais que depuis un mois, durant lequel nous avions travaillé sur les nombres. <br />
<br />
Un mois, ce n’est pas beaucoup mais ça suffit pour commencer à savoir travailler ensemble, à trouver naturel pour ces élèves de n’avoir devant eux, durant la trentaine de minutes réservée au cours stricto sensu, qu’un bloc et un stylo sur leur table.<br />
<br />
À trouver également naturel de dialoguer entre eux et avec moi, avec toutefois une règle absolue : <br />
ne jamais couper la parole à qui que ce soit (et tout de même, je ne vais pas mentir, m’accorder une certaine priorité).<br />
<br />
Une classe de 30 élèves, tous actifs, mais pour éviter un foisonnement de prénoms à la Tolstoï je vais très arbitrairement attribuer les dialogues de cette reconstitution à cinq d’entre eux… <br />
<br />
et ne garder parmi les très nombreuses interventions que les plus significatives, <br />
que ce soit pour la progression ou pour l’ambiance. </span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><i><b> </b></i></span></span></div><div style="text-align: left;"><p class="ioran" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span><span><span style="font-family: helvetica;"><b>…</b></span></span></span></p>
<div style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-00.pdf" target="_blank"><span><span><b>La suite est ici ...</b></span></span></a></span></span></div><p class="MsoNoSpacing"><span style="font-family: helvetica;"> </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être êtes-vous déja passé(e) par cette " case départ " ? Si vous désirez découvrir les stations suivantes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez-les ici</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><span style="font-family: helvetica;"></span><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><span style="font-family: helvetica;"><span style="font-size: medium;"><i><b> </b></i></span></span></div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com2tag:blogger.com,1999:blog-7769345495767743104.post-67602979329943759652023-10-20T10:03:00.001-07:002024-01-18T15:21:18.191-08:00Juste une info !<p> </p><div style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span class="break-words"><span dir="ltr"><span style="font-size: medium;"><span style="font-family: helvetica;">Non, je n'ai <b>PAS</b> peur de m'y ennuyer… c'est juste que ça me ferait plaisir 🙂</span></span><span class="white-space-pre"> </span><span><br /></span></span></span></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8vIKoXNhY3lS7dyzXXXy6ybvhuOXXRFoJC1ut0Pr3ADVAiVsyT5xE895oJ6ZtknDYypo3IBZOfqMCzjNGcklxS3Vo0LEx4JEwwApwLfMT2HSADv5VsjyWuXcPo6_8mO8KQYahPAhQv64RhSYCWu4npZJwRwddYwRAyRCzR1MibbxRej1Ohmo8yEwM_pk/s1075/haut-de--vous-venez.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="786" data-original-width="1075" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8vIKoXNhY3lS7dyzXXXy6ybvhuOXXRFoJC1ut0Pr3ADVAiVsyT5xE895oJ6ZtknDYypo3IBZOfqMCzjNGcklxS3Vo0LEx4JEwwApwLfMT2HSADv5VsjyWuXcPo6_8mO8KQYahPAhQv64RhSYCWu4npZJwRwddYwRAyRCzR1MibbxRej1Ohmo8yEwM_pk/w526-h384/haut-de--vous-venez.jpg" width="526" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfR0KkKKLM8Nfp4YRtY8lCgm7wdWzmlWrFIa0xjEWXInoddmZqZixYgeAxcaNqNHq8RPKVegbtjDFOQNye1uCD8ngWvUItyNs4owLHhN7TTVKRRchjB7Mqf-dCQRM8AHHbTexMBINN3m98Quyq7yZNHlHRRXjrebVwjiIfJhOFJOf8xMt0aruMSx7QFK4/s1084/bas-de--vous-venez.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="586" data-original-width="1084" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfR0KkKKLM8Nfp4YRtY8lCgm7wdWzmlWrFIa0xjEWXInoddmZqZixYgeAxcaNqNHq8RPKVegbtjDFOQNye1uCD8ngWvUItyNs4owLHhN7TTVKRRchjB7Mqf-dCQRM8AHHbTexMBINN3m98Quyq7yZNHlHRRXjrebVwjiIfJhOFJOf8xMt0aruMSx7QFK4/w527-h285/bas-de--vous-venez.jpg" width="527" /></a></div><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span><p></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-47679787331555449422023-10-02T08:13:00.002-07:002024-01-18T15:21:40.714-08:00Des étoiles plein les yeux !<p> </p><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><img border="0" data-original-height="339" data-original-width="1665" height="109" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRrizBwahzdElFWJroZxl3FuFAdu02-aJj_WTSYbbQMuofAm1g6IOlcXCzLKic6wyIUrkoSIYMvO_tWfwW6bkPyJUV0oefNM3HJc1IFKvxz5qiqghp5-Gsv9EksVUp2fzRJ53P2xDHA7VLMa_Clf93PRqFw41VhgomV6Ql8JtZRggGwlg_oWItTRI5-Y/w535-h109/bandeau-lmcjla.jpg" style="margin-left: auto; margin-right: auto;" width="535" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRrizBwahzdElFWJroZxl3FuFAdu02-aJj_WTSYbbQMuofAm1g6IOlcXCzLKic6wyIUrkoSIYMvO_tWfwW6bkPyJUV0oefNM3HJc1IFKvxz5qiqghp5-Gsv9EksVUp2fzRJ53P2xDHA7VLMa_Clf93PRqFw41VhgomV6Ql8JtZRggGwlg_oWItTRI5-Y/s1665/bandeau-lmcjla.jpg" style="margin-left: 1em; margin-right: 1em;"> </a></div><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; 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Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
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<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
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<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
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<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
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<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
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<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
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<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
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<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
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<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
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<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
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<w:LsdException Locked="false" Priority="32" QFormat="true"
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<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
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<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
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<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
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<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
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Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
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Name="List Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
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<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 6"/>
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<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hashtag"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Unresolved Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Smart Link"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tableau Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:8.0pt;
mso-para-margin-left:0cm;
line-height:107%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
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<![endif]--><span face=""Calibri", sans-serif" style="line-height: 107%;"><span style="font-size: large;"><a href="https://www.donc-dapres.com/" target="_blank">https://www.donc-dapres.com/</a></span></span> <br /></div><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiANJ343hJ25h5eiyXfR-7PwpghBuSURgdP5B64KjSUNVwUzTU8SEbXFZeLalkD6VV6q2hHzR-S75MACWx-OL1wsO22venDoleDLkQMsY1zvejQbjhdzUulNNLmfNGSainNlrMArgaPMPgY9HgCT5gUKbMdR-EualdHgokETiphG12xTqSFYYqobp1yjRw/s1865/DDA-couv1-web-75pc.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1865" data-original-width="1860" height="468" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiANJ343hJ25h5eiyXfR-7PwpghBuSURgdP5B64KjSUNVwUzTU8SEbXFZeLalkD6VV6q2hHzR-S75MACWx-OL1wsO22venDoleDLkQMsY1zvejQbjhdzUulNNLmfNGSainNlrMArgaPMPgY9HgCT5gUKbMdR-EualdHgokETiphG12xTqSFYYqobp1yjRw/w467-h468/DDA-couv1-web-75pc.gif" width="467" /></a></div><br /> </div><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="color: #2b00fe; font-size: large;"><b>Bien sûr que je suis ému ! </b></span></span></span></span></span></p><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;">Et 10 ans plus
tard, j'aime toujours autant les dessins de Lauréline 😁 . </span></span></span></span></span></p><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;">Bon, le début
n'a pas toujours été facile, facile… </span></span></span></span></span></p><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;">et puis il y a eu la nomination au
prix Tangente 2014, l'appréciation du jury du prix du livre
d'enseignement scientifique 2019 de l'Académie des sciences.</span></span></span></span></span></p><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;"><br />Et tous ces merveilleux commentaires au cours des années 🤗 🤗 <br /><br />Un immense merci à toutes et à tous !</span></span></span></span></span></p><p><span style="font-size: medium;"><i style="font-family: helvetica;"><span class="break-words"><span><span dir="ltr"> Et </span></span></span><span><span><span>merci également de votre fidélité à ce blog.</span></span></span></i></span></p><p><span style="font-size: medium;"><i style="font-family: helvetica;"><span><span><span> </span></span><span><span><span><span>Peut-être à bientôt ? </span></span></span></span></span></i></span></p><div class="MsoNoSpacing" style="text-align: left;"><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p></div><p><span class="break-words"><span><span dir="ltr"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></span></span></span><br /> </p><p></p><p><br /></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-82128202370483255612023-09-25T08:52:00.003-07:002024-01-18T15:21:58.531-08:00Ce n'est encore qu'un bébé-site...<p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><br /></td></tr></tbody></table><p></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="630" data-original-width="918" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhATnMcQpQLNmqmHxFo03lJwRu02N1He6n77yGcVkPbjWv5PhIHfuz8ANSWQFyBKMSaut4xvkCXsy7KReWtAcPh8pJPfC1aYixYcumq--8cuP65zDnZF3Imt7FoXi8eAJ-9-S43EM58wPTpNXsFcZ9_r-kG26DAJqGRVE_ExwaKutTn_68eZy3ddlXoL5w/w527-h362/pour-pdf-ont-leur-site-OKOK.jpg" width="527" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image !</span></span><br /></a></td></tr></tbody></table><p></p><p style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">ou <br /></span></span></p><div align="center" class="MsoNoSpacing"><span style="font-size: medium;"><a href="https://lesmathscommejelesaime.fr/" style="font-family: helvetica;" target="_blank"><b><span><span>cliquez ici ...<br /><br /></span></span></b></a></span></div><div align="center" class="MsoNoSpacing"><span style="font-size: medium;"><span><span><span style="font-family: helvetica;">(oui, c'est le même site 😊 !)</span></span></span><b><span><span><br /></span></span></b><br /></span></div><div align="center" class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><b><i><span><span> </span></span><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"> <br /></span></i></b></span></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></div><div class="MsoNoSpacing" style="text-align: left;"><p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span><span>Merci de votre fidélité à ce blog, et</span></span><span><span> </span></span><span><span><span><span>peut-être à bientôt ?</span></span></span></span></i></span></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p></div><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-89542228058781707402023-09-21T00:00:00.000-07:002024-01-18T15:22:25.234-08:00Les maths comme je les aime : le récap'<br /><p style="text-align: left;"><span style="font-size: medium;"></span></p><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="709" data-original-width="1123" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitB8TpSUBW43ffkx8GM89i66Gq4hrx5CW4_axhBdSBY7d7cN8mSY_agq0EgX31usJckNzULRkI-LvmV8BW9ES0PafYMfsAZIn9ExQULVyTKija02ARrTfKL9OzaXptRC7kjIoQK7GCmiO8Kf5WDoR3t0tcQIv4wFkpJc9f7GI6VVYZYc7iYGcnH13Aiqo/w461-h291/00-recap-final.jpg" width="461" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"></span></div><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span><p></p><p style="text-align: left;"></p><p class="reader-text-block__paragraph" style="text-align: left;">
</p><p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">Ces articles</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> ne sont pas des « articles de maths » mais des articles <b>à propos de maths</b>
: j’essaie d’y raconter ... </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span><span style="font-family: helvetica; font-size: medium;"><b><i>l</i></b></span><span style="font-size: medium;"><span style="font-family: helvetica;"><b><i>es maths comme je les aime</i></b></span></span><span style="font-size: medium;"><span style="font-family: helvetica;">,</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> comme elles se sont construites dans
ma tête, petit à petit. Comme je me les suis appropriées.
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;"> Ce ne sont <b>PAS DU TOUT</b> des cours, tout juste une promenade personnelle parmi
les mathématiques du collège, du lycée et des premières années du
supérieur. Une promenade où se mêlent les maths comme vous les connaissez déjà et les mêmes maths... comme vous ne les connaissez peut-être pas ! Et aussi quelques histoires plus ou moins farfelues 😊. </span></span></p><span style="font-family: helvetica; font-size: medium;">Vous pouvez bien sûr retrouver chacun de ces articles pêle-mêle dans ce blog mais vous pouvez également en trouver ici la liste à jour – avec pour chaque article un (vague !) début de description mais surtout un lien d'accès - et une version pdf.</span><p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span><!--[if gte mso 9]><xml>
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table.MsoNormalTable
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mso-ligatures:standardcontextual;
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</p><div align="center" class="MsoNoSpacing"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><b><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez ici p</span></span></b><b><span style="font-family: helvetica;"><span style="font-size: medium;">our ouvrir le récap'</span></span></b></a></div><div align="center" class="MsoNoSpacing"><b><i><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"> <br /></span></i></b></div><div class="separator" style="clear: both; text-align: center;"> </div><div class="MsoNoSpacing" style="text-align: left;"><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p></div><div align="center" class="MsoNoSpacing"> <p></p>
<br /><b><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"><br /></span></i></b></div><div align="center" class="MsoNoSpacing"><b><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"></span></i></b></div><div align="center" class="MsoNoSpacing"><b><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"><br /><br /> </span></i></b></div><p align="center" class="MsoNoSpacing" style="text-align: center;"><b><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"> </span></i></b></p>
<p></p><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-52404332331835209012023-09-20T12:32:00.005-07:002024-01-18T15:22:48.346-08:00Les maths comme je les aime /8<div style="text-align: left;"> </div><div style="text-align: left;"><br /> <span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-08.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="655" data-original-width="957" height="332" src="https://blogger.googleusercontent.com/img/a/AVvXsEhMlvr18z2Ne8DvNwuT0utZhjfVOj-QWNPUc30lbqpG6HiXA7DGtT99zKz4DCURBcU7X5NQGKM0JqzrOrqCzNzE1lIuSW_oK15QnEnI6OA3Z_ZnkMqaI98WzB4Wqu8-01nNjHvFxl79JKAzm04P13KdvfsSAlWI4jtNFBWswon_K802fBwbWDMO2SImjW4=w485-h332" width="485" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-08.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span></a></td></tr></tbody></table><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-08.pdf" target="_blank"><br /></a></span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica; font-size: medium;"><span><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div style="text-align: left;"><!--[if gte mso 9]><xml>
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</xml><![endif]--><span style="font-family: helvetica; font-size: medium;">De rien à… un peu plus : chaque nouvel épisode
s'appuie sur les précédents pour raconter un peu plus de maths. </span>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;"> *** *** *** </span></p>
<h4 class="MsoNormal" style="line-height: normal; text-align: left;"><span style="font-family: helvetica; font-size: medium;"><b>Bien sûr que
vous pouvez ajouter des points ! </b></span></h4>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;"><b>Vous pouvez même multiplier les points entre eux</b>… <br />mais ça, ce sera pour le prochain épisode 😊 </span></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;">Bon, après avoir défini les nombres comme de
simples attributs des points, </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;">puis une relation d’ordre entre nombres <br />comme la
simple transcription numérique <br />d’une relation d’ordre entre points... </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;">n’est-il
pas raisonnable de mettre en place une addition entre points <br />puis de lui
associer un alter ego numérique : <br />l’addition telle que vous la connaissez
? </span></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica; font-size: medium;"> Vous allez voir, ça va vraiment se faire
tout seul ! </span></p>
<div style="text-align: left;"><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><b style="font-family: helvetica;"><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-08.pdf" target="_blank"><b>L'épisode /8 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
[ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><i style="font-family: helvetica;">Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p></div> </div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-68492872991984554292023-08-31T07:37:00.007-07:002024-01-18T15:23:10.929-08:00Les maths comme je les aime /7<p> </p><p></p><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-07.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="654" data-original-width="957" height="370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmWjU0PW7BvdXHA9WYR7PhsLimc0QPxki341NmUyXVXMCQ7-7pXRdxQbI5g9wdu-IHmOMGrgDu3fh5ISo8gJ1xm7uW3bMs9i9nVUkQwyWUDVV4lOspWoRJd0Okf2Nam8B880nAFXKDA7s1wO0HN5jWqfcmSZOiGYqMAVab5fvO7vRjPwx-c_ayJsNsBLA/w541-h370/Bleu-07.jpg" width="541" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-07.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span></a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><br /><br /><p></p><div style="text-align: center;"><a href="https://colliard.fr/philippe/les-maths-comme-je-les-aime/les-maths-comme-je-les-aime-06.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"></span></a></div><br /><p></p><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> <span class="break-words"><span dir="ltr">Une petite coupure estivale... et c'est reparti !</span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;">
<span style="font-size: medium;"><span style="font-family: helvetica;"><i>Comme les précédents (épisodes /4 et /5) cet épisode s’appuie très librement sur l’article « </i><i><a href="https://images.math.cnrs.fr/Les-harpes-de-Thales.html">les harpes de Thalès</a></i><i> » que j’ai publié sur le site </i><i><a href="https://images.math.cnrs.fr/">« Images des mathématiques (CNRS)</a></i><i> » : </i><b><i>une approche géométrique des nombres</i></b><i>. Très librement parce qu’ici je n’écris pas des maths, </i><b><i>je les raconte…</i></b><i> </i><b><i>comme je les aime</i></b><i> </i>😊<i>. Et comme je voudrais les partager avec vous. Mais bien sûr, fondamentalement ce sont les mêmes maths !</i></span></span>
</div>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">
*** *** ***
</span></span></p><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr">Au menu d’aujourd’hui : comment comparer deux points de d ? </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr">Mais ça veut dire QUOI, comparer deux points de d ? </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr">Qu’est-ce qu’on compare ? Leur couleur, leur âge, leur brillance ? … 🤔 ? ? </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr">Rien
de tout ça, évidemment. En réalité, dire que je compare deux points de d
est un abus de langage, une facilité que je me donne, parce que ce ne
sont pas les points que je compare mais leurs positions respectives sur d
...</span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr">une comparaison résolument géométrique dont les relations d'ordre entre nombres seront une conséquence !</span></span></span></span></div><div style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div><div style="text-align: left;"><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><b style="font-family: helvetica;"><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-07.pdf" target="_blank"><b>L'épisode /7 est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
[ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><i style="font-family: helvetica;">Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span><i><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></i></p><p><i><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span></i></p><p><i><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span></i></p><span style="font-family: helvetica;"><span style="font-size: medium;"><span class="break-words"><span dir="ltr"> </span></span></span></span></div>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-46264802524677760662023-07-28T08:31:00.002-07:002024-01-18T15:23:28.177-08:00Les maths comme je les aime /6<p> </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-06.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="655" data-original-width="960" height="387" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCJvGtVxw6KJEyNu1v2xSiiHMWKagS363sL8y9h9ORWUguQd1ZonD9Sq0uQkMP4T58p0o3NW6PMCdqwgc_mlv7ODJRP4WCUpR0gbEjlOfn1Lliet5fdzXC2QwnH6HPFxnzj6n0fX4CLffdAy-hHNpuV8CMifpEt1k2PIToyEhuVn0MXUVSVQeYchZrAKg/w568-h387/Bleu-06.jpg" width="568" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-06.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><p></p><p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span style="font-family: helvetica;"><i>Comme le précédent (/4) cet épisode s’appuie très librement sur l’article « </i><i><a href="https://images.math.cnrs.fr/Les-harpes-de-Thales.html">les harpes de Thalès</a></i><i> » que j’ai publié sur le site </i><i><a href="https://images.math.cnrs.fr/">« Images des mathématiques (CNRS)</a></i><i> » : </i><b><i>une approche géométrique des nombres</i></b><i>. Très librement parce qu’ici je n’écris pas des maths, </i><b><i>je les raconte…</i></b><i> </i><b><i>comme je les aime</i></b><i> </i>😊<i>. Et comme je voudrais les partager avec vous. Mais bien sûr, fondamentalement ce sont les mêmes maths !</i></span></span>
</p>
<p class="reader-text-block__paragraph" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;">
*** *** ***
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Vous vous rappelez le robot-arpenteur de l’épisode précédent (<i><a href="https://colliard.fr/philippe/les-maths-comme-je-les-aime/les-maths-comme-je-les-aime-04.pdf">/4 Et si les nombres n’étaient que des noms ?</a></i>
🙄) ? Le lointain cousin de l’allumeur de réverbères du Petit Prince
qui, comme lui, allume sans se poser de questions, parce que c’est la
consigne. Sauf que lui, bien sûr, il n’allume et n’éteint pas
constamment le même réverbère (jour, nuit… jour, nuit…), il passe son
éternité à allumer des points différents d’une même droite.
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Des points que j’ai appelés « points-entiers ».
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Ah non, ne commencez pas à chicaner, nous savons très bien, vous
et moi, qu’on ne peut pas allumer un point. Parce qu’un point, ce n’est
qu’un endroit : l’arpenteur, « allume » un point en lui introduisant un
objet ponctuel brillant.
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
(<i>Je suis peut-être un peu grognon ces temps-ci, ça doit être
l’âge… alors excusez-moi si je m’énerve à tort : peut-être n’avez-vous
vraiment pas lu l’épisode 4. En ce cas, s’il vous plaît, lisez-le : cet
épisode en est la suite !</i>)
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><b style="font-family: helvetica;"><i>. . .</i></b></span>
</p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-06.pdf" target="_blank"><b>La suite est ici ...</b></a><b> </b></span></span>
</p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
[ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes,<a href="https://lesmathscommejelesaime.fr/" target="_blank"> retrouvez ici le début du voyage</a> 🙂 ]
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
</span></span></p>
<p class="reader-text-block__paragraph">
<span style="font-size: medium;"><i style="font-family: helvetica;">Merci de votre fidélité et peut-être à bientôt ?</i></span>
</p><p>
<span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><i><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></i></p><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-44313343299472720562023-07-17T06:46:00.003-07:002024-01-18T15:24:41.971-08:00Les maths comme je les aime /5b<p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05b.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="657" data-original-width="960" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoZyOrEYTa7Gf0FCQF6dTKvfTcT3JkV1bzsOdbgHQhRFFxuKEKr-dwaAOB2a5JacVbTZYJywthCBlyaq7W6NoxsE4-g94DB88Z13lF874ZW7nWh1KUdBrnVR6YoaEmxo1D-yYtjmNAujTT8ra5KIL_kFEcKEnx8z0-cPcNp_27X_gE51hyyjkyQJ2Mc-A/w579-h396/Bleu-05b.jpg" width="579" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05b.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span></a></td></tr></tbody></table><br /><div style="text-align: left;"><br /><i><br /></i></div><i><!--[if gte mso 9]><xml>
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<p class="MsoNormal"><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Oui, encore une histoire</i> 😊...</span></span></p><p><span style="font-size: medium;"><i style="font-family: helvetica;">et non, bien entendu, ça ne s'est PAS passé comme ça !</i></span></p>
<p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> "Hi-Ati , ou la création des dizaines" est la seconde histoire que</i> <i>j'ai composée<br />
sur le modèle des " Histoires comme ça " de Kipling… mais sans son talent ! </i></span></span></p>
<p><span style="font-size: medium;"><i style="font-family: helvetica;">Elle n’a naturellement d’intérêt qu’en complément de l’article 4 !</i></span></p>
<p><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Ce ne sont que des histoires<br />
mais elles m’ont très longtemps permis d’introduire la numération. </i></span></span></p>
<p><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Soyez indulgent(e)s !</i></span></span><i><span style="font-family: helvetica;"><br /></span>
</i></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">. . .</span></i></b></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><span style="font-family: helvetica; font-size: x-large; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">Hi-Ati et la création des dizaines </span><span style="font-size: x-large;"><span style="font-family: helvetica;"><i><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"><br /></span></i></span></span></b></p><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"> <span><span>Or, écoute bien, il arriva un jour que Ji-Déhem, le papa de Hi-Ati, </span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span>fit une pêche vraiment très réussie, et qu'il attrapa beaucoup de poissons. </span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span>Il avait encore plus de poissons que de harpons dans son sac : </span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span>s'il prenait un harpon dans son sac et qu'il le posait à côté d'un poisson, </span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span>il n'avait pas assez de harpons pour en mettre un à côté de chaque poisson.</span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span><br />Je vais dessiner ce qui se passait :</span></span></span></span></div><div class="reader-text-block__paragraph" style="text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;"><span><span> </span></span></span></span></div><div style="text-align: center;"><img alt="" height="174" 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width="535" /></div><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: left;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></i></b><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></p>
<div class="MsoNormal" style="line-height: normal; text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05b.pdf" target="_blank"><b><span style="font-family: helvetica;"><span style="font-size: medium;">La suite est ici ...</span></span></b></a></div><div class="MsoNormal" style="line-height: normal; text-align: center;"><br /><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></div>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-82221149475414322342023-07-06T08:18:00.006-07:002024-01-18T15:26:00.646-08:00Les maths comme je les aime... C'est quoi ce truc ???<p> </p><div style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"><img border="0" data-original-height="658" data-original-width="961" height="328" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWwQ5Dirv8X-rvuPjL7gsW2Tj04Htvu77a4yt5MwKM8V26GyT0Yq4T3s26fIM12VAJLWfc_ovsWuMjonfqWgWASjwH_ah-eEyrlFGugZaw5WOOGarXF15So5PxRnF9ajO3PIA6-gKO24kz9pTiPVl3FH8jZMIeaWfFh_K1TRwL1rXZRIir2X2RIPv2fqo/w478-h328/Bleu-cest-quoi.jpg" width="478" /></a></div><p></p><p><!--[if gte mso 9]><xml>
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="envelope return"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="line number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="page number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="table of authorities"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="macro"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="toa heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 5"/>
<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Closing"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Signature"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="true"
UnhideWhenUsed="true" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Message Header"/>
<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
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</p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Lorsque j’ai publié
« <a href="https://donc-dapres.com/">donc, d’après</a> », il y a exactement 10
ans (non, ça ne me rajeunit pas !), un commentaire m’a énormément touché, celui
du blogueur Olivier Legay, <a href="https://donc-dapres.com/commentaires.htm" target="_blank">dans un article</a> qu’il a consacré à ce livre :</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"></i></span></p><blockquote><span style="font-size: medium;"><i style="font-family: helvetica;">Philippe Colliard a passé beaucoup de temps pour
penser et écrire cette géométrie qu'il explique au lecteur, supposé être un
collégien et qu'il tutoie dès le début du livre. Ce n'est pas le tutoiement de celui
qui sait devant l'ignorant, mais plutôt de l'ami qui t'emmène par la main pour
te montrer un chemin…</i></span></blockquote><p></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"> </i><span style="font-family: helvetica;">C’est dans le même
esprit que je conçois « <i>les maths comme je les aime</i> » mais avec une différence
majeure : cette série d’articles parle de maths… mais ce n’est <i>PAS</i> un
livre de maths !</span></span></p>
<h3 class="MsoNoSpacing" style="text-align: left;"><span style="font-size: medium;"><span style="font-family: helvetica;">Alors, « <i>c’est
quoi ce truc ?</i> »</span></span></h3>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;"><span>Une succession
de textes qui petit à petit racontent une histoire « idéale » des maths depuis
leur apparition. Et qui la racontent sans « faire des maths », sans aucun autre
préalable que de savoir lire.</span></i></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Pourquoi une
histoire « idéale » ? </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Parce que pour les
mathématiciens ça ne s’est pas du tout passé comme ça :</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> imaginez
les mathématiques comme une créature vivante, une sorte de plante souterraine,
peut-être, une racine minuscule à l’origine mais qui durant des millénaires a
grandi tranquillement dans son monde caché, loin des hommes. </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Et
puis certains d’entre eux y ont débarqué, en ont débusqué des fragments en
creusant un peu partout.</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Petit
à petit ils ont relié ces fragments à d’autres, ils ont dressé une sorte de
cartographie des mathématiques. Puis d’autres hommes ont retracé la chronologie
de leurs efforts.</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><b>ÇA,
c’est la « <i>vraie</i> histoire des mathématiques »</b>, toute remplie d’espoirs
et de désespoirs, d’essais-erreurs, d’acharnements, de fausses pistes, de culs-de-sac…</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Ça
ressemble à l’évolution biologique, qui elle aussi procède par essais-erreurs :
<b>le cheminement des cyanobactéries à l’être humain était bien loin d’être
prévisible – mais maintenant que nous l’avons cartographié rien ne nous empêche
d’y faire apparaître une progression dépouillée de ses errements.</b></span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><b> C’est cette
reconstruction des maths <i>a posteriori</i> que j’imagine dans ces textes :</b> une
origine puis des liens et des ramifications logiques, une expansion
harmonieuse, sans heurts.</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Ça ne s’est pas
passé comme ça ? Non, bien sûr… et alors ? Je n’écris pas des maths, je les raconte,
je les conte. </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> À travers une
construction, une évolution plausibles, rien de plus. </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> À travers également
quelques histoires plus ou moins farfelues mais… je les aime 😊<br /> <br /></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"></span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><span></span></span></span></p>
<div class="MsoNoSpacing" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/" target="_blank"> Le récapitulatif des articles déjà publiés est ici</a> 😊 😊</span></span></div>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Voilà, vous savez tout. </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Non, encore un point : un petit mot de votre part, ça me
ferait vraiment plaisir (sauf s’il est trop désagréable, bien sûr !) </span></span></p><div class="MsoNoSpacing" style="text-align: left;"><p><span style="font-size: medium;"><i><span><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span><span style="font-family: helvetica;"> </span></span><span><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></span></p></div><div class="MsoNoSpacing" style="text-align: left;"><p><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span></p><p><span style="font-size: medium;"><i><span><span style="font-family: helvetica;"> </span></span></i></span></p><p><span style="font-size: medium;"><i><span><span style="font-family: helvetica;"> </span></span></i></span></p></div>
Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-8614522673394269912023-06-28T02:44:00.010-07:002024-01-18T15:26:24.664-08:00Les maths comme je les aime /5a<p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05a.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="656" data-original-width="959" height="393" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwn0GbiN9WEdgeGG91un7D6PgvemdZY2Up6tm_6vzYfztALvUGSgk-AN_OLgTETBV97E58feVT3urz1CZMhz16uANlOT-Ej4KFbvdzgbm6wmfdB5sWCR_zbGdLqY6O7yjbvdU3Pc2SOYCqVjfV4d3N1aCfcnZOTRrPHOcmPezkDoS0DPjALFB__0QfAmQ/w574-h393/Bleu-05a.jpg" width="574" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05a.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><div style="text-align: left;"><i><br /></i></div><i><!--[if gte mso 9]><xml>
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<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
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<p class="MsoNormal"><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Oui, encore une histoire</i> 😊 <i>!</i></span></span></p>
<p class="MsoNormal"><i><span style="font-size: medium;"><span style="font-family: helvetica;">(Avez-vous remarqué que les logos des histoires sont sur
fond « or » et que ces histoires sont associées à l’article qu’elles illustrent
par l’ajout d’une lettre – a, b… – au numéro de l’article ?)</span></span></i></p>
<p class="MsoNormal"><i><span style="font-size: medium;"><span style="font-family: helvetica;">J’avais déjà créé un lien vers cette histoire dans mon
article sur <a href="http://images.math.cnrs.fr/" target="_blank">Images des mathématiques</a> « <a href="https://images.math.cnrs.fr/Les-harpes-de-Thales.html" target="_blank"><b>les harpes de Thalès</b></a> », évidemment à propos de l’écriture des nombres
entiers… mais il m’a semblé qu’elle avait encore davantage sa place ici, avec
le statut « les maths comme je les aime » !</span></span></i></p>
<p class="MsoNormal"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Elle n’a évidemment d’intérêt qu’en complément de l’article 4
! <br /></span></span></i></p>
<p class="MsoNormal"><i><span style="font-size: medium;"><span style="font-family: helvetica;">[ Une histoire 4b, « Hi-Ati et la création des dizaines »
arrivera très prochainement. Ensuite j’avancerai à nouveau sur </span></span><span style="font-size: medium;"><span style="font-family: helvetica;">« </span></span><span style="font-size: medium;"><span style="font-family: helvetica;">les nombres
par la géométrie » – et sur « les harpes de Thalès », que bien
sûr rien ne vous empêche de consulter déjà ici, si vous appréciez des maths
(légèrement) plus formelles ! ]<br /></span></span></i></p>
<p class="MsoNormal"><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Pour la petite histoire Hi-Ati est la première histoire que
j’ai « vendue », en... 1980 (et non, elle ne m’a pas rendu millionnaire !)</i> 😊 😊</span></span></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">. . .</span></i></b></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><span style="font-family: helvetica; font-size: x-large; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">Hi-Ati et la création des chiffres </span><span style="font-size: x-large;"><span style="font-family: helvetica;"><i><span style="mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"><br /></span></i></span></span></b></p><p class="reader-text-block__paragraph"> <span style="font-size: medium;"><span style="font-family: helvetica;"><br />Il y a très longtemps, bien avant que l'Europe n'existe - en ces
temps-là, je crois bien qu'elle était encore rattachée à l'Afrique -
les hommes vivaient dans des cavernes, et leurs familles aussi . Pour se
nourrir, ils tuaient des poissons et des ours avec leurs harpons, de
grandes tiges en bois très pointues et très dures.
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Naturellement ils ne savaient pas compter, puisque personne encore n’avait inventé les chiffres !
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Dans une petite caverne tout près d'une grande rivière vivaient
Hi-Ati et ses parents. Hi-Ati était une petite fille très intelligente,
dont le nom voulait dire : jeune péronnelle trop curieuse. Elle
s'intéressait toujours à tout .
</span></span></p>
<p class="reader-text-block__paragraph"><span style="font-size: medium;"><span style="font-family: helvetica;">
Un jour, son papa revint de la pêche et posa ses harpons et les
poissons juste devant l'entrée de la caverne. Et ce jour là, Hi-Ati et
son papa créèrent les chiffres...
</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: left;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></i></b><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></p>
<div class="MsoNormal" style="line-height: normal; text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05a.pdf" target="_blank"><b><span style="font-family: helvetica;"><span style="font-size: medium;">La suite est ici ...</span></span></b></a></div><div class="MsoNormal" style="line-height: normal; text-align: center;"><b><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></b><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></div>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span><br /><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-37954738642615984472023-06-21T06:34:00.008-07:002024-01-18T15:26:45.759-08:00Les maths comme je les aime /5<div style="text-align: left;"><br /></div><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="658" data-original-width="956" height="385" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxePluK9TL3uB65sUUetwBD6a0iLN6y8Ao12J1-JKtjcE6anr-I49BHL1YvCwLuhnCqv8fZDFBTTYlEcG1MPkHmVJJ35UL_NCPHrbFo6Pw1ic6o5dY9MD9_SM9N-JuN-Xo8-YQS0moguM7jN4pyhSuuziFPFn-lHrJ_EIgHLN40jeZQNdZtuvD7HWpeis/w561-h385/Bleu-05.jpg" width="561" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table><p></p><br /><p><span style="font-size: medium;"><span style="font-family: helvetica;">J’ai entendu vos soupirs et vos murmures :</span></span><i><span style="font-size: medium;"><span style="font-family: helvetica;"><br /></span></span>
<span style="font-size: medium;"><span style="font-family: helvetica;"><br />
– vous nous… euh, fatiguez avec votre géométrie, vos points, vos points, vos points !<br />
On veut des <b>vraies</b> maths, des maths avec des nombres partout !
<br /></span></span>
<span style="font-size: medium;"><span style="font-family: helvetica;"><br />
</span></span></i><span style="font-size: medium;"><span style="font-family: helvetica;">Bon, d’accord, on va s’attaquer aux nombres. </span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;">À tous les nombres, des entiers aux complexes. <br />
Et aux structures numériques qui vont avec. </span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;">Évidemment, ça va prendre un peu de temps<br />
et quelques articles. Mais qui est pressé </span></span><i><span style="font-size: medium;"><span style="font-family: helvetica;">?</span></span></i></p>
<p><span style="font-size: medium;"><span style="font-family: helvetica;">Les
nombres, nous allons les débusquer ensemble, les amener petit à petit à
la lumière alors que tout ce qu’ils souhaitent, eux, c’est qu’on les
laisse tranquilles, chacun dans son point.
<i><br />
<br />
– Dans son </i></span></span><span style="font-size: x-large;"><span style="font-family: helvetica;"><i><b>quoi ?</b></i></span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><i> Vous voulez dire « dans son </i></span></span><span style="font-size: large;"><span style="font-family: helvetica;"><i><b>coin</b></i></span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><i> » ?</i></span></span></p><p><span style="font-size: medium;"><span style="font-family: helvetica;"><i> </i></span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">. . .</span></i></b><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></p>
<div class="MsoNormal" style="line-height: normal; text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-05.pdf" target="_blank"><b><span style="font-family: helvetica;"><span style="font-size: medium;">La suite est ici ...</span></span></b></a></div><div class="MsoNormal" style="line-height: normal; text-align: center;"><b><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></b><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></div>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><p></p><br /><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-73678637131544544372023-05-10T07:50:00.019-07:002024-01-18T15:27:26.681-08:00Les maths comme je les aime /3<h1 style="text-align: center;"><span style="font-family: helvetica; font-size: large;"><b><span><div class="separator" style="clear: both; text-align: center;"><span style="font-family: helvetica; font-size: large;"><b><span> </span></b></span></div><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-03.pdf" target="_blank"><span style="font-size: medium;"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="657" data-original-width="959" height="323" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRA7MH4yrpw7dgu1pdGUnw2u7E-qxyAIl8g7mVzlSDhhmNf3Sb0aS0-KHcS1RZqElDr69Ur9uPeBTVEpWX8Cw9w8p70QMg5TQDSwwIbpaC07HiDL9toe3JvOBJt0Tvwa2mId0U-_W56zNgkFoCxcmPyhRDovz8cD6VoVXfPydpgn7hDypWeA7_LRm1WE8/w472-h323/Bleu-3.jpg" width="472" /></span></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-03.pdf" target="_blank"><span style="font-size: medium;">Cliquez sur l'image</span><br /></a></td></tr></tbody></table><span style="font-family: helvetica; font-size: large;"><span><b> </b></span></span><br /></div></span></b></span></h1><div class="MsoNoSpacing" style="text-align: left;">
<p class="MsoNormal" style="line-height: normal; text-align: left;"><span style="font-size: small;"><span style="font-family: trebuchet;"><i><span>On avance, on avance…</span></i><span></span></span></span></p>
<p class="MsoNormal" style="line-height: normal; text-align: left;"><span style="font-size: small;"><span style="font-family: trebuchet;"><i><span>vous vous en doutiez, maintenant que nous savons
(enfin) ce qu’est une ligne nous allons évidemment nous intéresser à LA ligne
fondamentale, la droite !</span></i></span></span><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"></span></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 3; text-align: center;"><b><i><span style="font-family: helvetica; font-size: medium; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">*** *** ***</span></i></b><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><i>Pourquoi me suis-je tellement attardé sur l’objet
ponctuel, le point, </i><a href="https://colliard.fr/philippe/les-maths-comme/les-maths-02.pdf"><i>la
ligne</i></a><i> ? Parce que ce sont les éléments de base de la géométrie, bien
sûr… mais tout particulièrement parce que ce sont les « parents » de la droite.
Et sans droite, la géométrie euclidienne n’irait pas bien loin !</i></span><i style="font-family: helvetica;"><span> <br /></span></i></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;">Comment dites-vous ? La droite, c’est facile, c’est
une ligne qui va tout droit ? </i></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: helvetica;">Soupir :<span> </span>d’abord
une ligne c’est un endroit, ça ne va nulle part…</i></span></p>
<p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;"> et
ensuite un objet qui « va tout droit », qu’est-ce que ça veut dire ? Dans notre
univers physique, à part les photons, il n’y a pas beaucoup d’objets qui vont
toujours tout droit (et même les photons peuvent dévier) </span></span>!</i></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-align: center;"><b><i><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;">. . .</span></i></b><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></p>
<div class="MsoNormal" style="line-height: normal; text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-03.pdf" target="_blank"><b><span style="font-family: helvetica;"><span style="font-size: medium;">La suite est ici ...</span></span></b></a><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></div>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> <b><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></b><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> </p>
</div><br />Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-24132911909943310282023-04-16T03:40:00.025-07:002024-01-18T15:27:48.654-08:00Les maths comme je les aime /2<div><h1 style="text-align: center;"><span style="font-family: helvetica; font-size: large;"><b><span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-02.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="655" data-original-width="957" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI23Rl3C1bJBr6sDssy2GB4A4SV0NgP_xoceXbTqznzE0JCAFgvJz5O-AzIleBZ2Dm3OtBgp-MTIqE5KsaP6g7BL5Zo45CoqWR02YYherwALLtdTPoj-UZgJz-7_oo1X483GrHFs90PZy6kFmEMiZDfbT8nRiowXKpzBvo9RWZ76_RC7Y2LHLMIGDyRpY/w459-h315/Bleu-2.jpg" width="459" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-02.pdf" target="_blank"><span style="font-size: medium;">Cliquez sur l'image</span><br /></a></td></tr></tbody></table></span></b></span></h1></div><p></p><div class="MsoNoSpacing" style="text-align: center;"><span style="font-family: helvetica; font-size: large;"><span><b> </b></span><b><i><span><br /></span></i></b></span></div><div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: medium;"><i style="font-family: trebuchet;"><span>Bon, il me semble avoir
suffisamment insisté sur l’objet ponctuel, non ?</span></i></span></div><p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: trebuchet;"><span> </span></i><span style="font-family: trebuchet;"><i><span>Mais ce n’est pas
seulement parce que je suis monomaniaque, c’est également parce qu’il est à
l’origine de notre géométrie euclidienne. Je l’ai écrit dès le premier « voyage
» de « </span></i><a href="https://donc-dapres.com/"><i><span>donc, d’après</span></i></a><i><span> » :<br /></span></i></span><i style="font-family: trebuchet;"><span style="color: #c00000;"><br /></span><span style="color: #2b00fe;">pour
commencer notre géométrie, je devais inventer ou l’objet ponctuel, ou le point…
l’autre suit assez simplement. J’ai choisi d’inventer l’objet ponctuel, parce
qu’il me semble plus facile d’imaginer la réduction d’un objet que celle d’un
endroit. </span></i></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><i style="font-family: trebuchet;"><span style="color: #c00000;"> </span></i><i><span><span style="font-family: trebuchet;">Maintenant que nous
savons ce qu’est un objet ponctuel – et ce qu’est un point – nous allons
pouvoir passer à la question suivante : <b>qu’est-ce qu’une ligne ? </b>(Nooooon,<b>
ce n’est pas un trait</b>, pas plus qu’un point n’est une tache !)</span></span></i></span></p>
<p class="MsoNoSpacing" style="text-align: center;"><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"><span> <span style="font-family: helvetica;"><span style="font-size: medium;">*** *** ***</span></span></span> <br /></span></p><p class="MsoNoSpacing" style="text-align: left;"><span style="font-family: helvetica; font-size: medium;">Vous vous rappelez <a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-01a.pdf" target="_blank"><i>Ioran</i></a>
et <a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-01b.pdf" target="_blank"><i>Opa</i></a>
, le mage et l’Atlante devenus objets ponctuels ?</span><span style="font-size: medium;"><span style="font-family: helvetica;">Quand ils se déplacent ils
traversent un ensemble de points : c’est ça, une ligne !</span></span></p>
<p class="MsoNoSpacing" style="text-align: left;"><span style="font-size: medium;"><span style="font-family: helvetica;"><b><span>Une ligne est le trajet
d’un objet ponctuel en déplacement </span></b><span>(l’ensemble
des points qu’il traverse).</span></span></span></p>
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</p><div class="nu2" style="margin-left: 0cm; text-align: left;"><span style="font-family: helvetica;"><span style="font-size: medium;">Une ligne,
donc, est un ensemble de points… qui sont des endroits. Et un ensemble
d’endroits est aussi un endroit donc <b>une ligne est un endroit :</b> on peut
l’occuper ou la traverser mais ni la saisir, ni la déplacer !</span></span></div>
<p></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><i><span>Si Ioran ou Opa – en
mode brillant – se déplaçait suffisamment rapidement vous auriez l’impression
de voir une ligne brillante mais bien sûr ce n’est pas vrai : un endroit ça ne
brille pas. Vous seriez juste victime de la persistance rétinienne, à chaque
instant il n’y aurait bien qu’un seul point éclairé </span></i><i><span>(mais nous n’allons pas nous embarquer sur «
l’effet phi », ça nous emmènerait un peu loin)</span></i><i><span> !</span></i></span><i style="font-family: helvetica;"><span> <br /></span></i></span></p>
<p class="nu2" style="margin-left: 0cm;"><span style="font-size: medium;"><span style="font-family: helvetica;"><b><span>Et un
trait, alors ?</span></b><span> C’est juste un
bricolage humain qui nous permet de nous faire une idée d’une ligne
particulière. Une idée très approximative mais nous n’avons pas le choix. </span></span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><b style="font-family: helvetica;"><span>Deux différences <i>de
nature</i> entre une ligne et un trait :</span></b></span></p>
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<![endif]--><p></p><p class="ioran" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span><span><span style="font-family: helvetica;"><b>…</b></span></span></span></p>
<div style="text-align: center;"><span><span style="font-family: helvetica;"><span><span style="font-size: medium;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-02.pdf" target="_blank"><b>La suite est ici ...</b></a></span><span style="font-size: large;"><i><a href="https://colliard.fr/philippe/les-maths-comme-je-les-aime/les-maths-comme-je-les-aime-02.pdf" target="_blank"> </a></i></span></span></span></span></div><p class="MsoNoSpacing"><b><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></b><b><span style="font-family: "Times New Roman",serif; font-size: 13.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: FR; mso-font-kerning: 0pt; mso-ligatures: none;"> </span></b></p>
<p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté les stations précédentes, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><span style="font-family: helvetica;"></span><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><p class="MsoNoSpacing" style="text-align: left;"></p><p class="MsoNoSpacing" style="text-align: left;"><br /></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0tag:blogger.com,1999:blog-7769345495767743104.post-58703123381800149332023-04-06T06:44:00.021-07:002024-01-18T15:28:08.757-08:00Les maths comme je les aime /1b<p></p><p><!--[if gte mso 9]><xml>
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</p><div class="MsoNoSpacing" style="text-align: center;"><h1><span style="font-size: small;"><i><span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-01b.pdf" target="_blank"><span style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="652" data-original-width="957" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh986uYcl4hpYCOuFYFt885hD-2M2h0WebT5nOMBRPNrsRkmMDcZcylSrwsaUh7rg46sfI0R2Lr0mT10jmm0yN_AnyMqFKxjEJ2HKDlhMyYqmAHgcBNlendXzBZyo2pTClrAsCIX2YEC9_s7oLER1JTkPEcY0tUzBYM28XE35QoEo9WU1hM4GaCmhwFSjA/w398-h271/Bleu-1b.jpg" width="398" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-01b.pdf" target="_blank"><span style="font-family: helvetica;"><span style="font-size: medium;">Cliquez sur l'image</span></span><br /></a></td></tr></tbody></table></span></i></span></h1></div><div class="MsoNoSpacing" style="text-align: center;"><h3><span style="color: #3d85c6; font-family: helvetica;"><b><span><i><span style="font-size: medium;"> </span></i></span></b></span></h3></div><div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>Ma toute première
histoire sur le point, en 1993 ! Elle est idiote mais je l’adore. </span></i></span></div>
<div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>Depuis, le point, je ne
l’ai plus quitté : j’ai écrit « Ioran » en 2003, et surtout bien sûr
« Donc, d’après » en 2014… c’est ça, la monomanie </span></i><span face=""Segoe UI Emoji", sans-serif">😊</span><i><span></span></i></span></div>
<div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span> </span></i></span></div>
<div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>Je n’ai jamais achevé «
Ioran » (une histoire pour les 12 ans de ma fille) : </span></i></span></div><div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>JK Rowling est passée par
là… je ne faisais pas le poids ! </span></i></span></div>
<div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span> </span></i></span></div><div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>« Donc, d’après », c’est
autre chose : </span></i></span></div><div class="MsoNoSpacing" style="text-align: left;"><span style="font-size: small;"><i><span>bien qu’évidemment fondamental, le point n’en était… qu’un point
de départ.</span></i></span></div>
<p class="MsoNoSpacing" style="text-align: center;"><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"><span> *** *** ***</span> <br /></span></p><p class="MsoNoSpacing"><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: FR;"> </span><span style="font-size: medium;"><span style="font-family: helvetica;">Il y a longtemps, très longtemps, Opa (qui ne s’appelait
pas encore Opa) avait été un<i> </i>Atlante plein de talents.</span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Et puis personne ne comprit ce qui se passa :</span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><span> </span><span> </span><span> </span><span> </span> l'Atlantide
se mit à rétrécir…</span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span>et à rétrécir…</span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span>et à rétrécir !</span></span></p><p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span>Et les Atlantes aussi rétrécissaient !</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Quand il sentit qu'il ne pourrait bientôt plus rétrécir
davantage Opa, comme tous les autres Atlantes, revêtit sa plus belle tunique
dorée, fit ses adieux à tous ses amis – qui, eux aussi, rétrécissaient – et se
prépara à disparaître.</span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;"> Puis comme ça, sans raison, il accrocha à sa tunique une
lampe de poche, une de ces formidables lampes atlantes qui duraient des
millénaires et éclairaient l'océan jusqu'à des milliers de mètres de
profondeur. </span></span></p>
<p class="MsoNoSpacing"><span style="font-size: medium;"><span style="font-family: helvetica;">Et aussi, à tout hasard, une grande thermos de chocolat
très chaud ! Enfin, grande, elle ne l'était plus vraiment,
maintenant ! Mais le bruit du chocolat chaud qui glougloutait dans la
bouteille avait un petit côté rassurant. Et puis, Opa ADORAIT le chocolat
chaud.</span></span></p><p class="ioran" style="text-align: center;"><span style="font-size: medium;"><span style="font-family: helvetica;"> </span><span><span style="font-family: helvetica;"><b>…</b></span></span></span></p>
<div style="text-align: center;"><span><span style="font-family: helvetica;"><a href="https://lesmathscommejelesaime.fr/episodes/lesmathscommejelesaime-01b.pdf" target="_blank"><span><span style="font-size: medium;"><b>La
suite est ici ...</b></span><span style="font-size: large;"><i> </i></span></span></a></span></span></div><p class="MsoNoSpacing"><span style="font-family: helvetica;"> </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> [ Mais peut-être prenez-vous le train en route ? Si vous avez raté la station précédente, <a href="https://lesmathscommejelesaime.fr/" target="_blank">retrouvez ici le début du voyage</a> 🙂 ]</span></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: helvetica;"><span style="font-size: medium;"> </span></span></p><span style="font-family: helvetica;"></span><p class="MsoNoSpacing"><i><span style="font-size: medium;"><span style="font-family: helvetica;">Merci de votre fidélité à ce blog, et</span></span><span style="font-size: medium;"><span style="font-family: helvetica;"> </span></span><span style="font-size: medium;"><span style="font-family: helvetica;"><span><span>peut-être à bientôt ?</span></span></span></span></i></p><p class="MsoNoSpacing"><span style="font-family: helvetica; font-size: medium;"><i>Philippe Colliard </i><span><i><a href="https://www.colliard.fr/philippe/" target="_blank">Qui je suis</a></i></span></span>
</p><p class="MsoNoSpacing" style="text-align: left;"></p><br /><p></p>Mathémagique-comhttp://www.blogger.com/profile/18112059906903095372noreply@blogger.com0