{"id":998,"date":"2015-05-06T14:54:37","date_gmt":"2015-05-06T14:54:37","guid":{"rendered":"http:\/\/pageperso.math.univ-toulouse.fr\/hippocampe\/?p=998"},"modified":"2015-05-06T14:54:37","modified_gmt":"2015-05-06T14:54:37","slug":"lycee-saint-joseph-toulouse-dimension","status":"publish","type":"post","link":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/","title":{"rendered":"Lyc\u00e9e Saint-Joseph (Toulouse) &#8211; Dimension"},"content":{"rendered":"<p style=\"text-align: justify\">Les \u00e9l\u00e8ves du lyc\u00e9e Saint-Joseph de Toulouse sont venus \u00e0 l&#8217;universit\u00e9 Paul Sabatier avec leur professeure de math\u00e9matiques pour d\u00e9couvrir le travail de chercheur. Guid\u00e9s par un membre de l&#8217;institut de math\u00e9matiques et par des doctorants, ils ont r\u00e9fl\u00e9chi \u00e0 la notion de dimension et \u00e0 des concepts reli\u00e9s.<\/p>\n<p style=\"text-align: justify\">Tout le monde conna\u00eet les dimensions 1, 2 et 3 qui sont associ\u00e9es \u00e0 une droite, un plan et \u00e0 l&#8217;espace. Mais qu&#8217;en est-il des dimensions sup\u00e9rieures ? Comment les formaliser math\u00e9matiquement et existe-t-il une interpr\u00e9tation dans la vie de tous les jours ? Une solution math\u00e9matique a \u00e9t\u00e9 propos\u00e9e par un groupe d&#8217;\u00e9l\u00e8ves et ils ont m\u00eame r\u00e9ussi \u00e0 d\u00e9finir des dimensions non enti\u00e8res associ\u00e9es \u00e0 des fractales ! Pendant ce temps, un autre groupe a interpr\u00e9t\u00e9 la dimension 4 comme l&#8217;espace-temps. Saurez-vous donner un exemple de votre quotidien qui se mod\u00e9lise \u00e0 l&#8217;aide de la dimension 5 ?<\/p>\n<p style=\"text-align: justify\">Le stage de trois jours s&#8217;est conclu par la cr\u00e9ation de posters sur lesquels on peut d\u00e9couvrir le bilan de leurs fructueuses recherches. Ils les ont pr\u00e9sent\u00e9 avec beaucoup d&#8217;entrain et d&#8217;aisance aux enseignants et chercheurs de l&#8217;institut de math\u00e9matiques. Chaque poster raconte une probl\u00e9matique diff\u00e9rente et ouvre vers des questions que les trois jours n&#8217;ont pas suffi \u00e0 r\u00e9soudre&#8230; \u00c0\u00a0vous de les aider, voil\u00e0 les th\u00e8mes :<\/p>\n<ul>\n<li>reconstruction d&#8217;un scanner \u00e0 l&#8217;aide d&#8217;une densit\u00e9 de mati\u00e8re (les matrices),<\/li>\n<li>section du cube par un plan,<\/li>\n<li>construction d&#8217;un tr\u00e8s grand pont sans colle,<\/li>\n<li>projection de la Terre sur un plan,<\/li>\n<li>cr\u00e9ation de labyrinthes,<\/li>\n<li>lire des lettres dans un cube,<\/li>\n<li>dimension fractale et<\/li>\n<li>squelette d&#8217;un (hyper)cube.<\/li>\n<\/ul>\n\n\t\t<style>\n\t\t\t#gallery-1 {\n\t\t\t\tmargin: auto;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-item {\n\t\t\t\tfloat: left;\n\t\t\t\tmargin-top: 10px;\n\t\t\t\ttext-align: center;\n\t\t\t\twidth: 33%;\n\t\t\t}\n\t\t\t#gallery-1 img {\n\t\t\t\tborder: 2px solid #cfcfcf;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-caption {\n\t\t\t\tmargin-left: 0;\n\t\t\t}\n\t\t\t\/* see gallery_shortcode() in wp-includes\/media.php *\/\n\t\t<\/style>\n\t\t<div id='gallery-1' class='gallery galleryid-998 gallery-columns-3 gallery-size-thumbnail'><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2571\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2571-e1430923078622-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-999\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-999'>\n\t\t\t\tLes matrices\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2572\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2572-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1000\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1000'>\n\t\t\t\tSections du cube\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2573\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2573-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1001\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1001'>\n\t\t\t\tPont infini\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2574\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2574-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1002\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1002'>\n\t\t\t\tPont infini\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2576\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2576-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1003\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1003'>\n\t\t\t\tProjection\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2578\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2578-e1430923102684-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1004\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1004'>\n\t\t\t\tLabyrinthe\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon portrait'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2580\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2580-e1430923447274-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1005\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1005'>\n\t\t\t\tFractale\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2581\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2581-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1006\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1006'>\n\t\t\t\tDimension\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2582\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2582-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1007\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1007'>\n\t\t\t\tDimension\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/2015\/05\/06\/lycee-saint-joseph-toulouse-dimension\/img_2583\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2583-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-1008\" srcset=\"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2583-150x150.jpg 150w, https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2583-300x300.jpg 300w, https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/files\/2015\/05\/IMG_2583-1024x1024.jpg 1024w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-1008'>\n\t\t\t\tDes lettres dans un cube\n\t\t\t\t<\/dd><\/dl>\n\t\t\t<br style='clear: both' \/>\n\t\t<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Les \u00e9l\u00e8ves du lyc\u00e9e Saint-Joseph de Toulouse sont venus \u00e0 l&#8217;universit\u00e9 Paul Sabatier avec leur professeure de math\u00e9matiques pour d\u00e9couvrir le travail de chercheur. Guid\u00e9s par un membre de l&#8217;institut de math\u00e9matiques et par des doctorants, ils ont r\u00e9fl\u00e9chi \u00e0 la notion de dimension et \u00e0 des concepts reli\u00e9s. Tout le monde conna\u00eet les dimensions [&hellip;]<\/p>\n","protected":false},"author":131,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-998","post","type-post","status-publish","format-standard","hentry","category-stages"],"_links":{"self":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/posts\/998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/users\/131"}],"replies":[{"embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/comments?post=998"}],"version-history":[{"count":10,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/posts\/998\/revisions"}],"predecessor-version":[{"id":1018,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/posts\/998\/revisions\/1018"}],"wp:attachment":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/media?parent=998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/categories?post=998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/hippocampe\/wp-json\/wp\/v2\/tags?post=998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}