{"id":15181,"date":"2024-04-19T14:00:00","date_gmt":"2024-04-19T12:00:00","guid":{"rendered":"http:\/\/samuserensemble.fr\/?p=15181"},"modified":"2024-04-01T17:58:11","modified_gmt":"2024-04-01T15:58:11","slug":"dessiner-un-pentagone-avec-une-regle-et-un-compas","status":"publish","type":"post","link":"http:\/\/samuserensemble.fr\/?p=15181","title":{"rendered":"Dessiner un pentagone avec une r\u00e8gle et un compas"},"content":{"rendered":"\n

Lors d’une visite-atelier \u00e0 l’Institut du monde arabe, nous avons appris \u00e0 tracer un pentagone avec la m\u00e9thode \u00e9gyptienne : pour cela, nous ne disposions que d’un compas et d’une r\u00e8gle… Nous avons voulu voir si nous parvenions \u00e0 retrouver les \u00e9tapes, mais cette fois-ci en utilisant Geogebra, tout en gardant les m\u00eames contraintes bien s\u00fbr.<\/p>\n\n\n\n

Au d\u00e9part, on dispose de deux segments perpendiculaires et de m\u00eame longueur, [A0H] et [MP], qui se croisent en O.<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On trace un cercle de centre O et de rayon OP.<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On cherche les milieux R de [MO] et S de [OP].<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On trace les cercles de centre R et de rayon [RM] et de centre S et de rayon [SP].<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On trace une demi-droite (HS].<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On place T \u00e0 l’intersection, la plus proche de H, de (HS] et du cercle de centre S.<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On trace un cercle de centre H et de rayon [HT].<\/p>\n\n\n\n

\"Pentangone<\/figure>\n\n\n\n

On place U \u00e0 l’autre intersection de (HS] et du cercle de centre S.<\/p>\n\n\n\n

\"Pentangone<\/figure>\n\n\n\n

Puis, on trace un cercle (un arc-de-cercle suffit) de centre H et de rayon HU.<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

Enfin, on place A1 \u00e0 l’intersection, sur la droite, de cet arc-de-cercle et du cercle de centre O, A2 \u00e0 l’intersection sur la droite du cercle de centre O et du cercle de centre H, A3 \u00e0 l’intersection sur la gauche du cercle de centre H et du cercle de centre O, A4 \u00e0 l’autre intersection, sur la gauche de l’art-de-cercle et du cercle de centre O.<\/p>\n\n\n\n

\"Pentagone<\/figure>\n\n\n\n

On relie A0, A1, A2, A3 et A4.<\/p>\n\n\n\n

\"Pentangone<\/figure>\n\n\n\n

On voit le pentagone appara\u00eetre.<\/p>\n\n\n\n

\"Pentangone<\/figure>\n\n\n\n

On peut effacer les traits de construction.<\/p>\n\n\n\n

\"Pentangone<\/figure>\n\n\n\n

C’est fait, avec seulement une r\u00e8gle et un compas !<\/p>\n","protected":false},"excerpt":{"rendered":"

Lors d’une visite-atelier \u00e0 l’Institut du monde arabe, nous avons appris \u00e0 tracer un pentagone avec la m\u00e9thode […]<\/p>\n","protected":false},"author":1,"featured_media":15201,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[699,704],"tags":[50,175,275,413,434,453,495,609],"class_list":["post-15181","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-en-samusant","category-creer-ensemble","tag-art","tag-dessin","tag-geometrie","tag-mathematiques","tag-monde-arabe","tag-musee","tag-paris","tag-sortie"],"aioseo_notices":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2024\/03\/16-Institut-du-monde-arabe-Polygones-12-scaled.jpg","_links":{"self":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/15181","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=15181"}],"version-history":[{"count":5,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/15181\/revisions"}],"predecessor-version":[{"id":15489,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/15181\/revisions\/15489"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/media\/15201"}],"wp:attachment":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15181"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}