{"id":641,"date":"2016-12-08T21:56:04","date_gmt":"2016-12-08T20:56:04","guid":{"rendered":"http:\/\/darrigan.net\/blog\/?p=641"},"modified":"2025-06-08T12:13:06","modified_gmt":"2025-06-08T10:13:06","slug":"traces-regulateurs-de-polygones-reguliers-a-n-cotes","status":"publish","type":"post","link":"https:\/\/darrigan.net\/blog\/traces-regulateurs-de-polygones-reguliers-a-n-cotes\/","title":{"rendered":"Trac\u00e9s r\u00e9gulateurs de polygones r\u00e9guliers \u00e0 <i>n<\/i> c\u00f4t\u00e9s"},"content":{"rendered":"<h3>avec <em>n<\/em> = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16<\/h3>\n<p>Constructions \u00e0 la r\u00e8gle et au compas pour trouver les longueurs des c\u00f4t\u00e9s\u00a0de polygones \u00e0 <em>n<\/em> c\u00f4t\u00e9s (<em>n<\/em> indiqu\u00e9 en rouge).<\/p>\n<p>Permet aussi de diviser une tarte en 3, 4, 5, \u2026, 16 parts \u00e9gales (angle indiqu\u00e9 en vert) chez des amis, tout en passant pour un extraterrestre.<!--more--><\/p>\n<ul>\n<li>Tracer un segment [AC], trouver sa m\u00e9diatrice au compas et la tracer, elle coupe [AC] en O. Pointe en O, tracer le cercle passant par A, il coupe la m\u00e9diatrice en B et D.<\/li>\n<li>[AB] = P(4) (comprendre : <em>le segment AB est le c\u00f4t\u00e9 du\u00a0polygone\u00a0r\u00e9gulier \u00e0 4 c\u00f4t\u00e9s<\/em>).<\/li>\n<li>Pointe en\u00a0B, tracer l&rsquo;arc n\u00b01 (indiqu\u00e9 au crayon) passant par O. Celui-ci coupe le cercle en J et E.<\/li>\n<li>Pointe en D, tracer l&rsquo;arc n\u00b02 partant de J, coupant (AC) en L.<\/li>\n<li>Pointe en L, tracer l&rsquo;arc n\u00b03 partant de D, coupant [OA] en N et rejoignant B.<\/li>\n<li>Pointe en A, tracer l&rsquo;arc n\u00b04 partant de N, coupant le cercle en M et P.<\/li>\n<li>[AM] = P(9)<\/li>\n<li>Pointe en A, tracer l&rsquo;arc n\u00b05 partant de O, coupant le cercle en F.<\/li>\n<li>[AF] = P(6)<\/li>\n<li>Pointe en E, tracer l&rsquo;arc n\u00b06 partant de F, coupant [OD] en G et [OC] en H, et le cercle en I.<\/li>\n<li>[FG] = P(11),\u00a0[GH] = P(8),\u00a0[HI] = P(7),\u00a0[BI] = P(12), [OG] = P(10), [DG] = P(16), [OH] = P(14), [AI] = P(3)<\/li>\n<li>Compas de rayon [OG], pointe en I, tracer l&rsquo;arc coupant le cercle en K (non indiqu\u00e9 sur la figure, \u00e0 c\u00f4t\u00e9 de J).<\/li>\n<li>[CK] = P(15)<\/li>\n<li>Pour P(13), j&rsquo;ai perdu la trace\u2026<\/li>\n<\/ul>\n<p><a href=\"http:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers.png\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter size-full wp-image-651\" src=\"http:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers.png\" alt=\"\" width=\"1023\" height=\"1304\" srcset=\"https:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers.png 1023w, https:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers-235x300.png 235w, https:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers-768x979.png 768w, https:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers-803x1024.png 803w, https:\/\/darrigan.net\/blog\/wp-content\/uploads\/2016\/12\/Polygones-reguliers-624x795.png 624w\" sizes=\"(max-width: 1023px) 100vw, 1023px\" \/><\/a><\/p>\n<p>Source :\u00a0l&rsquo;excellent livre <a href=\"http:\/\/amzn.eu\/3yAjjHG\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Cr\u00e9er avec un compas<\/em>, Daniel-Jacques Allonsius, \u00e9ditions Dessain et Tolra (1986)<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>avec n = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 Constructions \u00e0 la r\u00e8gle et au compas pour trouver les longueurs des c\u00f4t\u00e9s\u00a0de polygones \u00e0 n c\u00f4t\u00e9s (n indiqu\u00e9 en rouge). Permet aussi de diviser une tarte en 3, 4, 5, \u2026, 16 parts \u00e9gales (angle indiqu\u00e9 en [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,3],"tags":[69,67,56,68],"_links":{"self":[{"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/posts\/641"}],"collection":[{"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":16,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/posts\/641\/revisions"}],"predecessor-version":[{"id":781,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/posts\/641\/revisions\/781"}],"wp:attachment":[{"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/media?parent=641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/categories?post=641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/darrigan.net\/blog\/wp-json\/wp\/v2\/tags?post=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}