{"id":7,"date":"2021-10-12T20:13:47","date_gmt":"2021-10-12T18:13:47","guid":{"rendered":"http:\/\/curvica974.re\/?p=7"},"modified":"2026-01-01T10:53:12","modified_gmt":"2026-01-01T06:53:12","slug":"pavage-hyperbolique-dynamique","status":"publish","type":"post","link":"https:\/\/curvica974.re\/?p=7","title":{"rendered":"Exploration des pavages hyperboliques P(3,k) pour k=7,8 et 9"},"content":{"rendered":"\n<p>Dans la figure de cet article, on vous propose de construire une suite de triangles \u00e9quilat\u00e9raux pour illustrer une approche heuristique de P(3, 7), P(3, 8) et P(3,9), c&rsquo;est-\u00e0-dire de pavages construits \u00e0 partir de triangles \u00e9quilat\u00e9raux.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full is-resized\"><img decoding=\"async\" width=\"380\" height=\"422\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2021\/10\/Capture-de\u0301cran-2021-10-26-a\u0300-13.28.28.png\" alt=\"\" class=\"wp-image-707\" style=\"width:197px;height:219px\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2021\/10\/Capture-de\u0301cran-2021-10-26-a\u0300-13.28.28.png 380w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/10\/Capture-de\u0301cran-2021-10-26-a\u0300-13.28.28-270x300.png 270w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/figure><\/div>\n\n\n<p>Pour cela un plan de construction est propos\u00e9 dans la galerie suivante. Des points sont nomm\u00e9s pour d\u00e9tailler les actions \u00e0 effectuer, mais il n\u2019est pas n\u00e9cessaire de les nommer dans votre construction.<\/p>\n\n\n\n<p>En g\u00e9n\u00e9ral on utilise seulement les macro-constructions ci-contre, mais \u00e0 l\u2019\u00e9tape 2, il faut utiliser les outils euclidiens : on construit la figure dans un mod\u00e8le d\u2019o\u00f9 le m\u00e9lange des deux environnements. Dans l\u2019\u00e9tape 4, on a renomm\u00e9 <strong>Sym Ortho Hyper <\/strong>une macro d\u2019inversion. Elle ne demande pas le cercle horizon, seulement le segment axe de sym\u00e9trie et le point dont on veut le sym\u00e9trique. Les trois autres macros n\u00e9cessitent de montrer d&rsquo;abord le cercle horizon. <br>On peut revoir la pr\u00e9sentation de l&rsquo;utilisation des macros \u00e0 <a href=\"http:\/\/curvica974.re\/?page_id=51\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?page_id=51\" target=\"_blank\" rel=\"noreferrer noopener\">cette page<\/a>.<\/p>\n\n\n\n<p>On pourra remarquer que pour P(3, 8) les points oppos\u00e9s sont align\u00e9s car on reporte 4 fois 45\u00b0. Le pavage P(3, 7) n\u2019est pas constructible \u00e0 la r\u00e8gle et au compas. Plus g\u00e9n\u00e9ralement, pour ce qui est des angles constructibles,  il y a \u00e9quivalence entre la g\u00e9om\u00e9trie hyperbolique et euclidienne .<\/p>\n\n\n<p><center><\/center><\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>Explorer la galerie<\/em> d<em>e pr\u00e9sentation de la construction<\/em> <em>(11 images) &#8230;<\/em> cliquer sur l&rsquo;image<\/p>\n\n\n<p><center><iframe src=\"https:\/\/www.dgpad.net\/responsive.php?url=https:\/\/drive.google.com\/file\/d\/19_1mL6DAx0EZlhcwBScOJdt2KFgNpDf7\/view?usp=drive_link\" style=\"width:800px;height:550px;border-style:solid;border-width:1px;box-shadow: 6px 6px 3px #888888;\"><\/iframe><\/center><\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>&#8230; et suivre simplement  la proc\u00e9dure propos\u00e9e dans la galerie<\/em><\/p>\n\n\n\n<p>Pr\u00e9f\u00e9rer <a href=\"https:\/\/www.dgpad.net\/index.php?url=https:\/\/drive.google.com\/file\/d\/19_1mL6DAx0EZlhcwBScOJdt2KFgNpDf7\/view?usp=drive_link\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/GeomHyp\/ExploreP3k_blog.dgp\" target=\"_blank\" rel=\"noreferrer noopener\">ouvrir cette figure<\/a> dans un nouvel onglet.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\">Anticipation sur les prochains articles de blog<\/h2>\n\n\n\n<p><strong>R\u00e9alisation de la g\u00e9n\u00e9ration 2<\/strong> du vrai pavage hyperbolique P(3,8), \u00e0 partir de son cercle de pavage. Vous pouvez d\u00e9placer le centre O pendant l&rsquo;animation.<\/p>\n\n\n<p><center><iframe src=\"https:\/\/www.dgpad.net\/responsive.php?url=https:\/\/drive.google.com\/file\/d\/1NUNSXW_VgmpTq0OQWwklFDaaxytx6iFx\/view?usp=drive_link\" style=\"width:650px;height:650px;border-style:solid;border-width:1px;box-shadow: 6px 6px 3px #888888;\"><\/iframe><\/center><\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>Agir sur O pendant l&rsquo;anination<\/em><\/p>\n\n\n\n<p>Pr\u00e9f\u00e9rer <a href=\"https:\/\/www.dgpad.net\/index.php?url=https:\/\/drive.google.com\/file\/d\/1fpL8O_M1ABpa7TfWYpH1xcO8wpTS_Mi3\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\">ouvrir cette figure<\/a> dans un nouvel onglet.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dans la figure de cet article, on vous propose de construire une suite de triangles \u00e9quilat\u00e9raux pour illustrer une approche heuristique de P(3, 7), P(3, 8) et P(3,9), c&rsquo;est-\u00e0-dire de pavages construits \u00e0 partir de triangles \u00e9quilat\u00e9raux. Pour cela un plan de construction est propos\u00e9 dans la galerie suivante. Des [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[18],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/posts\/7"}],"collection":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7"}],"version-history":[{"count":30,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/posts\/7\/revisions"}],"predecessor-version":[{"id":8550,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/posts\/7\/revisions\/8550"}],"wp:attachment":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}