{"id":2691,"date":"2022-01-27T11:39:48","date_gmt":"2022-01-27T07:39:48","guid":{"rendered":"http:\/\/curvica974.re\/?page_id=2691"},"modified":"2022-11-05T21:03:31","modified_gmt":"2022-11-05T17:03:31","slug":"psh-pavage-p38","status":"publish","type":"page","link":"https:\/\/curvica974.re\/?page_id=2691","title":{"rendered":"PSH &#8211; Pavages P(3,8) et P(8,3)"},"content":{"rendered":"\n<p>La seule chose \u00e0 savoir pour r\u00e9aliser les figures de cette page est le rayon du cercle de pavage.  Il v\u00e9rifie \\(ch38= ch(r_{38})= \\displaystyle \\frac{1}{\\sqrt{6}-\\sqrt{3}} \\). Cet <a href=\"http:\/\/curvica974.re\/?p=5132\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?p=5132\" target=\"_blank\" rel=\"noreferrer noopener\">article de blog<\/a> traite du calcul d rayons des cercles de pavage.<\/p>\n\n\n\n<p>Ceci \u00e9tant donn\u00e9, la construction se fait comme \u00e0 la page pr\u00e9c\u00e9dente. On arrive ainsi \u00e0 un premier triangle \u00e9quilat\u00e9ral d&rsquo;angle au sommet de 45\u00b0 que l&rsquo;on peut manipuler dans la figure suivante<\/p>\n\n\n<p><center><iframe src=\"https:\/\/www.dgpad.net\/responsive.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_1TR_R.dgp\" style=\"width:750px;height:530px;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 has-small-font-size\"><em>Comme pour les triangles uniques de la page pr\u00e9c\u00e9dente, ne pas h\u00e9siter \u00e0 manipuler tous les param\u00e8tres <\/em><\/p>\n\n\n\n<p>Pr\u00e9f\u00e9rer <a rel=\"noreferrer noopener\" href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_1TR.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_1TR.dgp\" target=\"_blank\">lancer la figure<\/a> dans un nouvel onglet<\/p>\n\n\n\n<p>  <\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>Illustration de pr\u00e9sentation de la figure P(3,8)<\/strong><\/h2>\n\n\n\n<p>Comme les angles au sommet sont de 45\u00b0 on peut optimiser la figure en n&rsquo;utilisant la polaire que d&rsquo;une droite sur deux. On peut aussi &#8211; c&rsquo;est ce que l&rsquo;on a fait dans un premier temps &#8211; utiliser cette possibilit\u00e9s pour construire un point sur deux de deux fa\u00e7ons diff\u00e9rentes (avec l&rsquo;orthogonalit\u00e9 et sans) et avoir ainsi une v\u00e9rification que la figure est correcte. <\/p>\n\n\n\n<p>Avec 8 triangles autour d&rsquo;un point on peut jouer avec les param\u00e8tres d&rsquo;affichage de la figure finale. Voici des illustrations de quelques possibilit\u00e9s<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRverticaux.jpg\" alt=\"\" class=\"wp-image-2692\" width=\"717\" height=\"566\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRverticaux.jpg 768w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRverticaux-300x237.jpg 300w\" sizes=\"(max-width: 717px) 100vw, 717px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Quatre triangles \u00e9quilat\u00e9raux de 45\u00b0 dans une configuration plus \u00ab\u00a0verticale\u00a0\u00bb sur la PSH.<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRvueDessus.jpg\" alt=\"\" class=\"wp-image-2693\" width=\"769\" height=\"539\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRvueDessus.jpg 796w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRvueDessus-300x210.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRvueDessus-768x538.jpg 768w\" sizes=\"(max-width: 769px) 100vw, 769px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Autre configuration de quatre triangles du pavage dans une vue de dessus.<br>On voit clairement sur la <strong>PSH<\/strong> que l&rsquo;ensemble fait un peu plus d&rsquo;un tour<\/em><\/p>\n\n\n\n<p>Mais peut jouer aussi \u00e0 des configurations plus a\u00e9r\u00e9es comme celle-ci en \u00ab\u00a0ailes de moulin\u00a0\u00bb<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRmoulins-1.jpg\" alt=\"\" class=\"wp-image-2695\" width=\"798\" height=\"549\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRmoulins-1.jpg 881w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRmoulins-1-300x207.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRmoulins-1-768x529.jpg 768w\" sizes=\"(max-width: 798px) 100vw, 798px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>On remarque sur cette illustration, que contrairement aux pavages P54 et P45, on peut garder les huit triangles enti\u00e8rement sur la pseudosph\u00e8re hyperbolique tout en prenant le centre du cercle de pavage assez loin de la fronti\u00e8re de la feuille principale, alors que pour les pavages pr\u00e9c\u00e9dents, il devait \u00eatre presque coll\u00e9 au m\u00e9ridien vert de la fronti\u00e8re.<\/em><\/p>\n\n\n\n<p>Ou encore cette configuration que l&rsquo;on dira \u00ab\u00a0du papillon\u00a0\u00bb<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"882\" height=\"611\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon-1.jpg\" alt=\"\" class=\"wp-image-2697\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon-1.jpg 882w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon-1-300x208.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon-1-768x532.jpg 768w\" sizes=\"(max-width: 882px) 100vw, 882px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>On remarquera, ci-dessous, que le centre \\(O\\) du cercle  est au del\u00e0 de la longitude nulle (milieu de la feuille principale).<br>En agissant sur la latitude \\(u_O\\) et sur le point \\(A\\), le pavage rentre sur la surface et m\u00eame, selon la valeur de \\(x_p\\), enti\u00e8rement sur la feuille principale (ici non car on a voulu illustrer la grande mobilit\u00e9 du centre du cercle).<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"831\" height=\"603\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon3.jpg\" alt=\"\" class=\"wp-image-2699\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon3.jpg 831w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon3-300x218.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_4TRpapillon3-768x557.jpg 768w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/figure><\/div>\n\n\n\n<p>Enfin une illustration avec les huit triangles affich\u00e9s<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"863\" height=\"617\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_8TR.jpg\" alt=\"\" class=\"wp-image-2700\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_8TR.jpg 863w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_8TR-300x214.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/01\/PSHP38_8TR-768x549.jpg 768w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/><\/figure><\/div>\n\n\n\n<p><strong>La figure \u00e0 manipuler<\/strong><\/p>\n\n\n\n<p>M\u00eames remarques &#8211; consignes &#8211; qu&rsquo;\u00e0 la figure de la page pr\u00e9c\u00e9dente.<\/p>\n\n\n<p><center><iframe src=\"https:\/\/www.dgpad.net\/responsive.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_CheckBox_R.dgp\" style=\"width:840px;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 has-small-font-size\"><em>Pour explorer les diff\u00e9rentes possibilit\u00e9s de ce (d\u00e9but de) pavage P(3,8)<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Pr\u00e9f\u00e9rer <a rel=\"noreferrer noopener\" href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_1TR.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_1TR.dgp\" target=\"_blank\">l<\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_CheckBox.dgp\" data-type=\"URL\" target=\"_blank\">ancer la figure<\/a> dans un nouvel onglet, ou encore utiliser <a href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_CheckBox40.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P38_CheckBox40.dgp\" target=\"_blank\" rel=\"noreferrer noopener\">cette version<\/a> ou les segments sur la <strong>PSH<\/strong> sont \u00e0 densit\u00e9 40 au lieu de 20 pour la figure pr\u00e9c\u00e9dente.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\">Construction autour du pavage P(8,3)<\/h2>\n\n\n\n<p>Cette partie est l&rsquo;occasion de belles illustrations, un peu impr\u00e9vues, car il rentre plus d&rsquo;octogones que \u00ab\u00a0pr\u00e9vu\u00a0\u00bbsur la <strong>PSH<\/strong>. Tout d&rsquo;abord le classique octogone seul (donc de 120\u00b0).<\/p>\n\n\n<p><center><iframe src=\"https:\/\/www.dgpad.net\/responsive.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_1Octo120_de_P83_R.dgp\" style=\"width:840px;height:620px;border-style:solid;border-width:1px;box-shadow: 6px 6px 3px #888888;\"><\/iframe><\/center><\/p>\n\n\n\n<p>Pr\u00e9f\u00e9rer <a href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_1Octo120_de_P83.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_1Octo120_de_P83.dgp\" target=\"_blank\" rel=\"noreferrer noopener\">ouvrir la figure<\/a> dans un nouvel onglet.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\">Premi\u00e8re illustrations autour du pavage P(3,8)<\/h2>\n\n\n\n<p>On commence par le pavage lui-m\u00eame, soit trois octogone autour d&rsquo;un point &#8230; m\u00eame si c&rsquo;est un peu d\u00e9concertant.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"780\" height=\"648\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a1_Pavage039_face.jpg\" alt=\"\" class=\"wp-image-2802\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a1_Pavage039_face.jpg 780w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a1_Pavage039_face-300x249.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a1_Pavage039_face-768x638.jpg 768w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>D&rsquo;abord une vue de face, ensuite une vue de dessus : on voit peut-\u00eatre mieux le chevauchement des octogones<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"777\" height=\"406\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a2_Pavage039_dessus.jpg\" alt=\"\" class=\"wp-image-2803\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a2_Pavage039_dessus.jpg 777w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a2_Pavage039_dessus-300x157.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a2_Pavage039_dessus-768x401.jpg 768w\" sizes=\"(max-width: 777px) 100vw, 777px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>On poursuit par la vue de deux des trois octogones dans la configuration g\u00e9om\u00e9trique pr\u00e9c\u00e9dente<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"782\" height=\"626\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a3_BleuVert_039_Face.jpg\" alt=\"\" class=\"wp-image-2804\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a3_BleuVert_039_Face.jpg 782w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a3_BleuVert_039_Face-300x240.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_a3_BleuVert_039_Face-768x615.jpg 768w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\">Placer un quatri\u00e8me octogone dans P(8,3)<\/h2>\n\n\n\n<p>On voir bien que pour certains r\u00e9glages, il peut y avoir \u00ab\u00a0de la place sur la <strong>PSH<\/strong>\u00a0\u00bb pour un quatri\u00e8me octogone, on y consacre donc cette section. On propose ici une illustration d\u00e9taill\u00e9e en prenant les octogones deux par deux.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"833\" height=\"431\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b1_Les4_043_BleuVert_dessus.jpg\" alt=\"\" class=\"wp-image-2805\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b1_Les4_043_BleuVert_dessus.jpg 833w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b1_Les4_043_BleuVert_dessus-300x155.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b1_Les4_043_BleuVert_dessus-768x397.jpg 768w\" sizes=\"(max-width: 833px) 100vw, 833px\" \/><\/figure>\n\n\n\n<p class=\"has-small-font-size\"><em>On notera plusieurs choses sur cette illustration. Tout d&rsquo;abord, m\u00eame s&rsquo;il n&rsquo;appara\u00eet pas, on lit sur sa longitude que<\/em> <em>le centre du cercle de pavage est sur la feuille principale mais \u00e0 sa toute limite inf\u00e9rieure puisque sa longitude est tr\u00e8s proche (pour la manipulation \u00e0 la souris en tout cas) de la valeur extr\u00e9male de \\(-\\pi\\).<br>On remarquera aussi qu&rsquo;un c\u00f4t\u00e9 de l&rsquo;hexagone bleu est quasiment sur le m\u00e9ridien vert de la fronti\u00e8re de la feuille principale. On a colori\u00e9 aussi en vert le segment issu de \\(K\\), commun aux hexagones bleu et vert. Ci dessous la m\u00eame configuration de face.<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"802\" height=\"648\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b2_Les4_043_BleuVert_face.jpg\" alt=\"\" class=\"wp-image-2806\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b2_Les4_043_BleuVert_face.jpg 802w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b2_Les4_043_BleuVert_face-300x242.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b2_Les4_043_BleuVert_face-768x621.jpg 768w\" sizes=\"(max-width: 802px) 100vw, 802px\" \/><\/figure>\n\n\n\n<p><strong>Ajout d&rsquo;un quatri\u00e8me octogone, \u00e0 droite &#8211; sur KB &#8211; du bleu<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b3_Les4_043_BleuRose_dessus.jpg\" alt=\"\" class=\"wp-image-2809\" width=\"840\" height=\"423\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b3_Les4_043_BleuRose_dessus.jpg 842w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b3_Les4_043_BleuRose_dessus-300x151.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b3_Les4_043_BleuRose_dessus-768x388.jpg 768w\" sizes=\"(max-width: 840px) 100vw, 840px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>On note les m\u00eames rep\u00e8res, le c\u00f4t\u00e9 vert de l&rsquo;octogone bleu (qui bizarrement ne se voit pas sur <strong>KB<\/strong>) et le c\u00f4t\u00e9 de l&rsquo;octogone (vertical sur <strong>KB<\/strong>) qui est sur le m\u00e9ridien fronti\u00e8re vert.<br>Et sur l&rsquo;illustration ci-dessous, on remarque qu&rsquo;un des sommets de l&rsquo;octogone initial orange (celui pilot\u00e9 par le point \\(K\\)) est proche du m\u00eame m\u00e9ridien vert.<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"831\" height=\"422\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b4_Les4_043_OrangeRose_dessus.jpg\" alt=\"\" class=\"wp-image-2810\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b4_Les4_043_OrangeRose_dessus.jpg 831w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b4_Les4_043_OrangeRose_dessus-300x152.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b4_Les4_043_OrangeRose_dessus-768x390.jpg 768w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Ce<\/em> <em>qui est int\u00e9ressant c&rsquo;est la m\u00eame configuration de face<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"846\" height=\"631\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b5_Les4_043_OrangeRose_face.jpg\" alt=\"\" class=\"wp-image-2811\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b5_Les4_043_OrangeRose_face.jpg 846w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b5_Les4_043_OrangeRose_face-300x224.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b5_Les4_043_OrangeRose_face-768x573.jpg 768w\" sizes=\"(max-width: 846px) 100vw, 846px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Et enfin les<\/em> <em>quatre octogones ensemble<\/em>, <em>toujours dans la m\u00eame<\/em> <em>configuration<\/em>, vus de face<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"838\" height=\"626\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b7_Les4_043_face.jpg\" alt=\"\" class=\"wp-image-2812\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b7_Les4_043_face.jpg 838w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b7_Les4_043_face-300x224.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b7_Les4_043_face-768x574.jpg 768w\" sizes=\"(max-width: 838px) 100vw, 838px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Et de<\/em> <em>dessus (trop joli)<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"840\" height=\"435\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b6_Les4_043_dessus.jpg\" alt=\"\" class=\"wp-image-2819\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b6_Les4_043_dessus.jpg 840w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b6_Les4_043_dessus-300x155.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_b6_Les4_043_dessus-768x398.jpg 768w\" sizes=\"(max-width: 840px) 100vw, 840px\" \/><\/figure><\/div>\n\n\n\n<p>Ouvrir <a href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P83_4octo_p043.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P83_4octo_p043.dgp\" target=\"_blank\" rel=\"noreferrer noopener\">la figure de cette configuration<\/a> dans un nouvel onglet (\u00eatre en mode consultation, sans outil s\u00e9lectionn\u00e9)<\/p>\n\n\n\n<p><strong>Les octogones orange et rose dans d&rsquo;autres r\u00e8glages &#8211; en particulier d&rsquo;autres valeurs de \\(P\\)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"844\" height=\"449\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_dessus.jpg\" alt=\"\" class=\"wp-image-2815\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_dessus.jpg 844w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_dessus-300x160.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_dessus-768x409.jpg 768w\" sizes=\"(max-width: 844px) 100vw, 844px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Illustration de l&rsquo;illusion du contact : ils sont au contraire \u00e0 une diff\u00e9rence de l&rsquo;ordre d&rsquo;un demi-tour<\/em> <br><em>(il faut faire tourner la <strong>PSH<\/strong> pour mieux voir ce qu&rsquo;il en est)<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"835\" height=\"462\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_face.jpg\" alt=\"\" class=\"wp-image-2816\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_face.jpg 835w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_face-300x166.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_c1_OrangeRose_062_face-768x425.jpg 768w\" sizes=\"(max-width: 835px) 100vw, 835px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Autre situation <\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"853\" height=\"464\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d1_OrangeRose_068_dessus.jpg\" alt=\"\" class=\"wp-image-2817\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d1_OrangeRose_068_dessus.jpg 853w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d1_OrangeRose_068_dessus-300x163.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d1_OrangeRose_068_dessus-768x418.jpg 768w\" sizes=\"(max-width: 853px) 100vw, 853px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\"><em>Cette fois-ci ils sont bien face \u00e0 face &#8230;<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"847\" height=\"519\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d2_OrangeRose_068_face.jpg\" alt=\"\" class=\"wp-image-2818\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d2_OrangeRose_068_face.jpg 847w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d2_OrangeRose_068_face-300x184.jpg 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_d2_OrangeRose_068_face-768x471.jpg 768w\" sizes=\"(max-width: 847px) 100vw, 847px\" \/><\/figure><\/div>\n\n\n\n<p>Ouvrir <a href=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P83_OrangeRose_p067.dgp\" data-type=\"URL\" data-id=\"https:\/\/www.dgpad.net\/index.php?url=http:\/\/curvica974.re\/FigSite\/PSH\/PSH_P83_OrangeRose_p067.dgp\" target=\"_blank\" rel=\"noreferrer noopener\">la figure de cette configuration<\/a> dans un nouvel onglet (\u00eatre en mode consultation, sans outil s\u00e9lectionn\u00e9)<\/p>\n\n\n\n<p>Enfin un cas avec une <strong>PSH<\/strong> plus resserr\u00e9e<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"784\" height=\"642\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_e1_OrangeRose_039_face.png\" alt=\"\" class=\"wp-image-2820\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_e1_OrangeRose_039_face.png 784w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_e1_OrangeRose_039_face-300x246.png 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2022\/02\/P83_e1_OrangeRose_039_face-768x629.png 768w\" sizes=\"(max-width: 784px) 100vw, 784px\" \/><\/figure><\/div>\n\n\n\n<p>On n&rsquo;a pas plac\u00e9 cette figure dans une iframe, car il suffit d&rsquo;ouvrir une des deux figures propos\u00e9es ci-dessus pour explorer toutes les situations possibles. On notera que dans ce cas le centre du cercle est toujours sur a feuille principale.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La seule chose \u00e0 savoir pour r\u00e9aliser les figures de cette page est le rayon du cercle de pavage. Il v\u00e9rifie . Cet article de blog traite du calcul d rayons des cercles de pavage. Ceci \u00e9tant donn\u00e9, la construction se fait comme \u00e0 la page pr\u00e9c\u00e9dente. On arrive ainsi [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/template-fullwidth.php","meta":{"footnotes":""},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages\/2691"}],"collection":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/types\/page"}],"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=2691"}],"version-history":[{"count":11,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages\/2691\/revisions"}],"predecessor-version":[{"id":5191,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages\/2691\/revisions\/5191"}],"wp:attachment":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}