{"id":2145,"date":"2021-12-21T17:38:29","date_gmt":"2021-12-21T13:38:29","guid":{"rendered":"http:\/\/curvica974.re\/?page_id=2145"},"modified":"2024-03-31T12:36:38","modified_gmt":"2024-03-31T08:36:38","slug":"regionnement-dynamique-de-linterieur-a-lellipse-pour-lorthogonalite-a-une-h-droite","status":"publish","type":"page","link":"https:\/\/curvica974.re\/?page_id=2145","title":{"rendered":"R\u00e9gionnement dynamique de l&rsquo;int\u00e9rieur \u00e0 l&rsquo;ellipse pour l&rsquo;orthogonalit\u00e9 \u00e0 une H-droite"},"content":{"rendered":"\n<p>Le contexte ici est diff\u00e9rent de la page pr\u00e9c\u00e9dente, et plus simple \u00e0 traiter. Dans cette page, on se donne une H-droite \\((AB)\\) avec \\(A\\) et \\(B\\) \u00e0 l\u2019int\u00e9rieur de l\u2019ellipse, et un point \\(M\\), lui aussi \u00e0 l\u2019int\u00e9rieur de l\u2019ellipse. Le r\u00e9gionnement de l\u2019ellipse consiste \u00e0 colorier les cas o\u00f9 il n\u2019y a aucune perpendiculaire, deux perpendiculaires &#8211; dans ce cas c\u2019est une hibertienne et une euclidienne car il ne peut y avoir deux hilbertiennes, et le cas o\u00f9 il n\u2019y a qu\u2019une seule perpendiculaire euclidienne.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-large is-resized\"><img decoding=\"async\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20-1024x343.png\" alt=\"\" class=\"wp-image-2146\" width=\"557\" height=\"186\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20-1024x343.png 1024w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20-300x101.png 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20-768x258.png 768w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20-1536x515.png 1536w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/image-20.png 1604w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/figure><\/div>\n\n\n<p>On a choisi de ne pas colorier le cas le plus trivial, celui o\u00f9 il n\u2019y a qu\u2019une perpendiculaire hilbertienne car c\u2019est, en g\u00e9n\u00e9ral, la plus grande partie \u00e0 l\u2019int\u00e9rieur de l\u2019ellipse comme on le voit sur cette illustration.  La H-orthogonalit\u00e9 est l&rsquo;orthogonalit\u00e9 euclidienne de deux cercles : celui circonscrit \u00e0 \\(A, B\\) et \\(F\\) et celui passant par \\(M, F\\) et orthogonal au pr\u00e9c\u00e9dent.<\/p>\n\n\n\n<p>Les trois autres r\u00e9gions sont des parties de l\u2019ellipse qui partent de ses points d\u2019intersection avec la H-droite \\((AB)\\).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"245\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1-1024x245.png\" alt=\"\" class=\"wp-image-2147\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1-1024x245.png 1024w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1-300x72.png 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1-768x184.png 768w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1-1536x368.png 1536w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-1.png 1802w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>La partie \u00e0 une seule perpendiculaire euclidienne peut \u00eatre assez importante, ici avec deux droites \\((AB)\\) diff\u00e9rentes.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"266\" src=\"http:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre-1024x266.png\" alt=\"\" class=\"wp-image-2148\" srcset=\"https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre-1024x266.png 1024w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre-300x78.png 300w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre-768x199.png 768w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre-1536x399.png 1536w, https:\/\/curvica974.re\/wp-content\/uploads\/2021\/12\/Deux-Reg-Int-2-a\u0300-reprendre.png 1794w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p>     <\/p>\n\n\n\n<p>En fait la figure finale n&rsquo;est pas tr\u00e8s op\u00e9rationnelle &#8230; elle n&rsquo;est correcte qu&rsquo;\u00e0 60% des cas. La r\u00e9daction a \u00e9t\u00e9 annul\u00e9e et fait partie des prochaines mises \u00e0 jour &#8230;.<\/p>\n\n\n\n<p>Un peu d\u00e9sol\u00e9 &#8230; mais temporaire &#8230;<\/p>\n\n\n\n<p>    <\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"http:\/\/curvica974.re\/?page_id=136\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?page_id=136\" target=\"_blank\" rel=\"noreferrer noopener\">Intro orthogonalit\u00e9<\/a> | <a rel=\"noreferrer noopener\" href=\"http:\/\/curvica974.re\/?page_id=2069\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?page_id=2069\" target=\"_blank\">H-ortho 1<\/a> (triangles)  |   <a href=\"http:\/\/curvica974.re\/?page_id=2104\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?page_id=2104\" target=\"_blank\" rel=\"noreferrer noopener\">H-ortho 2<\/a> (r\u00e9gionnement ext\u00e9rieur)   |   <a href=\"http:\/\/curvica974.re\/?page_id=2145\" data-type=\"URL\" data-id=\"http:\/\/curvica974.re\/?page_id=2145\" target=\"_blank\" rel=\"noreferrer noopener\">H-ortho 3<\/a> (r\u00e9gionnement int\u00e9rieur)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Le contexte ici est diff\u00e9rent de la page pr\u00e9c\u00e9dente, et plus simple \u00e0 traiter. Dans cette page, on se donne une H-droite avec et \u00e0 l\u2019int\u00e9rieur de l\u2019ellipse, et un point , lui aussi \u00e0 l\u2019int\u00e9rieur de l\u2019ellipse. Le r\u00e9gionnement de l\u2019ellipse consiste \u00e0 colorier les cas o\u00f9 il n\u2019y [&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\/2145"}],"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=2145"}],"version-history":[{"count":3,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages\/2145\/revisions"}],"predecessor-version":[{"id":7261,"href":"https:\/\/curvica974.re\/index.php?rest_route=\/wp\/v2\/pages\/2145\/revisions\/7261"}],"wp:attachment":[{"href":"https:\/\/curvica974.re\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}