{"id":5149,"date":"2019-01-29T17:58:05","date_gmt":"2019-01-29T15:58:05","guid":{"rendered":"http:\/\/pimedios.es\/?p=5149"},"modified":"2019-01-29T17:58:05","modified_gmt":"2019-01-29T15:58:05","slug":"el-teorema-de-ceva-y-la-ceviana","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=5149","title":{"rendered":"El teorema de Ceva y la ceviana"},"content":{"rendered":"<div class=\"wp-caption alignleft\" style=\"width: 328px;\">\n<p><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Ceva%27s_theorem_1.svg#\/media\/File:Ceva%27s_theorem_1.svg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c7\/Ceva%27s_theorem_1.svg\/1200px-Ceva%27s_theorem_1.svg.png\" alt=\"Ceva's theorem 1.svg\" width=\"328\" height=\"237\" \/><\/a><\/p>\n<p>De 4C &#8211; <span class=\"int-own-work\" lang=\"es\">Trabajo propio<\/span>, <a title=\"Creative Commons Attribution-Share Alike 3.0\" href=\"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/\">CC BY-SA 3.0<\/a>, <a href=\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=1054185\">Enlace<\/a><\/p>\n<\/div>\n<p>En geometr\u00eda del tri\u00e1ngulo, el teorema de Ceva establece que dado un tri\u00e1ngulo ABC, y los puntos D, E, y F que se encuentran sobre los lados BC, CA, y AB respectivamente, los segmentos AD, BE y CF son concurrentes si y solo si<br \/>\n$${\\displaystyle {\\frac {AF}{FB}}\\cdot {\\frac {BD}{DC}}\\cdot {\\frac {CE}{EA}}=1,}$$<\/p>\n<p>El nombre se lo debemos a Giovanni Ceva, que lo demostr\u00f3 en 1678, en su trabajo \u00a0<a class=\"external text\" href=\"http:\/\/gutenberg.beic.it\/webclient\/DeliveryManager?pid=828340&amp;search_terms=DTL6\" rel=\"nofollow\"><i>De lineis rectis se invicem secantibus statica constructio<\/i><\/a>.<\/p>\n<p>Este resultado tambi\u00e9n nos ha dado paso a crear el t\u00e9rmino ceviana.<\/p>\n<p style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/qlzngbcFBP8\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Lo m\u00e1s probable es que\u00a0\u00a0<a title=\"Giovanni Ceva\" href=\"https:\/\/es.wikipedia.org\/wiki\/Giovanni_Ceva\">Giovanni Ceva<\/a>\u00a0desconociese que con anterioridad <a title=\"Al-Mutam\u00e1n\" href=\"https:\/\/es.wikipedia.org\/wiki\/Al-Mutam%C3%A1n\">Yusuf Al-Mutam\u00e1n ibn H\u0171d<\/a> lo hab\u00eda mostrado. Del mismo modo que Al-Mutam\u00e1n lo deducir\u00eda del trabajo de\u00a0\u00a0<a class=\"mw-redirect\" title=\"Thabit ibn Qurra\" href=\"https:\/\/en.wikipedia.org\/wiki\/Thabit_ibn_Qurra\">Thabit ibn Qurra<\/a>, que previamente hab\u00eda tratado el<br \/>\n<a class=\"mw-redirect\" title=\"\" href=\"https:\/\/es.wikipedia.org\/wiki\/Teorema_de_Menelaus\">Teorema de Menelaus<\/a>\u00a0(el\u00a0<a title=\"Dualidad (geometr\u00eda proyectiva)\" href=\"https:\/\/es.wikipedia.org\/wiki\/Dualidad_(geometr%C3%ADa_proyectiva)\">dual<\/a>\u00a0del teorema de Ceva).<\/p>\n<p>Seg\u00fan\u00a0Agust\u00ed Revent\u00f3s Tarrida[Affine Maps, Euclidean Motions and Quadrics], el t\u00e9rmino ceviana fue introducido por Auguste Poulain en 1888, pero no indica referencias de ellos, por lo que me decanto a pensar que ser\u00eda en su trabajo <em>Principes de la nouvelle g\u00e9om\u00e9trie du triangle\u00a0<\/em>(1892).<\/p>\n<blockquote><p>Esta entrada participa en la\u00a0<a href=\"https:\/\/gaussianos.com\/edicion-7-6-la-banda-de-mobius-del-carnaval-de-matematicas\/\">Edici\u00f3n 7.6<\/a>\u00a0del Carnaval de Matem\u00e1ticas, que en esta ocasi\u00f3n organiza\u00a0<a href=\"https:\/\/gaussianos.com\/\">Gaussianos<\/a>.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>El teorema de Ceva y la ceviana: de la matem\u00e1tica de Al-Mutam\u00e1n a Giovanni Ceva.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[728,727,726,729],"class_list":["post-5149","post","type-post","status-publish","format-standard","hentry","category-historia","category-personajes","tag-al-mutaman","tag-ceviana","tag-giovanni-ceva","tag-thabit-ibn-qurra","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5149"}],"version-history":[{"count":1,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5149\/revisions"}],"predecessor-version":[{"id":5150,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5149\/revisions\/5150"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5149"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}