{"id":4907,"date":"2016-05-25T12:55:49","date_gmt":"2016-05-25T10:55:49","guid":{"rendered":"http:\/\/pimedios.es\/?p=4907"},"modified":"2017-03-22T00:26:35","modified_gmt":"2017-03-21T22:26:35","slug":"el-stick-de-hockey","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=4907","title":{"rendered":"El \u00abstick de hockey\u00bb"},"content":{"rendered":"<p>Lo llamamos el tri\u00e1ngulo de Pascal aunque Tartaglia(siglo XVI), Yang Hui (siglo XIII) y Omar Khayyam (siglo XII) entre otros lo conoc\u00edan. Estamos hablando del tri\u00e1ngulo que obtenemos con los coeficientes de las potencias de un binomio:<\/p>\n<figure style=\"width: 466px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Pascal%27s_triangle_5.svg#\/media\/File:Pascal%27s_triangle_5.svg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/f\/f6\/Pascal%27s_triangle_5.svg\/1200px-Pascal%27s_triangle_5.svg.png\" alt=\"Pascal's triangle 5.svg\" width=\"466\" height=\"336\" \/><\/a><figcaption class=\"wp-caption-text\">By <a title=\"User:Conrad.Irwin\" href=\"\/\/commons.wikimedia.org\/wiki\/User:Conrad.Irwin\">User:Conrad.Irwin<\/a> originally <a title=\"User:Drini\" href=\"\/\/commons.wikimedia.org\/wiki\/User:Drini\">User:Drini<\/a> &#8211; Extracted from <a title=\"File:PascalSimetria.svg\" href=\"\/\/commons.wikimedia.org\/wiki\/File:PascalSimetria.svg\">Image:PascalSimetria.svg<\/a> with minor alterations, <a title=\"Creative Commons Attribution-Share Alike 3.0\" href=\"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\">CC BY-SA 3.0<\/a>, https:\/\/commons.wikimedia.org\/w\/index.php?curid=3105222<\/figcaption><\/figure>\n<p>Fue Pierre Raymond de Montmort (1708) quien lo llam\u00f3 \u00abTable de M. Pascal pour les combinaisons\u00bb y Abraham de Moivre (1730) lo bautiz\u00f3 como \u00abTriangulum Arithmeticum PASCALIANUM\u00bb. En gran medida esos honores eran debidos al trabajo de Blaise Pascal en el tri\u00e1ngulo.<\/p>\n<figure style=\"width: 371px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:TrianguloPascal.jpg#\/media\/File:TrianguloPascal.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/6\/66\/TrianguloPascal.jpg\" alt=\"TrianguloPascal.jpg\" width=\"371\" height=\"308\" \/><\/a><figcaption class=\"wp-caption-text\">By <a class=\"extiw\" title=\"en:Blaise Pascal\" href=\"\/\/en.wikipedia.org\/wiki\/Blaise_Pascal\">Blaise Pascal<\/a> &#8211; Cambridge University Library, Public Domain, https:\/\/commons.wikimedia.org\/w\/index.php?curid=2819977<\/figcaption><\/figure>\n<p>Muchas son las curiosidades que se extraen de \u00e9l, que Pascal public\u00f3 en su <i>Trait\u00e9 du triangle arithm\u00e9tique<\/i>(1665). Una de ellas es la que hoy conocemos como el \u00ab<em>stick de Hockey<\/em>\u00ab:<\/p>\n<blockquote><p><strong>Si imaginamos una escalera semejante a la coloreada, la suma de todos los n\u00fameros de los pelda\u00f1os que la integran se encuentran justo debajo del \u00faltimo de ellos, en la diagonal contraria.<\/strong><\/p><\/blockquote>\n<figure id=\"attachment_4908\" aria-describedby=\"caption-attachment-4908\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-4908\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/2016\/05\/triangulo_pascal-300x260.png\" alt=\"1+4+10+20=35\" width=\"300\" height=\"260\" srcset=\"http:\/\/pimedios.jesussoto.es\/wp-content\/uploads\/2016\/05\/triangulo_pascal-300x260.png 300w, http:\/\/pimedios.jesussoto.es\/wp-content\/uploads\/2016\/05\/triangulo_pascal.png 380w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-4908\" class=\"wp-caption-text\">1+4+10+20=35<\/figcaption><\/figure>\n<p>Este resultado tiene una f\u00e1cil demostraci\u00f3n utilizando los n\u00fameros binomiales. Lo mostramos con un ejemplo.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/iCNVNTdxxWk\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><em>Esta entrada participa en la <a href=\"https:\/\/ztfnews.wordpress.com\/2016\/05\/09\/edicion-7-4-del-carnaval-de-matematicas\/\" target=\"_blank\"><strong>edici\u00f3n 7.4<\/strong><\/a> del <strong><a href=\"http:\/\/carnavaldematematicas.bligoo.es\/\" target=\"_blank\">Carnaval de Matem\u00e1ticas<\/a><\/strong><\/em>,<em> cuyo blog anfitri\u00f3n es <a href=\"https:\/\/ztfnews.wordpress.com\" target=\"_blank\"><strong>::ZTFNews<\/strong><\/a>;<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El \u00abstick de hockey\u00bb en el tri\u00e1ngulo de Pascal.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,8],"tags":[537],"class_list":["post-4907","post","type-post","status-publish","format-standard","hentry","category-historia","category-ocio","tag-blaise-pascal","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4907","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=4907"}],"version-history":[{"count":3,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4907\/revisions"}],"predecessor-version":[{"id":4911,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4907\/revisions\/4911"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4907"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}