{"id":388,"date":"2011-03-15T07:00:07","date_gmt":"2011-03-15T11:00:07","guid":{"rendered":"http:\/\/blogs.williams.edu\/Morgan\/?p=388"},"modified":"2011-03-15T07:00:07","modified_gmt":"2011-03-15T11:00:07","slug":"pompas-de-jabon-y-las-matematicas","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/Morgan\/2011\/03\/15\/pompas-de-jabon-y-las-matematicas\/","title":{"rendered":"Pompas de Jab\u00f3n y las Matem\u00e1ticas"},"content":{"rendered":"<p style=\"text-align: left\">[&#8220;Soap Bubbles and Mathematics,&#8221; written for the <a href=\"http:\/\/carnavaldematematicas.bligoo.es\/\">Spanish Math Carnival<\/a>]<\/p>\n<p style=\"text-align: left\">\u00bfPor qu\u00e9 son las pompas de jab\u00f3n tan perfectamente redondas?<\/p>\n<p style=\"text-align: center\"><a href=\"http:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sph156.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-400 aligncenter\" src=\"https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sph156-300x300.jpg\" alt=\"\" width=\"143\" height=\"143\" srcset=\"https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sph156-300x300.jpg 300w, https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sph156-150x150.jpg 150w, https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sph156.jpg 400w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a><\/p>\n<p style=\"text-align: left\"><!--more-->Porque la esfera redonda es la forma de \u00e1rea minima que encierra un   determinado volumen de aire, como demostr\u00f3 matem\u00e1ticamente Schwarz en 1884. Del mismo modo la pompa doble formada por dos   pompas cuando se unen es la forma de \u00e1rea m\u00ednima que encierra y separa dos   vol\u00famenes dados de aire:<\/p>\n<p style=\"text-align: center\"><a href=\"http:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sdb2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-401 aligncenter\" src=\"https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/sdb2.jpg\" alt=\"\" width=\"114\" height=\"143\" \/><\/a><\/p>\n<p style=\"text-align: left\">Este hecho no fue demostrado hasta el a\u00f1o 2000, mediante en trabajo desarrollado por dos   matem\u00e1ticos de la Universidad de Granada, <a href=\"http:\/\/www.ugr.es\/ ~ Ritor\u00e9\">Manuel Ritor\u00e9<\/a> y <a href=\"http:\/\/www.ugr.es\/ ~  aros \/\">Antonio Ros<\/a>, y un ex  estudiante universitario de  investigaci\u00f3n <a href=\"http:\/\/math.berkeley.edu\/index . php? module = mathfacultyman   y sView MATHFACULTY_MAN_op = &amp; MATHFACULTY_id = 52\">Michael   Hutchings<\/a>, ahora profesor asociado de matem\u00e1ticas en la Universidad   de California, Berkeley. Se puede ver el <a href=\"http:\/\/www.maa.org\/features\/mathchat\/mathchat_3_18_00.html\">anuncio<\/a> en mi p\u00e1gina web <a href=\"http:\/\/www.maa.org\/features\/mathchat\/mathchat_archives.html\">MathChat<\/a>.<\/p>\n<p style=\"text-align: left\">Sigue siendo una pregunta abierta hoy si la pompa triple familiar   es la forma de menor \u00e1rea que encierra y separa tres vol\u00famenes dados de aire.<\/p>\n<p style=\"text-align: center\"><a href=\"http:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/triple-156.jpeg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-399 aligncenter\" src=\"https:\/\/sites.williams.edu\/Morgan\/files\/2011\/02\/triple-156.jpeg\" alt=\"\" width=\"164\" height=\"136\" \/><\/a><\/p>\n<p style=\"text-align: left\">Estas im\u00e1genes y <a href=\"http:\/\/torus.math.uiuc.edu\/jms\/Images\/\">m\u00e1s<\/a> se deben a\u00a0<a href=\"http:\/\/www.math.tu-berlin.de\/~sullivan\/\">John M. Sullivan<\/a>.  Hay algunas <a href=\"http:\/\/www.trendhunter.com\/trends\/richard-heeks-photography-bubble\">fotos<\/a> maravillosas de la explosi\u00f3n de una pompa debidas a Richard Heeks.<\/p>\n<p style=\"text-align: left\">Este post es una colaboraci\u00f3n del blog de Frank Morgan para la <a href=\"http:\/\/gaussianos.com\/carnaval-de-matematicas-edicion-2-2-del-14-al-25-de-marzo-de-2011-en-gaussianos\/\">Edici\u00f3n 2.2<\/a> <a href=\"http:\/\/carnavaldematematicas.bligoo.es\/\">del Carnaval de Matem\u00e1ticas<\/a>, que organiza el blog <a href=\"http:\/\/gaussianos.com\">Gaussianos<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[&#8220;Soap Bubbles and Mathematics,&#8221; written for the Spanish Math Carnival] \u00bfPor qu\u00e9 son las pompas de jab\u00f3n tan perfectamente redondas?<\/p>\n","protected":false},"author":269,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[14042,14043],"tags":[],"class_list":["post-388","post","type-post","status-publish","format-standard","hentry","category-general-interest","category-math"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts\/388","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/users\/269"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/comments?post=388"}],"version-history":[{"count":0,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/posts\/388\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/media?parent=388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/categories?post=388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/Morgan\/wp-json\/wp\/v2\/tags?post=388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}