{"id":8367,"date":"2016-06-19T19:00:31","date_gmt":"2016-06-19T22:00:31","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=8367"},"modified":"2016-06-19T19:00:31","modified_gmt":"2016-06-19T22:00:31","slug":"o-pentgono-mgico-de-frolov","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2016\/06\/o-pentgono-mgico-de-frolov\/","title":{"rendered":"O Pent\u00e1gono M\u00e1gico de Frolov"},"content":{"rendered":"<p><a href=\"http:\/\/scienceblogs.com.br\/hypercubic\/files\/2016\/06\/frolov.jpg\" data-rel=\"lightbox-image-0\" data-rl_title=\"\" data-rl_caption=\"\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter\" style=\"float: none;padding-top: 0px;padding-left: 0px;margin-left: auto;padding-right: 0px;margin-right: auto;border: 0px\" title=\"\" src=\"http:\/\/scienceblogs.com.br\/hypercubic\/files\/2016\/06\/frolov_thumb.jpg\" alt=\"frolov\" width=\"504\" height=\"480\" border=\"0\" \/><\/a><\/p>\n<p style=\"padding-left: 30px\" align=\"justify\"><span style=\"font-family: Georgia;font-size: small\">Podemos observar que os cinco lados de cada pent\u00e1gono [acima] s\u00e3o iguais e que os cinco di\u00e2metros, de um \u00e2ngulo ao centro do lado oposto, somam 459 cada um, o que \u00e9 nove vezes o n\u00famero central, 51; este tamb\u00e9m \u00e9 o n\u00famero m\u00e9dio, pois a s\u00e9rie vai de 1 a 101. Adicionalmente, o pent\u00e1gono interno soma 510, dez vezes o n\u00famero m\u00e9dio; o pent\u00e1gono seguinte, 1020 ou 20 vezes o valor m\u00e9dio; a figura a seguir, 1530 ou 30 vezes a m\u00e9dia e o pent\u00e1gono mais externo soma 2040 ou 40 vezes a m\u00e9dia. \u2014 Edward Falkener, <em>Games Ancient and Oriental and How to Play Them<\/em> [<em>Jogos antigos e orientais e como jog\u00e1-los<\/em>], 1892, <a href=\"https:\/\/archive.org\/stream\/gamesancientorie00falkuoft#page\/308\/mode\/2up\">p. 308<\/a>.<\/span><\/p>\n<p align=\"justify\">Embora esteja numa obra dedicada a jogos da antiguidade, o pent\u00e1gono m\u00e1gico n\u00e3o era nem antigo nem oriental. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Edward_Falkener\">Falkener<\/a> [1814-1896] extraiu-o da obra de Mikhail Frolov, <em><a href=\"https:\/\/archive.org\/details\/lescarrsmagique00frolgoog\">Les carr\u00e9s magiques: nouvelle \u00e9tude<\/a> <\/em>[<em>Os quadrados m\u00e1gicos: novo estudo<\/em>], publicada em 1886. O arquiteto e escritor\u00a0ingl\u00eas deixou passar outra propriedade do pent\u00e1gono m\u00e1gico de Frolov: cada lado do pent\u00e1gono externo tamb\u00e9m soma 459.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Podemos observar que os cinco lados de cada pent\u00e1gono [acima] s\u00e3o iguais e que os cinco di\u00e2metros, de um \u00e2ngulo ao centro do lado oposto, somam 459 cada um, o que \u00e9 nove vezes o n\u00famero central, 51; este tamb\u00e9m \u00e9 o n\u00famero m\u00e9dio, pois a s\u00e9rie vai de 1 a 101. Adicionalmente, o pent\u00e1gono [&hellip;]<\/p>\n","protected":false},"author":486,"featured_media":8381,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[79,197,203,238],"tags":[1670,2161,2207,2641,3043],"class_list":["post-8367","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-curiosidades","category-livros","category-matematica","category-numeros","tag-games-ancient-and-oriental","tag-magico","tag-matemagica","tag-pentagono","tag-sec-xix"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>O Pent\u00e1gono M\u00e1gico de Frolov - hypercubic<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.blogs.unicamp.br\/hypercubic\/2016\/06\/o-pentgono-mgico-de-frolov\/\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Renato Pincelli\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2016\\\/06\\\/o-pentgono-mgico-de-frolov\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2016\\\/06\\\/o-pentgono-mgico-de-frolov\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\"O Pent\u00e1gono M\u00e1gico de Frolov\",\"datePublished\":\"2016-06-19T22:00:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2016\\\/06\\\/o-pentgono-mgico-de-frolov\\\/\"},\"wordCount\":194,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2016\\\/06\\\/o-pentgono-mgico-de-frolov\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/wp-content\\\/uploads\\\/sites\\\/249\\\/2016\\\/06\\\/frolov_thumb-1.jpg\",\"keywords\":[\"Games Ancient and Oriental\",\"m\u00e1gico\",\"matem\u00e1gica\",\"pent\u00e1gono\",\"s\u00e9c. 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