{"id":6210,"date":"2022-08-02T16:42:01","date_gmt":"2022-08-02T15:42:01","guid":{"rendered":"https:\/\/www2.ual.es\/neotrie\/?p=6210"},"modified":"2022-08-02T17:11:58","modified_gmt":"2022-08-02T16:11:58","slug":"apilamiento-de-balas-de-canon","status":"publish","type":"post","link":"https:\/\/www2.ual.es\/neotrie\/apilamiento-de-balas-de-canon\/","title":{"rendered":"Apilamientos de balas de ca\u00f1\u00f3n"},"content":{"rendered":"\n<p>Ayer empezamos apilando balas de ca\u00f1\u00f3n sobre una base triangular (equilateral) y pregunt\u00e1bamos cuantas hab\u00eda. Despu\u00e9s lo hicimos sobre una base cuadrada.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-tiktok wp-block-embed-tiktok\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"tiktok-embed\" cite=\"https:\/\/www.tiktok.com\/@neotrievr\/video\/7126974491921616134\" data-video-id=\"7126974491921616134\" data-embed-from=\"oembed\" style=\"max-width: 605px;min-width: 325px;\" > <section> <a target=\"_blank\" title=\"@neotrievr\" href=\"https:\/\/www.tiktok.com\/@neotrievr?refer=embed\">@neotrievr<\/a> <p><a title=\"empaquetamiento\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/empaquetamiento\">#empaquetamiento<\/a> <a title=\"education\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/education\">#education<\/a> <a title=\"3dgeometry\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/3dgeometry\">#3dgeometry<\/a> <a title=\"oculus\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/oculus\">#oculus<\/a> <a title=\"geometry\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/geometry\">#geometry<\/a>  <a title=\"realidadvirtual\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/realidadvirtual\">#realidadvirtual<\/a> <a title=\"virtualreality\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/virtualreality\">#virtualreality<\/a> <a title=\"matematicas\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/matematicas\">#matematicas<\/a> <a title=\"mathematics\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/mathematics\">#mathematics<\/a> <a title=\"quest2\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/quest2\">#quest2<\/a> <a title=\"neotrievr\" target=\"_blank\" href=\"https:\/\/www.tiktok.com\/tag\/neotrievr\">#neotrievr<\/a><\/p> <a target=\"_blank\" title=\"\u266c Roblox OOF Song - Misutra\" href=\"https:\/\/www.tiktok.com\/music\/Roblox-OOF-Song-6919911731137349634?refer=embed\">\u266c Roblox OOF Song &#8211; Misutra<\/a> <\/section> <\/blockquote> <script async src=\"https:\/\/www.tiktok.com\/embed.js\"><\/script>\n<\/div><\/figure>\n\n\n\n<p>La soluci\u00f3n nos la da el n\u00famero tetra\u00e9drico T_5=35. En general, el N-\u00e9simo n\u00famero tetra\u00e9drico es la suma de los N primeros n\u00fameros triangulares N(N+1)\/2, que coincide con N(N+1)(N+2)\/6. <\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"How many cannonballs are there?\" width=\"1080\" height=\"608\" src=\"https:\/\/www.youtube.com\/embed\/FkAuygUiuA4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Una vez que averigu\u00e1is que el resultado es la suma de los 5 primeros cuadrados, esto es 55, en general 1^2+2^2+&#8230;.+N^2=N(1+N)(2N+1)\/6, se puede plantear el problema famoso sobre balas de ca\u00f1\u00f3n que consiste en encontrar un n\u00famero cuadrado de balas M^2 que se apilen de forma piramidal, es decir  N(1+N)(2N+1)\/6 =M^2. <\/p>\n\n\n\n<p>A parte de N=1, existe una \u00fanica soluci\u00f3n que es N=24, M=70<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/es.wikipedia.org\/wiki\/Problema_de_las_balas_de_ca%C3%B1%C3%B3n#\/media\/Archivo:Cannonball_problem.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"731\" src=\"https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2022\/08\/image-1024x731.png\" alt=\"\" class=\"wp-image-6213\" srcset=\"https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2022\/08\/image-1024x731.png 1024w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2022\/08\/image-980x700.png 980w, https:\/\/www2.ual.es\/neotrie\/wp-content\/uploads\/2022\/08\/image-480x343.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) 1024px, 100vw\" \/><\/a><figcaption>Muestra la \u00fanica soluci\u00f3n. Fuente: <a href=\"https:\/\/es.wikipedia.org\/wiki\/Problema_de_las_balas_de_ca%C3%B1%C3%B3n#\/media\/Archivo:Cannonball_problem.png\">Wikipedia<\/a><\/figcaption><\/figure>\n\n\n\n<p>M\u00e1s informaci\u00f3n sobre este problema:<\/p>\n\n\n\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Cannonball_problem#:~:text=In%20the%20mathematics%20of%20figurate,arranged%20into%20a%20square%20pyramid.\">https:\/\/en.wikipedia.org\/wiki\/Cannonball_problem#:~:text=In%20the%20mathematics%20of%20figurate,arranged%20into%20a%20square%20pyramid.<\/a><\/p>\n\n\n\n<p>\u00bfAlg\u00fan voluntario para disparar 4900 veces la pistola? Quiz\u00e1 implementemos una funci\u00f3n que dispare autom\u00e1ticamente un n\u00famero dado de balas&#8230;  aunque no creo que lo soporte el juego. Podr\u00eda servir para dise\u00f1ar <a href=\"https:\/\/es.wikipedia.org\/wiki\/M%C3%A1quina_de_Galton\">M\u00e1quinas de Galton<\/a>, en 2 y 3d. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ayer empezamos apilando balas de ca\u00f1\u00f3n sobre una base triangular (equilateral) y pregunt\u00e1bamos cuantas hab\u00eda. Despu\u00e9s lo hicimos sobre una base cuadrada. La soluci\u00f3n nos la da el n\u00famero tetra\u00e9drico T_5=35. En general, el N-\u00e9simo n\u00famero tetra\u00e9drico es la suma de los N primeros n\u00fameros triangulares N(N+1)\/2, que coincide con N(N+1)(N+2)\/6. Una vez que averigu\u00e1is [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-6210","post","type-post","status-publish","format-standard","hentry","category-secundaria"],"aioseo_notices":[],"views":861,"_links":{"self":[{"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/posts\/6210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/comments?post=6210"}],"version-history":[{"count":22,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/posts\/6210\/revisions"}],"predecessor-version":[{"id":6242,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/posts\/6210\/revisions\/6242"}],"wp:attachment":[{"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/media?parent=6210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/categories?post=6210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www2.ual.es\/neotrie\/wp-json\/wp\/v2\/tags?post=6210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}