{"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":"2026-05-27T11:47:07","modified_gmt":"2026-05-27T10:47:07","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 class=\"wp-block-paragraph\">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 - Misutra<\/a> <\/section> <\/blockquote> <script async src=\"https:\/\/www.tiktok.com\/embed.js\"><\/script>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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+....+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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">M\u00e1s informaci\u00f3n sobre este problema:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">\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...  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":"","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"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":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"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. 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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. 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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. 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