{"id":2731,"date":"2022-06-22T20:12:36","date_gmt":"2022-06-22T18:12:36","guid":{"rendered":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/?p=2731"},"modified":"2023-02-06T14:55:10","modified_gmt":"2023-02-06T13:55:10","slug":"terminada-la-esponja-de-menger","status":"publish","type":"post","link":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/2022\/06\/22\/terminada-la-esponja-de-menger\/","title":{"rendered":"Terminada la \u00abEsponja de Menger\u00bb"},"content":{"rendered":"\n<p>Bueno, \u00a1\u00a1\u00a1\u00a1\u00a1\u00a1ahora s\u00ed que s\u00ed!!!!!! \ud83d\ude00 \ud83d\ude00 \ud83d\ude00<\/p>\n\n\n\n<p>\u00a1\u00a1\u00a1\u00a1\u00a1\u00a1\u00a1Hemos terminado la Esponja de Menger!!!!! \u00a1\u00a1\u00a1\u00a1\u00a1Yiiiiiiiijaaaaaa!!!!!<\/p>\n\n\n\n<p>Despu\u00e9s de tres cursos hemos logrado acabar este monstruo fractal de 18.048 piezas de papiroflexia (m\u00f3dulos de sonobe). Ha sido una gran locura colectiva en la que ha participado todo el instituto. Todo el alumnado ha realizado al menos una pieza y muchos\/as han realizado much\u00edsimas m\u00e1s y estructuras m\u00e1s avanzadas&#8230; El montaje tambi\u00e9n ha supuesto un trabajo enorme. Desde el Departamento de Tecnolog\u00eda tambi\u00e9n se colabor\u00f3 dise\u00f1ando un armaz\u00f3n, que queda oculto, para soportar el peso de la estructura.<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-2 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1599\" height=\"1200\" data-id=\"2733\" src=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM.jpeg\" alt=\"\" class=\"wp-image-2733\" srcset=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM.jpeg 1599w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM-300x225.jpeg 300w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM-1024x768.jpeg 1024w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM-768x576.jpeg 768w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-22-at-12.58.33-PM-1536x1153.jpeg 1536w\" sizes=\"auto, (max-width: 1599px) 100vw, 1599px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1121\" data-id=\"2732\" src=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg\" alt=\"\" class=\"wp-image-2732\" srcset=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg 1600w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-300x210.jpeg 300w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-1024x717.jpeg 1024w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-768x538.jpeg 768w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-1536x1076.jpeg 1536w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-400x280.jpeg 400w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/figure>\n<\/figure>\n\n\n\n<p>Han sido una barbaridad de horas de curro. Y es un aut\u00e9ntico placer verlo terminado. Un currazo gigantesco acompa\u00f1ado de cientos de chavales\/as haciendo piezas como locos en casa (trabajando la paciencia, concentraci\u00f3n, motricidad fina, etc.). Adem\u00e1s de trabajos sobre fractales e historia de la geometr\u00eda realizados en cursos de bachillerato (y algunos m\u00e1s sencillos en la ESO).<\/p>\n\n\n\n<p>Por supuesto, se aceptan visitas.\ud83d\ude09<\/p>\n\n\n\n<iframe loading=\"lazy\" src=\"https:\/\/mediateca.educa.madrid.org\/video\/ax98jyron296379q\/fs\" width=\"420\" height=\"315\" frameborder=\"0\" scrolling=\"no\" style=\"border:0;overflow:hidden\" allowfullscreen=\"\"><\/iframe>\n\n\n\n<h4 class=\"wp-block-heading\">Explicaci\u00f3n matem\u00e1tica del proyecto. La Esponja de Menger (Papiroflexia fractal). <a rel=\"noreferrer noopener\" href=\"https:\/\/www.educa2.madrid.org\/web\/educamadrid\/principal\/files\/7682dc7b-a25e-4e36-a796-4ad61750bb4e\/webies\/Esponja%20de%20Menger_AnexoProgramacionDpto.pdf?t=1635605324234\" target=\"_blank\">>>Ver anexo explicativo por niveles<\/a><\/h4>\n\n\n\n<p>La esponja de Karl Menger se construye bajo el mismo principio que el tri\u00e1ngulo de Sierpinski, pero no con un tri\u00e1ngulo sino con un cubo en 3 dimensiones. La esponja de Menger es el l\u00edmite de este proceso tras un n\u00famero infinito de iteraciones. Una imagen vale m\u00e1s que mil palabras:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"341\" src=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-1024x341.jpg\" alt=\"\" class=\"wp-image-2736\" srcset=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-1024x341.jpg 1024w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-300x100.jpg 300w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-768x256.jpg 768w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-1536x512.jpg 1536w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger1-2048x683.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n\n<p>Lo realmente curioso de este objeto fractal es lo siguiente:<\/p>\n\n\n\n<p><strong>Superficie<\/strong>: El \u00e1rea de esta figura es mayor en cada iteraci\u00f3n y en el l\u00edmite es&#8230; \u00a1\u00a1\u00a1INFINITA!!!<\/p>\n\n\n\n<p><strong>Volumen<\/strong>: El volumen por el contrario se va haciendo m\u00e1s peque\u00f1o en cada iteraci\u00f3n y en el l\u00edmite es&#8230; \u00a1\u00a1\u00a1CERO!!!<\/p>\n\n\n\n<p>\u00a1QU\u00c9 COSAS M\u00c1S RARAS! tenemos una superficie infinita encerrada en un cubo y esa superficie no encierra un volumen&#8230; Entonces, \u00bfde qu\u00e9 estamos hablando, de una superficie (2D) o de un cuerpo (3D)?<\/p>\n\n\n\n<p>Pues ni de lo uno de lo otro, estamos hablando de un objeto de dimensi\u00f3n fractal, es una cosa intermedia entre las superficies y los vol\u00famenes. Su dimensi\u00f3n es 2,7268&#8230; Un poco raro y un poco dif\u00edcil de explicar&#8230;<\/p>\n\n\n\n<p>Si nos fijamos bien en la imagen, podremos comprobar c\u00f3mo para cada iteraci\u00f3n necesitaremos 20 cubos como los de la iteraci\u00f3n anterior. Es decir, para el nivel 1, necesitamos 20 cubos; para la de nivel dos, 20 cubos como los de nivel 1 y as\u00ed sucesivamente.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"225\" src=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger2-300x225.jpg\" alt=\"\" class=\"wp-image-2737\" srcset=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger2-300x225.jpg 300w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger2-768x576.jpg 768w, https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/menger2.jpg 800w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>Para saber m\u00e1s:<\/p>\n\n\n\n<p><a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/La_naturaleza_y_los_fractales.pdf\">La_naturaleza_y_los_fractales<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/Formulas.pdf\">Formulas<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bueno, \u00a1\u00a1\u00a1\u00a1\u00a1\u00a1ahora s\u00ed que s\u00ed!!!!!! \ud83d\ude00 \ud83d\ude00 \ud83d\ude00 \u00a1\u00a1\u00a1\u00a1\u00a1\u00a1\u00a1Hemos terminado la Esponja de Menger!!!!! \u00a1\u00a1\u00a1\u00a1\u00a1Yiiiiiiiijaaaaaa!!!!! Despu\u00e9s de tres cursos hemos logrado acabar este monstruo fractal de 18.048 piezas de papiroflexia (m\u00f3dulos de sonobe). Ha sido una gran locura colectiva en la que ha participado todo el instituto. Todo el alumnado ha realizado al menos una [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":2732,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,5,18,10],"tags":[],"post_folder":[],"class_list":["post-2731","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-anuncios","category-cultura","category-matematicas","category-noticias"],"rttpg_featured_image_url":{"full":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",1600,1121,false],"landscape":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",1600,1121,false],"portraits":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",1600,1121,false],"thumbnail":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-150x150.jpeg",150,150,true],"medium":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-300x210.jpeg",300,210,true],"large":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-1024x717.jpeg",640,448,true],"thumblist":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-300x300.jpeg",300,300,true],"thumbrelated":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",500,350,false],"meccarouselthumb":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-474x324.jpeg",474,324,true],"gridsquare":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-391x260.jpeg",391,260,true],"tileview":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-300x400.jpeg",300,400,true],"1536x1536":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-1536x1076.jpeg",1536,1076,true],"2048x2048":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",1600,1121,false],"total-portfolio-thumb":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-400x400.jpeg",400,400,true],"total-team-thumb":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-350x420.jpeg",350,420,true],"total-blog-thumb":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-400x280.jpeg",400,280,true],"total-thumb":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-100x100.jpeg",100,100,true],"total-blog-header":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-720x360.jpeg",720,360,true],"sow-carousel-default":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM-272x182.jpeg",272,182,true],"sow-post-carousel-overlay-theme":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",360,252,false],"sow-post-carousel-cards-theme":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",343,240,false],"rt_custom":["https:\/\/site.educa.madrid.org\/ies.lacabrera\/\/wp-content\/uploads\/ies.lacabrera\/2022\/06\/WhatsApp-Image-2022-06-20-at-1.12.55-PM.jpeg",1600,1121,false]},"rttpg_author":{"display_name":"tic.ies.lacabrera","author_link":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/author\/cuenta_tic-ies-lacabrera\/"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/category\/noticias\/anuncios\/\" rel=\"category tag\">Anuncios<\/a> <a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/category\/noticias\/cultura\/\" rel=\"category tag\">Cultura<\/a> <a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/category\/noticias\/matematicas\/\" rel=\"category tag\">Matem\u00e1ticas<\/a> <a href=\"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/category\/noticias\/\" rel=\"category tag\">Noticias<\/a>","rttpg_excerpt":"Bueno, \u00a1\u00a1\u00a1\u00a1\u00a1\u00a1ahora s\u00ed que s\u00ed!!!!!! \ud83d\ude00 \ud83d\ude00 \ud83d\ude00 \u00a1\u00a1\u00a1\u00a1\u00a1\u00a1\u00a1Hemos terminado la Esponja de Menger!!!!! \u00a1\u00a1\u00a1\u00a1\u00a1Yiiiiiiiijaaaaaa!!!!! Despu\u00e9s de tres cursos hemos logrado acabar este monstruo fractal de 18.048 piezas de papiroflexia (m\u00f3dulos de sonobe). Ha sido una gran locura colectiva en la que ha participado todo el instituto. Todo el alumnado ha realizado al menos una&hellip;","post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/posts\/2731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/comments?post=2731"}],"version-history":[{"count":7,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/posts\/2731\/revisions"}],"predecessor-version":[{"id":3435,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/posts\/2731\/revisions\/3435"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/media\/2732"}],"wp:attachment":[{"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/media?parent=2731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/categories?post=2731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/tags?post=2731"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/site.educa.madrid.org\/ies.lacabrera\/index.php\/wp-json\/wp\/v2\/post_folder?post=2731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}