{"id":729,"date":"2016-03-17T08:41:12","date_gmt":"2016-03-17T07:41:12","guid":{"rendered":"http:\/\/agora.xtec.cat\/insderodadebara\/?p=729"},"modified":"2016-07-11T09:30:29","modified_gmt":"2016-07-11T08:30:29","slug":"el-triangle-de-sierpinski","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/insderodadebara\/eso\/el-triangle-de-sierpinski\/","title":{"rendered":"El triangle de Sierpinski"},"content":{"rendered":"<p>El <b>triangle de Sierpi\u0144ski<\/b> \u00e9s un objecte <a title=\"Fractal\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Fractal\">fractal<\/a>, que va ser introdu\u00eft per primera vegada en 1915 pel matem\u00e0tic polon\u00e8s<\/p>\n<p><a class=\"mw-redirect\" title=\"Waclaw Sierpi\u0144ski\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Waclaw_Sierpi%C5%84ski\"><img loading=\"lazy\" decoding=\"async\" class=\"  wp-image-732 alignright\" src=\"http:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/CdLWh46WEAAmowq-1024x576.jpg\" alt=\"CdLWh46WEAAmowq\" width=\"516\" height=\"290\" srcset=\"https:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/CdLWh46WEAAmowq.jpg 1024w, https:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/CdLWh46WEAAmowq-300x169.jpg 300w\" sizes=\"auto, (max-width: 516px) 100vw, 516px\" \/>Waclaw Sierpi\u0144ski<\/a>. \u00c9s un dels exemples b\u00e0sics de conjunt auto-semblant, una de les propietats fonamentals de les fractals.<\/p>\n<p>Per construir el triangle de Sierpi\u0144ski se segueix l&#8217;algoritme seg\u00fcent:<\/p>\n<ol>\n<li>A partir d&#8217;un triangle, s&#8217;uneixen els punts mitjans dels seus costats, dividint el triangle inicial en quatre triangles<\/li>\n<li>S&#8217;elimina el triangle interior<\/li>\n<li>En cada un dels tres triangles que queden es procedeix a fer el pas 1<\/li>\n<\/ol>\n<p>El triangle de Sierpi\u0144ski \u00e9s el l\u00edmit de fer el procediment anterior de manera infinita.<\/p>\n<p>En el nostre centre, els alumnes de l&#8217;Aula Oberta han constru\u00eft diversos triangles de Sierpinski i els han relacionat amb les pot\u00e8ncies de 3. Ho han fet gr\u00e0cies a la col\u00b7laboraci\u00f3 d&#8217;alumnes de tot el centre que han recollit llaunes per fer la construcci\u00f3<\/p>\n<p><a href=\"http:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/54ab4e17-efe6-4cdb-b7b7-9c64db748a671.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-731\" src=\"http:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/54ab4e17-efe6-4cdb-b7b7-9c64db748a671-1024x576.jpg\" alt=\"54ab4e17-efe6-4cdb-b7b7-9c64db748a67\" width=\"480\" height=\"271\" srcset=\"https:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/54ab4e17-efe6-4cdb-b7b7-9c64db748a671-1024x576.jpg 1024w, https:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/54ab4e17-efe6-4cdb-b7b7-9c64db748a671-300x169.jpg 300w, https:\/\/agora.xtec.cat\/insderodadebara\/wp-content\/uploads\/usu1145\/2016\/03\/54ab4e17-efe6-4cdb-b7b7-9c64db748a671.jpg 1600w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>El triangle de Sierpi\u0144ski \u00e9s un objecte fractal, que va ser introdu\u00eft per primera vegada en 1915 pel matem\u00e0tic polon\u00e8s Waclaw Sierpi\u0144ski. \u00c9s un dels exemples b\u00e0sics de conjunt auto-semblant, una de les propietats fonamentals de les fractals.&hellip;  <a href=\"https:\/\/agora.xtec.cat\/insderodadebara\/eso\/el-triangle-de-sierpinski\/\" title=\"Read El triangle de Sierpinski\">Llegeix m\u00e9s\u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":731,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[3],"tags":[79,41],"class_list":["post-729","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-eso","tag-aula-oberta","tag-matematiques"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/posts\/729","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/comments?post=729"}],"version-history":[{"count":3,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/posts\/729\/revisions"}],"predecessor-version":[{"id":775,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/posts\/729\/revisions\/775"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/media\/731"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/media?parent=729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/categories?post=729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/insderodadebara\/wp-json\/wp\/v2\/tags?post=729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}