{"id":1252,"date":"2018-03-07T19:48:08","date_gmt":"2018-03-07T18:48:08","guid":{"rendered":"http:\/\/agora.xtec.cat\/iesribotiserra\/?p=1252"},"modified":"2018-09-12T16:13:47","modified_gmt":"2018-09-12T14:13:47","slug":"triangle-se-sierspinski","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/iesribotiserra\/portada\/triangle-se-sierspinski\/","title":{"rendered":"Triangle de Sierspinski"},"content":{"rendered":"

Els alumnes de 4t d’ESO, a classe de matem\u00e0tiques, s’han apropat a les fractals realitzant una pr\u00e0ctica tridimensional del triangle de Sierpinski<\/strong><\/p>\n

\"\"<\/a><\/p>\n

El triangle de Sierpi\u0144ski \u00e9s un objecte fractal, que va ser introdu\u00eft per primera vegada el 1915 pel matem\u00e0tic polon\u00e8s Waclaw Sierpinski. \u00c9s un dels exemples b\u00e0sics de conjunt autosemblant, una de les propietats fonamentals de les fractals. Encara que va ser constru\u00eft inicialment a partir d’un triangle equil\u00e0ter, anomenat triangle de Sierpinski can\u00f2nic, es pot fer la construcci\u00f3 a partir de qualsevol triangle.<\/p>\n

Per construir el triangle de Sierpinski, se segueix l’algoritme seg\u00fcent:<\/p>\n

    \n
  1. A partir d’un triangle, s’uneixen els punts mitjans dels seus costats, dividint el triangle inicial en quatre triangles.<\/li>\n
  2. S’elimina el triangle interior.<\/li>\n
  3. En cada un dels tres triangles que queden es repeteix el primer pas.<\/li>\n<\/ol>\n

    El triangle de Sierpinski \u00e9s el l\u00edmit de fer el procediment anterior de manera infinita.<\/p>\n

    \"\"<\/a><\/p>\n

    Observem que en cada pas el triangle de Sierpinski s’obt\u00e9 amb tres figures del pas anterior, sent cadascuna d’elles semblant a la del pas anterior i amb ra\u00f3 de semblan\u00e7a de\u00a0\u00bd. Un objecte d’aquestes caracter\u00edstiques acte-semblant en diferents escales es diu fractal; aix\u00ed doncs, el triangle de Sierpinski \u00e9s un exemple de fractal.<\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    Els alumnes de 4t d’ESO, a classe de matem\u00e0tiques, s’han apropat a les fractals realitzant una pr\u00e0ctica tridimensional del triangle de Sierpinski El triangle de Sierpi\u0144ski \u00e9s un objecte fractal, que va ser introdu\u00eft per primera vegada el 1915 pel matem\u00e0tic polon\u00e8s Waclaw Sierpinski. \u00c9s un dels exemples b\u00e0sics de conjunt autosemblant, una de les […]<\/p>\n","protected":false},"author":1,"featured_media":1254,"comment_status":"closed","ping_status":"closed","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,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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