{"id":14938,"date":"2026-03-17T19:28:10","date_gmt":"2026-03-17T18:28:10","guid":{"rendered":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/?p=14938"},"modified":"2026-03-17T19:28:12","modified_gmt":"2026-03-17T18:28:12","slug":"impulsem-un-experiment-collectiu-per-calcular-el-nombre-%cf%80","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/noticies\/impulsem-un-experiment-collectiu-per-calcular-el-nombre-%cf%80\/","title":{"rendered":"Impulsem un experiment col\u00b7lectiu per calcular el nombre \u03c0"},"content":{"rendered":"\n<p>Enguany,<strong> el Duc ha celebrat el Dia Pi<\/strong> afegint un <strong>nova proposta que combina matem\u00e0tiques, tecnologia i participaci\u00f3 col\u00b7lectiva.<\/strong> A trav\u00e9s d\u2019un aplicatiu web propi, l&#8217;alumnat, les fam\u00edlies i altres participants poden col\u00b7laborar en un experiment basat en el m\u00e8tode de Montecarlo per obtenir una estimaci\u00f3 del valor del nombre \u03c0.<\/p>\n<p>La iniciativa <strong>convida<\/strong> la comunitat educativa<strong> a accedir al web <a href=\"http:\/\/pi.ducdemontblanc.cat\">pi.ducdemontblanc.cat<\/a><\/strong> <strong>i generar, amb un sol clic, 1.000 punts aleatoris.<\/strong> Aquests punts es distribueixen dins d\u2019un quadrat que cont\u00e9 un cercle inscrit, de manera que, segons si cauen dins o fora del cercle, es pot calcular una aproximaci\u00f3 del valor de \u03c0 a partir de la relaci\u00f3 entre les \u00e0rees.<\/p>\n<p>La resposta de la comunitat est\u00e0 sent molt positiva. En total, s\u2019han recollit 652.500 punts generats per 310 participants. D\u2019aquests, 512.417 punts han caigut dins del cercle i 140.083 fora. Amb aquestes dades, l\u2019estimaci\u00f3 global obtinguda ha estat: \u03c0 \u2248 3,1412536<\/p>\n<p>Aquest resultat presenta 3 xifres decimals coincidents amb el valor real de \u03c0, una aproximaci\u00f3 molt notable que posa de manifest l\u2019efic\u00e0cia del m\u00e8tode i la import\u00e0ncia de la participaci\u00f3 col\u00b7lectiva en aquest tipus d\u2019experiments.<\/p>\n<p>L\u2019activitat tamb\u00e9 serveix per mostrar de manera pr\u00e0ctica un dels principis essencials del m\u00e8tode de Montecarlo: com m\u00e9s gran \u00e9s el nombre de punts generats, m\u00e9s precisa \u00e9s l\u2019estimaci\u00f3. Aix\u00ed, l\u2019experiment ha perm\u00e8s treballar conceptes matem\u00e0tics i estad\u00edstics d\u2019una forma visual, participativa i significativa.<\/p>\n<p>A m\u00e9s del c\u00e0lcul final, el web de l\u2019experiment permet consultar altres aspectes relacionats amb el proc\u00e9s, com ara la converg\u00e8ncia del c\u00e0lcul, l\u2019error absolut o la comprovaci\u00f3 de l\u2019aleatorietat dels punts generats.<\/p>\n<p>Amb aquesta proposta, <strong>el Duc referma la seva aposta per activitats que connecten l\u2019aprenentatge amb l\u2019experi\u00e8ncia directa i la implicaci\u00f3 de tota la comunitat educativa<\/strong>, fent visible com les matem\u00e0tiques, l\u2019atzar i la participaci\u00f3 poden treballar plegats.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enguany, el Duc ha celebrat el Dia Pi afegint un nova proposta que combina matem\u00e0tiques, tecnologia i participaci\u00f3 col\u00b7lectiva. A [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":14939,"comment_status":"closed","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,"site-sidebar-layout":"no-sidebar","site-content-layout":"","ast-site-content-layout":"default","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":"set","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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8,3,4,5,6,7,1,29],"tags":[],"class_list":["post-14938","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-batxillerat","category-eso","category-eso-1","category-eso-2","category-eso-3","category-eso-4","category-noticies","category-portada"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/posts\/14938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/comments?post=14938"}],"version-history":[{"count":3,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/posts\/14938\/revisions"}],"predecessor-version":[{"id":14942,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/posts\/14938\/revisions\/14942"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/media\/14939"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/media?parent=14938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/categories?post=14938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesducdemontblanc\/wp-json\/wp\/v2\/tags?post=14938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}