En 1914, Ramanujan va proposar el seg\u00fcent problema en la revista de la Societat Matem\u00e0tica \u00cdndia: “prova que $$\u00a0 ( \\frac{1}{1}+\\frac{1}{1\\cdot 3}+\\frac{1}{1\\cdot 3\\cdot 5}+\\ldots ) + \\frac{1}{1+\\frac{1}{1+\\frac{2}{1+\\frac{3}{\\ldots}}}}=\\sqrt{\\frac{\\pi e}{2}}.”$$ Entre d’altres, Ramanujan \u00e9s fam\u00f3s perque, durant la seua carrera matem\u00e0tica, va demostrar o conjecturar moltes f\u00f3rmules com aquesta.<\/p>\n
En 2020, un grup d’investigadors va introduir la Ramanujan machine<\/a>, un sistema que fa \u00fas de la intelig\u00e8ncia artificial per a trobar noves relacions conjecturals entre constants matem\u00e0tiques (com \\(\\pi\\), \\(e\\), etc.) i fraccions cont\u00ednues (s\u00e8ries com la de la f\u00f3rmula anterior). Algunes d’aquestes conjectures han estat probades, per\u00f2 altres continuen sent un problema obert<\/a>.<\/p>\n Aquest treball combina una introducci\u00f3 a la teoria de fraccions cont\u00ednues, un rep\u00e0s a les f\u00f3rmules de Ramanujan i l’estudi de la matem\u00e0tica que est\u00e0 darrere dels algoritmes que generen aquestes noves conjectures. \u00c9s recomanable que l’estudiant tinga coneixements b\u00e0sics sobre xarxes neuronals.<\/p>\n","protected":false},"excerpt":{"rendered":" En 1914, Ramanujan va proposar el seg\u00fcent problema en la revista de la Societat Matem\u00e0tica \u00cdndia: “prova que $$\u00a0 ( \\frac{1}{1}+\\frac{1}{1\\cdot 3}+\\frac{1}{1\\cdot 3\\cdot 5}+\\ldots ) + \\frac{1}{1+\\frac{1}{1+\\frac{2}{1+\\frac{3}{\\ldots}}}}=\\sqrt{\\frac{\\pi e}{2}}.”$$ Entre d’altres, Ramanujan \u00e9s fam\u00f3s perque, durant la seua carrera matem\u00e0tica, va demostrar o conjecturar moltes f\u00f3rmules com aquesta. En 2020, un grup d’investigadors va introduir la […]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29,1],"tags":[22],"class_list":["post-507","post","type-post","status-publish","format-standard","hentry","category-analisi-matematica","category-general","tag-roberto-rubio"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/507","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=507"}],"version-history":[{"count":9,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/507\/revisions"}],"predecessor-version":[{"id":642,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/507\/revisions\/642"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}