{"id":101040,"date":"2025-12-17T13:23:32","date_gmt":"2025-12-17T11:23:32","guid":{"rendered":"https:\/\/www.lovendal.ro\/wp52\/?p=101040"},"modified":"2025-12-17T13:23:32","modified_gmt":"2025-12-17T11:23:32","slug":"formula-matematicianului-indian-ramanujan-pentru-numarul-lui-pi-veche-de-100-de-ani-ascunde-secretele-universului","status":"publish","type":"post","link":"https:\/\/www.lovendal.ro\/wp52\/formula-matematicianului-indian-ramanujan-pentru-numarul-lui-pi-veche-de-100-de-ani-ascunde-secretele-universului\/","title":{"rendered":"Formula matematicianului indian Ramanujan pentru num\u0103rul lui Pi – veche de 100 de ani – ascunde secretele Universului"},"content":{"rendered":"

\"\"<\/a>Un nou studiu dezv\u0103luie c\u0103 formulele vechi de un secol ale lui Srinivasa Ramanujan<\/strong> pentru calcularea lui pi<\/strong> apar \u00een mod nea\u0219teptat \u00een teoriile moderne ale fenomenelor critice, turbulen\u021bei \u0219i g\u0103urilor negre. \u00cen \u0219coal\u0103, mul\u021bi dintre noi \u00eent\u00e2lnim pentru prima dat\u0103 num\u0103rul ira\u021bional \u03c0 (pi)<\/strong> \u2013 rotunjit la 3,14, cu un num\u0103r infinit de cifre zecimale \u2013 atunci c\u00e2nd \u00eenv\u0103\u021b\u0103m cum se raporteaz\u0103 circumferin\u021ba unui cerc la diametrul s\u0103u. De atunci, puterea de calcul a avansat enorm, iar supercomputerele moderne pot acum determina trilioane de cifre ale acestei constante.<\/p>\n

Cercet\u0103torii de la Centrul pentru Fizica Energiilor \u00cenalte<\/strong> (CHEP<\/strong>), Institutul Indian de \u0218tiin\u021b\u0103<\/strong> (IISc<\/strong>), au demonstrat acum c\u0103 unele dintre formulele pur matematice create \u00een urm\u0103 cu un secol pentru a calcula pi sunt str\u00e2ns legate de fizica fundamental\u0103 actual\u0103. Aceste formule vechi reapar \u00een modelele teoretice folosite pentru a studia percolarea, turbulen\u021ba \u0219i anumite aspecte ale g\u0103urilor negre.<\/p>\n

Ne afl\u0103m \u00een anul 1914. Chiar \u00eenainte de a pleca din Madras spre Cambridge, renumitul matematician indian Srinivasa Ramanujan a publicat o lucrare care introducea 17 formule pentru calcularea lui pi. Aceste formule erau excep\u021bional de eficiente, permi\u021b\u00e2nd calcularea lui pi mai rapid dec\u00e2t cu alte metode disponibile la acea vreme. De\u0219i con\u021bineau doar un num\u0103r mic de termeni matematici, ele produceau totu\u0219i multe zecimale corecte ale lui pi. De-a lungul anilor, ele au devenit at\u00e2t de importante \u00eenc\u00e2t acum stau la baza tehnicilor computa\u021bionale \u0219i matematice moderne pentru evaluarea lui pi, inclusiv a metodelor utilizate pe supercomputerele de ast\u0103zi.<\/p>\n

„Oamenii de \u0219tiin\u021b\u0103 au calculat num\u0103rul pi p\u00e2n\u0103 la 200 de trilioane de cifre folosind un algoritm numit algoritmul Chudnovsky”<\/em>, spune Aninda Sinha<\/strong>, profesor la CHEP \u0219i autoare principal\u0103 a noului studiu. „Ace\u0219ti algoritmi se bazeaz\u0103 de fapt pe munca lui Ramanujan”.<\/em> \u00centrebarea pe care Sinha \u0219i Faizan Bhat –<\/strong> alt autor al studiului – a fost: De ce ar trebui s\u0103 existe astfel de formule uimitoare? \u00cen lucrarea lor, cei doi au c\u0103utat un r\u0103spuns bazat pe fizic\u0103. „Am vrut s\u0103 vedem dac\u0103 punctul de plecare al formulelor sale se \u00eencadreaz\u0103 \u00een mod natural \u00eentr-o anumit\u0103 fizic\u0103. Cu alte cuvinte, exist\u0103 o lume fizic\u0103 \u00een care matematica lui Ramanujan apare de sine st\u0103t\u0103toare?”<\/em>, a spus Sinha.<\/p>\n

Ei au descoperit c\u0103 formulele lui Ramanujan se \u00eencadreaz\u0103 \u00een mod natural \u00eentr-o clas\u0103 larg\u0103 de teorii numite teorii conforme ale c\u00e2mpurilor<\/strong>, mai exact \u00een cadrul teoriilor logaritmice conforme ale c\u00e2mpurilor. Teoriile conforme ale c\u00e2mpurilor descriu sisteme cu simetrie de invarian\u021b\u0103 la scal\u0103 – \u00een esen\u021b\u0103 sisteme care arat\u0103 identic indiferent de c\u00e2t de mult se m\u0103re\u0219te imaginea, precum fractalii. \u00centr-un context fizic, acest lucru poate fi observat la punctul critic al apei, o temperatur\u0103 \u0219i o presiune speciale la care at\u00e2t forma lichid\u0103, c\u00e2t \u0219i cea de vapori a apei devin indistictibile una de cealalt\u0103. \u00cen acest moment, apa prezint\u0103 o simetrie de invarian\u021b\u0103 la scal\u0103, iar propriet\u0103\u021bile sale pot fi descrise folosind teoria conform\u0103 a c\u00e2mpului. Comportamentul critic apare \u0219i \u00een percolare (modul \u00een care lucrurile se r\u0103sp\u00e2ndesc printr-un mediu), la debutul turbulen\u021bei \u00een fluide \u0219i \u00een anumite descrieri ale g\u0103urilor negre – fenomene care pot fi explicate prin teoriile conforma\u021bionale logaritmice ale c\u00e2mpului, mai specifice.<\/p>\n

Cercet\u0103torii au descoperit c\u0103 structura matematic\u0103 care st\u0103 la baza punctului de plecare al formulelor lui Ramanujan apare \u0219i \u00een matematica care st\u0103 la baza acestor teorii logaritmice conforme ale c\u00e2mpului. Folosind aceast\u0103 conexiune, au putut calcula eficient anumite cantit\u0103\u021bi din aceste teorii – unele care i-ar putea ajuta s\u0103 \u00een\u021beleag\u0103 mai bine fenomene precum turbulen\u021ba sau percolarea. Acest lucru este similar cu Ramanujan, pornind de la punctul de plecare al formulelor sale \u0219i deriv\u00e2nd eficient num\u0103rul pi.<\/p>\n

Studiul arat\u0103 c\u0103 formulele vechi de un secol ale lui Ramanujan au o aplica\u021bie ascuns\u0103 p\u00e2n\u0103 acum \u00een a face calculele actuale ale fizicii energiilor \u00eenalte mai rapide \u0219i mai u\u0219or de gestionat. Chiar \u0219i f\u0103r\u0103 acest lucru, Sinha \u0219i Bhat spun c\u0103 au fost pur \u0219i simplu nedumeri\u021bi de frumuse\u021bea matematicii lui Ramanujan. „Am fost pur \u0219i simplu fascina\u021bi de modul \u00een care un geniu care lucra la \u00eenceputul secolului al XX-lea \u00een India, aproape f\u0103r\u0103 niciun contact cu fizica modern\u0103, a anticipat structuri care sunt acum esen\u021biale pentru \u00een\u021belegerea noastr\u0103 a Universului”<\/em>, conchide Sinha.<\/p>\n

Sursa:<\/strong> studiul \u015ftiin\u0163ific „Ramanujan\u2019s 1\/\ud835\udf0b Series and Conformal Field Theories” \/ journals.aps.org<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Un nou studiu dezv\u0103luie c\u0103 formulele vechi de un secol ale lui Srinivasa Ramanujan pentru calcularea lui pi apar \u00een mod nea\u0219teptat \u00een teoriile moderne ale fenomenelor critice, turbulen\u021bei \u0219i g\u0103urilor negre. \u00cen \u0219coal\u0103, mul\u021bi dintre noi \u00eent\u00e2lnim pentru prima … <\/p>\n

Cititi mai multe<\/a><\/p>\n","protected":false},"author":1,"featured_media":101041,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[106],"tags":[601,463,348,12157,534,619,9975,1722,679,3507,787,13589,9803,13930,2358,1087],"class_list":["post-101040","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stiinta","tag-apa","tag-cambridge","tag-fizica","tag-fractali","tag-gauri-negre","tag-india","tag-madras","tag-matematica","tag-matematician","tag-numar","tag-pi","tag-ramanujan","tag-stiinta","tag-supercomputer","tag-temperatura","tag-univers","resize-featured-image"],"yoast_head":"\nFormula matematicianului indian Ramanujan pentru num\u0103rul lui Pi - veche de 100 de ani - ascunde secretele Universului - Secretele lui Lovendal<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.lovendal.ro\/wp52\/formula-matematicianului-indian-ramanujan-pentru-numarul-lui-pi-veche-de-100-de-ani-ascunde-secretele-universului\/\" \/>\n<meta property=\"og:locale\" content=\"ro_RO\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula matematicianului indian Ramanujan pentru num\u0103rul lui Pi - veche de 100 de ani - ascunde secretele Universului\" \/>\n<meta property=\"og:description\" content=\"Un nou studiu dezv\u0103luie c\u0103 formulele vechi de un secol ale lui Srinivasa Ramanujan pentru calcularea lui pi apar \u00een mod nea\u0219teptat \u00een teoriile moderne ale fenomenelor critice, turbulen\u021bei \u0219i g\u0103urilor negre. \u00cen \u0219coal\u0103, mul\u021bi dintre noi \u00eent\u00e2lnim pentru prima ... 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