{"id":3716,"date":"2023-03-01T22:03:37","date_gmt":"2023-03-01T22:03:37","guid":{"rendered":"https:\/\/sites.rutgers.edu\/french-magazine\/?p=3716"},"modified":"2023-03-10T13:08:16","modified_gmt":"2023-03-10T18:08:16","slug":"blaise-pascal","status":"publish","type":"post","link":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/","title":{"rendered":"Blaise Pascal"},"content":{"rendered":"

Vous souvenez-vous avoir appris le triangle de Pascal en cours d’alg\u00e8bre au lyc\u00e9e? Le triangle a un 1 sur la rang\u00e9e sup\u00e9rieure, la rang\u00e9e suivante a deux 1. Chaque rang\u00e9e commence et se termine par un 1 et elles ont toutes un chiffre de plus que la rang\u00e9e pr\u00e9c\u00e9dente. Ce chiffre est la somme des deux chiffres qui le pr\u00e9c\u00e8dent. Par exemple, le 2 de la troisi\u00e8me ligne est la somme de la deuxi\u00e8me ligne (1+1). Le triangle n\u2019a pas de fin.<\/span><\/p>\n

\"Pascal's<\/p>\n

L’importance du triangle\u00a0<\/strong><\/p>\n

Ce triangle a \u00e9t\u00e9 d\u00e9couvert il y a environ 1000 ans. Mais ce sera Blaise Pascal, un math\u00e9maticien et philosophe fran\u00e7ais du XVIIe si\u00e8cle qui les \u00e9tudiera\u00a0 et qui publiera le <\/span>Trait\u00e9 du triangle arithm\u00e9tique<\/span><\/i>. On l\u2019appelle Triangle de Pascal en son hommage, et non pas parce qu\u2019il l\u2019aurait d\u00e9couvert. Le Trait\u00e9 du triangle arithm\u00e9tique<\/em> est un livre qui d\u00e9crit le triangle avec 19 propri\u00e9t\u00e9s. Le reste du livre d\u00e9crit les applications du Triangle et il introduit la formule du bin\u00f4me de Newton. Une des propri\u00e9t\u00e9s est que le total des chiffres dans chaque ligne est \u00e9gale \u00e0 2^(<\/span>n-1)<\/span>. Par exemple, le total de la cinqui\u00e8me ligne (1\/4\/6\/4\/1) est 16. La variable est 5, et si on applique la formule, on obtient bien et 2^(5-1)= 2^4 = 16. La variable repr\u00e9sente la ligne.\u00a0<\/span><\/p>\n

La premi\u00e8re calculatrice<\/strong><\/p>\n

Pascal a aussi invent\u00e9 la premi\u00e8re calculatrice en 1642. C\u2019\u00e9tait une invention tr\u00e8s utile pour son p\u00e8re qui \u00e9tait collecteur d’imp\u00f4ts. Contrairement aux calculatrices d\u2019aujourd\u2019hui, La Pascaline pouvait seulement faire des additions et des soustractions.\u00a0<\/span><\/p>\n

\"Replica<\/p>\n

Aujourd\u2019hui, le triangle de Pascal est utile pour les \u00e9tudiants parce qu\u2019il fournit un formule pour calculer les coefficients dans l\u2019expansion binomiale. Les chiffres repr\u00e9sentent les coefficients de (1+x)<\/span>n-1<\/span>. Par exemple, (1+x)<\/span>2<\/span> est 1+2x+1x<\/span>2<\/span>. <\/span>Les coefficients 1, 2, 1 sont les chiffres dans la troisi\u00e8me ligne du triangle de Pascal.<\/span><\/p>\n

Math\u00e9maticien, physicien, et philosophe Blaise Pascal est n\u00e9 dans la ville de Clermont-Ferrand dans le centre de la France. Pascal est aussi connu pour avoir glorifi\u00e9 Dieu dans tout ce qu\u2019il faisait. Dans un ses \u00e9crits tr\u00e8s c\u00e9l\u00e8bres, il a formul\u00e9 le pari suivant concernant l’existence de Dieu: <\/span>\u00abPesons le gain et la perte en prenant croix que Dieu est. Estimons ces deux cas: si vous gagnez, vous gagnez tout, et si vous perdez, vous ne perdez rien: gagnez donc qu\u2019il est sans h\u00e9siter. Cela est admirable\u00bb Les Pens\u00e9es, Fragment 397.\u00a0<\/span><\/p>\n

Il est mort \u00e0 1661 et il a \u00e9t\u00e9 enterr\u00e9 dans l’\u00e9glise Saint-Etienne du Mont, \u00e0 Paris.\u00a0<\/span><\/p>\n

\"Blaise<\/p>\n

https:\/\/www.devoir-de-francais.com\/litterature\/pascal-les-pensees-fragment-397-extrait<\/span><\/a><\/p>\n

https:\/\/byjus.com\/maths\/pascals-triangle\/<\/span><\/a><\/p>\n

https:\/\/fr.wikipedia.org\/wiki\/Trait\u00e9_du_triangle_arithm\u00e9tique<\/span><\/a><\/p>\n

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

Vous souvenez-vous avoir appris le triangle de Pascal en cours d’alg\u00e8bre au lyc\u00e9e? Le triangle a un 1 sur la rang\u00e9e sup\u00e9rieure, la rang\u00e9e suivante a deux 1. Chaque rang\u00e9e … Read More<\/a><\/p>\n","protected":false},"author":2597,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[184],"tags":[393,394,395,392],"class_list":["post-3716","post","type-post","status-publish","format-standard","hentry","category-histoire","tag-blaise-pascal","tag-pari","tag-pascaline","tag-triangle-de-pascal"],"acf":[],"yoast_head":"\nBlaise Pascal - La P'tite Gazette<\/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:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Blaise Pascal - La P'tite Gazette\" \/>\n<meta property=\"og:description\" content=\"Vous souvenez-vous avoir appris le triangle de Pascal en cours d’alg\u00e8bre au lyc\u00e9e? Le triangle a un 1 sur la rang\u00e9e sup\u00e9rieure, la rang\u00e9e suivante a deux 1. Chaque rang\u00e9e … Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/\" \/>\n<meta property=\"og:site_name\" content=\"La P'tite Gazette\" \/>\n<meta property=\"article:published_time\" content=\"2023-03-01T22:03:37+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-03-10T18:08:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s\" \/>\n<meta name=\"author\" content=\"Rafael J. Peguero\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Rafael J. Peguero\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/\",\"url\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/\",\"name\":\"Blaise Pascal - La P'tite Gazette\",\"isPartOf\":{\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s\",\"datePublished\":\"2023-03-01T22:03:37+00:00\",\"dateModified\":\"2023-03-10T18:08:16+00:00\",\"author\":{\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/d25a9dee241785bd8fff44dbd2079ef7\"},\"breadcrumb\":{\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage\",\"url\":\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s\",\"contentUrl\":\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/sites.rutgers.edu\/french-magazine\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Blaise Pascal\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/#website\",\"url\":\"https:\/\/sites.rutgers.edu\/french-magazine\/\",\"name\":\"La P'tite Gazette\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sites.rutgers.edu\/french-magazine\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/d25a9dee241785bd8fff44dbd2079ef7\",\"name\":\"Rafael J. Peguero\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/9db2c459591d37da61db98bb096d151e?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/9db2c459591d37da61db98bb096d151e?s=96&d=mm&r=g\",\"caption\":\"Rafael J. Peguero\"},\"description\":\"19 years old\",\"url\":\"https:\/\/sites.rutgers.edu\/french-magazine\/author\/rjp292\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Blaise Pascal - La P'tite Gazette","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/","og_locale":"en_US","og_type":"article","og_title":"Blaise Pascal - La P'tite Gazette","og_description":"Vous souvenez-vous avoir appris le triangle de Pascal en cours d’alg\u00e8bre au lyc\u00e9e? Le triangle a un 1 sur la rang\u00e9e sup\u00e9rieure, la rang\u00e9e suivante a deux 1. Chaque rang\u00e9e … Read More","og_url":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/","og_site_name":"La P'tite Gazette","article_published_time":"2023-03-01T22:03:37+00:00","article_modified_time":"2023-03-10T18:08:16+00:00","og_image":[{"url":"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s"}],"author":"Rafael J. Peguero","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Rafael J. Peguero","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/","url":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/","name":"Blaise Pascal - La P'tite Gazette","isPartOf":{"@id":"https:\/\/sites.rutgers.edu\/french-magazine\/#website"},"primaryImageOfPage":{"@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage"},"image":{"@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage"},"thumbnailUrl":"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s","datePublished":"2023-03-01T22:03:37+00:00","dateModified":"2023-03-10T18:08:16+00:00","author":{"@id":"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/d25a9dee241785bd8fff44dbd2079ef7"},"breadcrumb":{"@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#primaryimage","url":"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s","contentUrl":"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcS_coZ9XdBAkOI9820yRbmZ_nlizLiADy2e9DM82_4eow&s"},{"@type":"BreadcrumbList","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/blaise-pascal\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sites.rutgers.edu\/french-magazine\/"},{"@type":"ListItem","position":2,"name":"Blaise Pascal"}]},{"@type":"WebSite","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/#website","url":"https:\/\/sites.rutgers.edu\/french-magazine\/","name":"La P'tite Gazette","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sites.rutgers.edu\/french-magazine\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/d25a9dee241785bd8fff44dbd2079ef7","name":"Rafael J. Peguero","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sites.rutgers.edu\/french-magazine\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/9db2c459591d37da61db98bb096d151e?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/9db2c459591d37da61db98bb096d151e?s=96&d=mm&r=g","caption":"Rafael J. Peguero"},"description":"19 years old","url":"https:\/\/sites.rutgers.edu\/french-magazine\/author\/rjp292\/"}]}},"_links":{"self":[{"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/posts\/3716"}],"collection":[{"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/users\/2597"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/comments?post=3716"}],"version-history":[{"count":7,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/posts\/3716\/revisions"}],"predecessor-version":[{"id":3961,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/posts\/3716\/revisions\/3961"}],"wp:attachment":[{"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/media?parent=3716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/categories?post=3716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.rutgers.edu\/french-magazine\/wp-json\/wp\/v2\/tags?post=3716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}