{"id":871,"date":"2019-07-09T10:39:22","date_gmt":"2019-07-09T08:39:22","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=871"},"modified":"2019-11-08T14:05:16","modified_gmt":"2019-11-08T13:05:16","slug":"les-mathematiques-du-certificat-detudes","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/07\/09\/les-mathematiques-du-certificat-detudes\/","title":{"rendered":"Les math\u00e9matiques du certificat d’\u00e9tudes"},"content":{"rendered":"

Au courant du XVIIe<\/sup> si\u00e8cle, les math\u00e9matiques de feu le certificat d\u2019\u00e9tudes \u00e9taient en place. Les ouvrages d\u2019apprentissage du nouveau calcul foisonnaient d\u2019exercices. Sous des dehors li\u00e9s \u00e0 la vie de tous les jours, leur but \u00e9tait d\u2019entra\u00eener \u00e0 l\u2019utilisation des algorithmes des op\u00e9rations (addition, soustraction, multiplication et division) ainsi qu\u2019au raisonnement math\u00e9matique.<\/p>\n

Un exemple de Simon Stevin<\/h2>\n
\"\"
Aune de tailleur.<\/figcaption><\/figure>\n

En particulier, La pratique de l\u2019arithm\u00e9tique<\/em> de Simon Stevin (1548 \u2013 1620) contient une foule d\u2019exercices du type\u00a0:<\/p>\n

14 aunes de drap co\u00fbtent 5 livres, 2 sous et 8 deniers, combien co\u00fbteront 25 aunes\u00a0?<\/em><\/p>\n

Pour r\u00e9soudre cet exercice, inutile de savoir ce que repr\u00e9sente une aune, il suffit de savoir qu\u2019une livre vaut 20 sous et un sou, 12 deniers. Le plus simple pour le r\u00e9soudre est de transformer la somme donn\u00e9e en deniers. Une livre vaut 20\u00a0x\u00a012\u00a0=\u00a0240 deniers donc 5 livres, 1200. Les 14 aunes valent donc 1232 deniers. On obtient le prix d\u2019une aune en divisant par 14, ce qui donne 88 deniers. Le prix de 25 aunes est donc \u00e9gal \u00e0 25\u00a0x\u00a088\u00a0=\u00a02200 deniers, qu\u2019il reste \u00e0 traduire dans le syst\u00e8me initial. En divisant 2200 par 240, on obtient 9 livres et il reste 40 deniers, ce qui fait 3 sous et 4 deniers. Finalement, les 25 aunes co\u00fbtent 9 livres, 3 sous et 4 deniers.<\/p>\n

Int\u00e9r\u00eat du syst\u00e8me d\u00e9cimal<\/h2>\n

\"\"<\/p>\n

Heureusement, l\u2019arithm\u00e9tique est devenue plus simple avec le syst\u00e8me d\u00e9cimal\u00a0! Pour le montrer, voici un exemple moderne\u00a0:<\/p>\n

Nicolas ach\u00e8te 350 grammes de pommes pour 1 \u20ac. Derri\u00e8re lui, Pimprenelle en ach\u00e8te 1 kilo 435. Combien va-t-elle payer\u00a0?<\/em><\/p>\n

Voici le raisonnement canonique pour r\u00e9soudre ce type de probl\u00e8me. Ici le terme \u00ab\u00a0canon\u00a0\u00bb n\u2019a rien \u00e0 voir avec l\u2019artillerie, il signifie \u00ab\u00a0r\u00e8gle\u00a0\u00bb comme toujours en math\u00e9matiques. Si 350 grammes co\u00fbtent 1 \u20ac, 1 gramme co\u00fbte 1\u00a0\/\u00a0350 \u20ac et 1435, 1435\u00a0\/\u00a0350 soit 4 \u20ac 10. Nous avons appliqu\u00e9 ici, sans l\u2019\u00e9crire, une r\u00e8gle de trois que certains nomment produit en croix. Peu importe l\u2019appellation, l\u2019esprit vaut mieux que la lettre. Dans les deux cas, le raisonnement sous-jacent est abstrait puisqu\u2019il consiste \u00e0 inventer une fiction\u00a0: la vente d\u2019un gramme de pommes\u00a0! Il montre que, m\u00eame dans les applications les plus \u00e9l\u00e9mentaires, il n\u2019existe pas de math\u00e9matiques sans abstraction, ou sans r\u00e9flexion. Leur apprentissage exige application, cogitation et quantit\u00e9 d\u2019exercices, comme l\u2019escalade, le tennis ou le football.<\/p>\n

La voie royale<\/h2>\n

Cela n\u2019est pas nouveau comme le montre l\u2019anecdote suivante, qu\u2019elle soit vraie ou non. Selon la l\u00e9gende, Euclide enseigna les math\u00e9matiques au roi d\u2019\u00c9gypte. Rapidement, celui-ci demanda un acc\u00e8s au savoir simplifi\u00e9, par \u00e9gard \u00e0 sa majest\u00e9. Euclide r\u00e9pondit\u00a0: D\u00e9sol\u00e9 sire, en math\u00e9matiques, il n\u2019y a pas de voie royale. <\/em>Il n\u2019en existe toujours pas, que cela soit pour les rois ou les enfants-rois. Vouloir en inventer sous pr\u00e9texte de faciliter l\u2019apprentissage des math\u00e9matiques est vou\u00e9 \u00e0 l\u2019\u00e9chec. L\u2019id\u00e9e ne fait qu\u2019en interdire l\u2019acc\u00e8s.<\/p>\n","protected":false},"excerpt":{"rendered":"

Au courant du XVIIe si\u00e8cle, les math\u00e9matiques de feu le certificat d\u2019\u00e9tudes \u00e9taient en place. Les ouvrages d\u2019apprentissage du nouveau calcul foisonnaient d\u2019exercices. Sous des dehors li\u00e9s \u00e0 la vie de tous les jours, leur but \u00e9tait d\u2019entra\u00eener \u00e0 l\u2019utilisation des algorithmes des op\u00e9rations (addition, soustraction, multiplication et division) ainsi qu\u2019au raisonnement math\u00e9matique. Un exemple … Continuer la lecture de Les math\u00e9matiques du certificat d’\u00e9tudes<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":873,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[63,29],"tags":[330,331,40,332],"class_list":["post-871","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-histoire","category-maths-2","tag-certificat-detudes","tag-examen","tag-mathematiques","tag-voie-royale"],"yoast_head":"\nLes math\u00e9matiques du certificat d'\u00e9tudes, par Herv\u00e9 Lehning<\/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:\/\/blogs.futura-sciences.com\/lehning\/2019\/07\/09\/les-mathematiques-du-certificat-detudes\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les math\u00e9matiques du certificat d'\u00e9tudes, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Au courant du XVIIe si\u00e8cle, les math\u00e9matiques de feu le certificat d\u2019\u00e9tudes \u00e9taient en place. 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