{"id":895,"date":"2019-07-23T16:32:11","date_gmt":"2019-07-23T14:32:11","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=895"},"modified":"2019-07-30T08:45:52","modified_gmt":"2019-07-30T06:45:52","slug":"fahrenheit-et-la-peur-des-nombres-negatifs","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/07\/23\/fahrenheit-et-la-peur-des-nombres-negatifs\/","title":{"rendered":"Fahrenheit et la peur des nombres n\u00e9gatifs"},"content":{"rendered":"

Sans doute pour \u00e9viter les nombres n\u00e9gatifs, Daniel Gabriel Fahrenheit (1686\u00a0\u2013\u00a01736) fixa l\u2019origine des temp\u00e9ratures (0\u00b0 Fahrenheit) \u00e0 la plus basse qu\u2019il ait observ\u00e9e. C\u2019\u00e9tait durant l\u2019hiver 1709 dans la ville de Dantzig, o\u00f9 il habitait. Pour 100\u00b0 Fahrenheit, il choisit la temp\u00e9rature corporelle d\u2019un cheval sain\u00a0! Dans son syst\u00e8me, l\u2019eau g\u00e8le \u00e0 32\u00b0 et elle bout \u00e0 212\u00b0 environ.<\/p>\n

\"\"
100\u00b0 Fahrenheit correspond \u00e0 la temp\u00e9rature corporelle d’un cheval sain.<\/figcaption><\/figure>\n

L’absolu du z\u00e9ro<\/h2>\n

Ces choix \u00e9tranges de Fahrenheit s\u2019expliquent par la r\u00e9ticence de l\u2019\u00e9poque devant les nombres n\u00e9gatifs. On pr\u00e9f\u00e9rait d\u2019ailleurs parler de quantit\u00e9s plut\u00f4t que de nombres. Il s\u2019agissait d\u2019artifices de calcul pour r\u00e9soudre des \u00e9quations, dont on \u00e9cartait ensuite les solutions n\u00e9gatives. Tout en \u00e9tant une origine, z\u00e9ro v\u00e9hicule une id\u00e9e d\u2019absolu, en dessous duquel on ne peut aller, comme on le voit chez Blaise Pascal (1623 \u2013 1662) qui, dans ses Pens\u00e9es<\/em>, \u00e9crit cette phrase surprenante :<\/p>\n

Trop de v\u00e9rit\u00e9 nous \u00e9tonne\u00a0; j\u2019en sais qui ne peuvent comprendre que, qui de z\u00e9ro \u00f4te 4, reste z\u00e9ro.<\/em><\/p>\n

Cette id\u00e9e a perdur\u00e9 jusqu\u2019au XIXe<\/sup> si\u00e8cle, Lazare Carnot (1753\u00a0\u2013\u00a01823) \u00e9crivait encore\u00a0:<\/p>\n

Pour obtenir r\u00e9ellement une quantit\u00e9 n\u00e9gative isol\u00e9e, il faudrait retrancher une quantit\u00e9 effective de z\u00e9ro, \u00f4ter quelque chose de rien\u00a0: op\u00e9ration impossible. Comment donc concevoir une quantit\u00e9 n\u00e9gative isol\u00e9e\u00a0?<\/em><\/p>\n

La solution de Cauchy<\/h2>\n

La question semble cependant r\u00e9solue avec <\/em>Augustin Louis Cauchy<\/em> (1789\u00a0\u2013\u00a01857) qui, dans son Cours d\u2019analyse de l\u2019Ecole royale polytechnique<\/em> d\u00e9finit les nombres relatifs comme une partie num\u00e9rique pr\u00e9c\u00e9d\u00e9e d\u2019un signe +<\/strong> ou \u2013\u00a0:<\/p>\n

Le signe + ou \u2013 plac\u00e9 devant un nombre en modifiera la signification, \u00e0-peu-pr\u00e8s comme un adjectif modifie celle du substantif.<\/em><\/p>\n

Conversion entre degr\u00e9s Celsius et degr\u00e9s Fahrenheit<\/h2>\n

\"\"<\/p>\n

Les variations \u00e9tant lin\u00e9aires dans les deux cas, la relation est affine, c\u2019est-\u00e0-dire de la forme\u00a0: TF<\/sub>\u00a0=\u00a0a<\/em>\u00a0TC<\/sub>\u00a0+\u00a0b<\/em>. Les deux co\u00efncidences donnent les relations\u00a0: b<\/em>\u00a0=\u00a032 et 100\u00a0a<\/em>\u00a0+\u00a0b<\/em>\u00a0=\u00a0212 d\u2019o\u00f9\u00a0: a<\/em>\u00a0=\u00a01,8 et b<\/em>\u00a0=\u00a032. Nous en d\u00e9duisons la formule\u00a0: TF<\/sub>\u00a0=\u00a01,8\u00a0TC<\/sub>\u00a0+\u00a032. Ainsi la temp\u00e9rature de 37\u00b0 Celsius donne\u00a0: 1,8\u00a0x\u00a037\u00a0+\u00a032\u00a0=\u00a098,6\u00b0 Fahrenheit.<\/p>\n","protected":false},"excerpt":{"rendered":"

Sans doute pour \u00e9viter les nombres n\u00e9gatifs, Daniel Gabriel Fahrenheit (1686\u00a0\u2013\u00a01736) fixa l\u2019origine des temp\u00e9ratures (0\u00b0 Fahrenheit) \u00e0 la plus basse qu\u2019il ait observ\u00e9e. C\u2019\u00e9tait durant l\u2019hiver 1709 dans la ville de Dantzig, o\u00f9 il habitait. Pour 100\u00b0 Fahrenheit, il choisit la temp\u00e9rature corporelle d\u2019un cheval sain\u00a0! Dans son syst\u00e8me, l\u2019eau g\u00e8le \u00e0 32\u00b0 et … Continuer la lecture de Fahrenheit et la peur des nombres n\u00e9gatifs<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":898,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[63,29,3,98],"tags":[335,205,206,336],"class_list":["post-895","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-histoire","category-maths-2","category-sciences","category-viequotidienne","tag-fahrenheit","tag-nombres-negatifs","tag-zero","tag-zero-absolu"],"yoast_head":"\nFahrenheit et la peur des nombres n\u00e9gatifs, 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\/23\/fahrenheit-et-la-peur-des-nombres-negatifs\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fahrenheit et la peur des nombres n\u00e9gatifs, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Sans doute pour \u00e9viter les nombres n\u00e9gatifs, Daniel Gabriel Fahrenheit (1686\u00a0\u2013\u00a01736) fixa l\u2019origine des temp\u00e9ratures (0\u00b0 Fahrenheit) \u00e0 la plus basse qu\u2019il ait observ\u00e9e. C\u2019\u00e9tait durant l\u2019hiver 1709 dans la ville de Dantzig, o\u00f9 il habitait. Pour 100\u00b0 Fahrenheit, il choisit la temp\u00e9rature corporelle d\u2019un cheval sain\u00a0! 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