{"id":603,"date":"2019-01-24T12:23:18","date_gmt":"2019-01-24T11:23:18","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=603"},"modified":"2019-11-06T14:30:50","modified_gmt":"2019-11-06T13:30:50","slug":"la-geometrie-des-fortifications-de-vauban","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/","title":{"rendered":"La g\u00e9om\u00e9trie des fortifications de Vauban"},"content":{"rendered":"

Les forts du Moyen-\u00c2ge peuvent avoir des formes polygonales. Celles-ci restent cependant convexes. La r\u00e8gle pour les forts de l\u2019\u00e9poque de Vauban est diff\u00e9rente. En terrain plat, on part d\u2019un polygone r\u00e9gulier convexe. La longueur des c\u00f4t\u00e9s correspond \u00e0 la port\u00e9e utile des pi\u00e8ces d\u2019artillerie de l\u2019\u00e9poque, un peu moins pour que l\u2019effet soit meilleur. La norme est de 330 m\u00e8tres. Le nombre de c\u00f4t\u00e9s d\u00e9pend alors de la taille de la ville \u00e0 ceinturer ainsi. Par exemple, un pentagone r\u00e9gulier de c\u00f4t\u00e9 \u00e9gal \u00e0 330 m\u00e8tres englobe une surface de 18 hectares, un hexagone, 28 et un octogone, 52.<\/span><\/span><\/p>\n

Partons ici d\u2019un pentagone comme pour la citadelle de Lille. Au milieu de chaque c\u00f4t\u00e9, perpendiculairement et vers l\u2019int\u00e9rieur, nous portons une longueur de 55 m\u00e8tres. Nous obtenons, un polygone plus compliqu\u00e9 en forme d\u2019\u00e9toile.<\/span><\/span><\/p>\n

\"\"
Sch\u00e9ma de base d’une fortification bastionn\u00e9e.<\/figcaption><\/figure>\n

 <\/p>\n

Ajout des bastions<\/h2>\n

Le but est d\u2019\u00e9tablir aux sommets du polygone initial de petits fortins appel\u00e9s \u00ab\u00a0bastions\u00a0\u00bb et destin\u00e9s \u00e0 recevoir des pi\u00e8ces d\u2019artillerie pouvant couvrir les c\u00f4t\u00e9s du polygone en \u00e9toile, appel\u00e9s \u00ab\u00a0courtines\u00a0\u00bb. Pour \u00e9viter d\u2019\u00eatre de trop bonnes cibles pour l\u2019artillerie adverse, ces remparts ne d\u00e9passent pas du paysage. Leur hauteur vient des foss\u00e9s situ\u00e9s autour. Ces murs sont essentiellement constitu\u00e9s de terre pour mieux r\u00e9sister aux boulets en fer. La ma\u00e7onnerie qui les entoure est destin\u00e9e \u00e0 tenir le tout. Du c\u00f4t\u00e9 de la place forte, elle se nomme l\u2019escarpe. De l\u2019autre c\u00f4t\u00e9, la contrescarpe. Un domaine est laiss\u00e9 vide et sans protection pour l\u2019ennemi tout autour. Il se nomme le glacis. Sa longueur correspond au minimum \u00e0 la port\u00e9e des canons. Vu du glacis, l\u2019assaillant n\u2019aper\u00e7oit que des murailles modestes puisque le foss\u00e9 les dissimule.<\/span><\/span><\/p>\n

Nous sommes maintenant en pr\u00e9sence de plusieurs polygones, l\u2019un ext\u00e9rieur joignant les extr\u00e9mit\u00e9s des bastions, l\u2019autre int\u00e9rieur dans le prolongement des courtines. Un autre limite le glacis.<\/span><\/span><\/p>\n

\"\"
Les bastions (en bleu) situ\u00e9s aux sommets du pentagone sont destin\u00e9s \u00e0 couvrir les courtines (en rouge). Les murs ext\u00e9rieurs des deux forment l\u2019escarpe. La contrescarpe n\u2019est pas indiqu\u00e9e sur cette figure. Elle est situ\u00e9e de l\u2019autre c\u00f4t\u00e9 du foss\u00e9 entourant le rempart.<\/figcaption><\/figure>\n

Multiplication des d\u00e9fenses externes<\/h2>\n
\"\"
Demi-lune vue du fort \u00e0 Mont-Dauphin. Cette fortification prot\u00e8ge la citadelle tout en restant sous le feu en provenant. L\u2019ennemi ne peut que difficilement s\u2019y maintenir apr\u00e8s l\u2019avoir prise.<\/figcaption><\/figure>\n

Pour \u00e9viter ce d\u00e9faut, Vauban a l\u2019id\u00e9e d\u2019ajouter deux d\u00e9fenses externes devant chaque courtine\u00a0: la tenaille \u00e0 son pied et la demi-lune devant. Chacune de ces d\u00e9fenses n\u2019offre aucune protection du c\u00f4t\u00e9 de la place forte elle-m\u00eame. Si l\u2019ennemi la prend, il s\u2019y trouve \u00e0 d\u00e9couvert, donc dans une position difficile \u00e0 tenir.<\/span><\/span><\/p>\n

\"\"
Les tenailles (pr\u00e8s du fort) et les demi-lunes (toutes en vert) sont destin\u00e9es \u00e0 retarder l\u2019ennemi dans sa progression. Ces fortifications ne sont pas fortifi\u00e9es du c\u00f4t\u00e9 de la place forte.<\/figcaption><\/figure>\n

Vauban g\u00e9n\u00e9ralisa ce principe en d\u00e9tachant les bastions de la place forte elle-m\u00eame. D\u2019autre part, le tout est entour\u00e9 d\u2019un dernier petit rempart parall\u00e8le et recouvert, appel\u00e9 \u00ab\u00a0chemin couvert\u00a0\u00bb. Ainsi, il se situe au sommet de la contrescarpe. Il s\u2019agit en m\u00eame temps de la premi\u00e8re ligne de d\u00e9fense et d\u2019un chemin de ronde, destin\u00e9 \u00e0 l\u2019observation.<\/span><\/span><\/p>\n

\"\"
Les bastions sont d\u00e9tach\u00e9s de la place. Sur cette photo, la direction de la meurtri\u00e8re montre leur usage. Il s\u2019agit de placer les courtines sous le feu de la place.<\/figcaption><\/figure>\n

 <\/p>\n

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

Les forts du Moyen-\u00c2ge peuvent avoir des formes polygonales. Celles-ci restent cependant convexes. La r\u00e8gle pour les forts de l\u2019\u00e9poque de Vauban est diff\u00e9rente. En terrain plat, on part d\u2019un polygone r\u00e9gulier convexe. La longueur des c\u00f4t\u00e9s correspond \u00e0 la port\u00e9e utile des pi\u00e8ces d\u2019artillerie de l\u2019\u00e9poque, un peu moins pour que l\u2019effet soit meilleur. … Continuer la lecture de La g\u00e9om\u00e9trie des fortifications de Vauban<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":610,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[5,63,29],"tags":[232,139,233],"class_list":["post-603","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts","category-histoire","category-maths-2","tag-fortification","tag-geometrie","tag-vauban"],"yoast_head":"\nLa g\u00e9om\u00e9trie des fortifications de Vauban, 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\/01\/24\/la-geometrie-des-fortifications-de-vauban\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"La g\u00e9om\u00e9trie des fortifications de Vauban, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Les forts du Moyen-\u00c2ge peuvent avoir des formes polygonales. Celles-ci restent cependant convexes. La r\u00e8gle pour les forts de l\u2019\u00e9poque de Vauban est diff\u00e9rente. En terrain plat, on part d\u2019un polygone r\u00e9gulier convexe. La longueur des c\u00f4t\u00e9s correspond \u00e0 la port\u00e9e utile des pi\u00e8ces d\u2019artillerie de l\u2019\u00e9poque, un peu moins pour que l\u2019effet soit meilleur. … Continuer la lecture de La g\u00e9om\u00e9trie des fortifications de Vauban →\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/\" \/>\n<meta property=\"og:site_name\" content=\"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\" \/>\n<meta property=\"article:published_time\" content=\"2019-01-24T11:23:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-11-06T13:30:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1181\" \/>\n\t<meta property=\"og:image:height\" content=\"791\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/\",\"name\":\"La g\u00e9om\u00e9trie des fortifications de Vauban, par Herv\u00e9 Lehning\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg\",\"datePublished\":\"2019-01-24T11:23:18+00:00\",\"dateModified\":\"2019-11-06T13:30:50+00:00\",\"author\":{\"@id\":\"\"},\"breadcrumb\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg\",\"contentUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg\",\"width\":1181,\"height\":791},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"La g\u00e9om\u00e9trie des fortifications de Vauban\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\",\"name\":\"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\",\"description\":\"Comment comprendre le monde moderne sans culture math\u00e9matique ? Acc\u00e9der \u00e0 celle-ci n\u2019exige cependant pas d\u2019apprendre \u00e0 r\u00e9soudre la moindre \u00e9quation.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blogs.futura-sciences.com\/lehning\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/author\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"La g\u00e9om\u00e9trie des fortifications de Vauban, par Herv\u00e9 Lehning","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:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/","og_locale":"fr_FR","og_type":"article","og_title":"La g\u00e9om\u00e9trie des fortifications de Vauban, par Herv\u00e9 Lehning","og_description":"Les forts du Moyen-\u00c2ge peuvent avoir des formes polygonales. Celles-ci restent cependant convexes. La r\u00e8gle pour les forts de l\u2019\u00e9poque de Vauban est diff\u00e9rente. En terrain plat, on part d\u2019un polygone r\u00e9gulier convexe. La longueur des c\u00f4t\u00e9s correspond \u00e0 la port\u00e9e utile des pi\u00e8ces d\u2019artillerie de l\u2019\u00e9poque, un peu moins pour que l\u2019effet soit meilleur. … Continuer la lecture de La g\u00e9om\u00e9trie des fortifications de Vauban →","og_url":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/","og_site_name":"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques","article_published_time":"2019-01-24T11:23:18+00:00","article_modified_time":"2019-11-06T13:30:50+00:00","og_image":[{"width":1181,"height":791,"url":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"","Dur\u00e9e de lecture estim\u00e9e":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/","url":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/","name":"La g\u00e9om\u00e9trie des fortifications de Vauban, par Herv\u00e9 Lehning","isPartOf":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/#website"},"primaryImageOfPage":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage"},"image":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage"},"thumbnailUrl":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg","datePublished":"2019-01-24T11:23:18+00:00","dateModified":"2019-11-06T13:30:50+00:00","author":{"@id":""},"breadcrumb":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/"]}]},{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#primaryimage","url":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg","contentUrl":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/01\/fortification4.jpg","width":1181,"height":791},{"@type":"BreadcrumbList","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/01\/24\/la-geometrie-des-fortifications-de-vauban\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/blogs.futura-sciences.com\/lehning\/"},{"@type":"ListItem","position":2,"name":"La g\u00e9om\u00e9trie des fortifications de Vauban"}]},{"@type":"WebSite","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/#website","url":"https:\/\/blogs.futura-sciences.com\/lehning\/","name":"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques","description":"Comment comprendre le monde moderne sans culture math\u00e9matique ? Acc\u00e9der \u00e0 celle-ci n\u2019exige cependant pas d\u2019apprendre \u00e0 r\u00e9soudre la moindre \u00e9quation.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blogs.futura-sciences.com\/lehning\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"","url":"https:\/\/blogs.futura-sciences.com\/lehning\/author\/"}]}},"_links":{"self":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/comments?post=603"}],"version-history":[{"count":3,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/603\/revisions"}],"predecessor-version":[{"id":612,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/603\/revisions\/612"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/media\/610"}],"wp:attachment":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/media?parent=603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/categories?post=603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/tags?post=603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}