{"id":777,"date":"2019-05-16T13:19:47","date_gmt":"2019-05-16T11:19:47","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=777"},"modified":"2019-05-21T09:26:43","modified_gmt":"2019-05-21T07:26:43","slug":"lart-du-defilement-vauban-et-gaspard-monge","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/05\/16\/lart-du-defilement-vauban-et-gaspard-monge\/","title":{"rendered":"L&#8217;art du d\u00e9filement, Vauban et Gaspard Monge"},"content":{"rendered":"<p>L\u2019un des probl\u00e8mes pour construire des fortifications \u00e0 l\u2019\u00e9poque de Vauban (1633 \u2013 1707) \u00e9tait\u00a0 :<\/p>\n<p><strong>Comment d\u00e9filer une fortification des tirs de l\u2019ennemi\u00a0? <\/strong><\/p>\n<p>Le verbe \u00ab\u00a0d\u00e9filer\u00a0\u00bb doit s\u2019entendre ici au sens commun de \u00ab\u00a0se d\u00e9filer\u00a0\u00bb. Comment cacher l\u2019int\u00e9rieur d\u2019un ouvrage aux vues et aux tirs de l\u2019agresseur\u00a0? Bien entendu, il suffit de b\u00e2tir partout des remparts assez hauts. L\u2019ennui est que la hauteur fragilise les remparts. Le tout doit rester \u00e9quilibr\u00e9. Sur le terrain, les bons ing\u00e9nieurs comme Vauban savaient d\u00e9filer leurs ouvrages mais comment s\u2019y prendre \u00e0 partir d\u2019un simple plan c\u00f4t\u00e9\u00a0?<\/p>\n<h2>La g\u00e9om\u00e9trie descriptive<\/h2>\n<p>Gaspard Monge (1746\u00a0\u2013\u00a01818) inventa la g\u00e9om\u00e9trie descriptive pour r\u00e9soudre ce probl\u00e8me. De fa\u00e7on g\u00e9n\u00e9rale, elle permettait d\u2019\u00e9tudier certains objets de l\u2019espace comme l\u2019intersection de deux tores dans l&#8217;\u00e9pure qui suit. Le r\u00e9sultat pouvait \u00eatre tr\u00e8s esth\u00e9tique, comme on peut le voir dans ce cas.<\/p>\n<figure id=\"attachment_778\" aria-describedby=\"caption-attachment-778\" style=\"width: 239px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-778 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/epureIHP-239x300.jpg\" alt=\"\" width=\"239\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/epureIHP-239x300.jpg 239w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/epureIHP.jpg 636w\" sizes=\"auto, (max-width: 239px) 100vw, 239px\" \/><figcaption id=\"caption-attachment-778\" class=\"wp-caption-text\">Dessin se trouvant dans Objets math\u00e9matiques, Institut Henri Poincar\u00e9, livre que nous recommandons fortement.<\/figcaption><\/figure>\n<h2>Les d\u00e9blais et remblais<\/h2>\n<p>Le m\u00eame Monge, sans doute \u00e9galement motiv\u00e9 par la construction de fortifications, publia un <em>M\u00e9moire sur la th\u00e9orie des d\u00e9blais et des remblais<\/em> o\u00f9 il se proposait de r\u00e9soudre un probl\u00e8me tr\u00e8s concret\u00a0: comment d\u00e9placer des tas de sable vers un certain nombre de destinations de la mani\u00e8re la plus \u00e9conomique possible\u00a0?<\/p>\n<figure id=\"attachment_779\" aria-describedby=\"caption-attachment-779\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-779 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/Deblais-remblais-300x260.jpg\" alt=\"\" width=\"300\" height=\"260\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/Deblais-remblais-300x260.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/05\/Deblais-remblais.jpg 404w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-779\" class=\"wp-caption-text\">Dessin explicatif du probl\u00e8me dans le m\u00e9moire de Monge.<\/figcaption><\/figure>\n<p>Ici il s\u2019agit de d\u00e9blayer la zone de gauche pour remblayer celle de droite (ou l\u2019inverse puisque les deux probl\u00e8mes sont \u00e9quivalents). Dans son m\u00e9moire, Monge \u00e9tudie ce probl\u00e8me mais ne le r\u00e9sout pas dans sa g\u00e9n\u00e9ralit\u00e9. Voir l\u2019article d\u2019\u00c9tienne Ghys dans <em>Image des math\u00e9matiques<\/em>.<\/p>\n<h2>Le transport optimal<\/h2>\n<p>Ce probl\u00e8me se g\u00e9n\u00e9ralise en probl\u00e8me du transport optimal\u00a0: comment un fournisseur peut-il livrer un certain nombre de points de vente de fa\u00e7on \u00e0 minimiser ses co\u00fbts\u00a0? Le probl\u00e8me de Monge a ainsi \u00e9t\u00e9 red\u00e9couvert par L\u00e9onid Kantorovitch (1912 \u2013 1986) qui obtint le prix Nobel d\u2019\u00e9conomie en 1975 pour ses avanc\u00e9es sur la question en ouvrant un nouveau domaine, celui de la programmation lin\u00e9aire. Plus r\u00e9cemment, C\u00e9dric Villani (n\u00e9 en 1973) a obtenu la m\u00e9daille Fields en revisitant le probl\u00e8me du transport optimal en le rapprochant du probl\u00e8me de la diffusion des gaz. Cette capacit\u00e9 de rapprochement entre des domaines <em>a priori<\/em> diff\u00e9rents est un marqueur des grands math\u00e9maticiens.<\/p>\n<p>&nbsp;<\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>L\u2019un des probl\u00e8mes pour construire des fortifications \u00e0 l\u2019\u00e9poque de Vauban (1633 \u2013 1707) \u00e9tait\u00a0 : Comment d\u00e9filer une fortification des tirs de l\u2019ennemi\u00a0? Le verbe \u00ab\u00a0d\u00e9filer\u00a0\u00bb doit s\u2019entendre ici au sens commun de \u00ab\u00a0se d\u00e9filer\u00a0\u00bb. Comment cacher l\u2019int\u00e9rieur d\u2019un ouvrage aux vues et aux tirs de l\u2019agresseur\u00a0? Bien entendu, il suffit de b\u00e2tir partout &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/05\/16\/lart-du-defilement-vauban-et-gaspard-monge\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">L&#8217;art du d\u00e9filement, Vauban et Gaspard Monge<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":12,"featured_media":781,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[5,12,63,29,98,10],"tags":[308,246,311,310,309],"class_list":["post-777","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts","category-graphismes","category-histoire","category-maths-2","category-viequotidienne","category-voyages","tag-kantorovitch","tag-monge","tag-optimal","tag-transport","tag-villani"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>L&#039;art du d\u00e9filement, Vauban et Gaspard Monge, 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\/05\/16\/lart-du-defilement-vauban-et-gaspard-monge\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"L&#039;art du d\u00e9filement, Vauban et Gaspard Monge, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"L\u2019un des probl\u00e8mes pour construire des fortifications \u00e0 l\u2019\u00e9poque de Vauban (1633 \u2013 1707) \u00e9tait\u00a0 : Comment d\u00e9filer une fortification des tirs de l\u2019ennemi\u00a0? Le verbe \u00ab\u00a0d\u00e9filer\u00a0\u00bb doit s\u2019entendre ici au sens commun de \u00ab\u00a0se d\u00e9filer\u00a0\u00bb. Comment cacher l\u2019int\u00e9rieur d\u2019un ouvrage aux vues et aux tirs de l\u2019agresseur\u00a0? 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