{"id":108,"date":"2018-03-03T11:02:49","date_gmt":"2018-03-03T10:02:49","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=108"},"modified":"2018-05-15T20:00:36","modified_gmt":"2018-05-15T18:00:36","slug":"surfaces-minimales-de-patrice-jeener","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/","title":{"rendered":"Les surfaces minimales de Patrice Jeener"},"content":{"rendered":"<p>Patrice Jeener est un graveur tomb\u00e9 amoureux des math\u00e9matiques en visitant l\u2019institut Henri Poincar\u00e9 quand il \u00e9tait \u00e9tudiant aux beaux-arts. Il suivait ainsi la trace de Man Ray, qui d\u00e9couvrit les mod\u00e8les de l\u2019institut dans les ann\u00e9es 30 et s\u2019en inspira pour sa s\u00e9rie de tableaux <em>\u00e9quations shakespeariennes<\/em> comme celui-ci intitul\u00e9 <em>le roi Lear\u00a0<\/em>:<\/p>\n<figure id=\"attachment_109\" aria-describedby=\"caption-attachment-109\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-109 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/RoiLear-300x300.jpg\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/RoiLear-300x300.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/RoiLear-150x150.jpg 150w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/RoiLear.jpg 424w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-109\" class=\"wp-caption-text\">Le roi Lear \u00a9 Man Ray<\/figcaption><\/figure>\n<h2>Les surfaces minimales<\/h2>\n<p><span style=\"margin: 0px;line-height: 200%;font-family: 'Times New Roman',serif;font-size: 12pt\"><span style=\"color: #000000\">Patrice Jeener s\u2019est particuli\u00e8rement int\u00e9ress\u00e9 aux surfaces minimales, c\u2019est-\u00e0-dire aux surfaces dont les aires sont minimales pour un bord donn\u00e9. On peut mat\u00e9rialiser la plupart d\u2019entre elles par des bulles de savon s\u2019appuyant sur un contour, car le film de savon tend \u00e0 minimiser son <\/span><a title=\"\u00c9nergie\" href=\"http:\/\/fr.wikipedia.org\/wiki\/%C3%89nergie\">\u00e9nergie<\/a><span style=\"color: #000000\">, donc sa surface. Elles ont des applications pratiques mais notre propos n\u2019est pas l\u00e0. Sur la photographie ci-dessous, notez la petite tige en bas \u00e0 droite qui permet de tenir l\u2019objet quand on le trempe dans l\u2019eau savonn\u00e9e\u00a0:<\/span><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-110 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SurfaceMinimale-300x267.jpg\" alt=\"\" width=\"300\" height=\"267\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SurfaceMinimale-300x267.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SurfaceMinimale.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><span style=\"margin: 0px;line-height: 200%;font-family: 'Times New Roman',serif;font-size: 12pt\"><span style=\"color: #000000\">Nous n\u2019\u00e9crirons pas leurs \u00e9quations ici, nous nous contenterons d\u2019en admirer l\u2019esth\u00e9tique \u00e0 travers quelques gravures. <\/span><\/span><\/p>\n<figure id=\"attachment_111\" aria-describedby=\"caption-attachment-111\" style=\"width: 266px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-111 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Surface-Schwartz-266x300.png\" alt=\"\" width=\"266\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Surface-Schwartz-266x300.png 266w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Surface-Schwartz.png 709w\" sizes=\"auto, (max-width: 266px) 100vw, 266px\" \/><figcaption id=\"caption-attachment-111\" class=\"wp-caption-text\">Surface minimale de Schwartz \u00a9 Patrice Jeener<\/figcaption><\/figure>\n<p>L\u2019\u00e9tude des surfaces r\u00e9servent quelques surprises comme l\u2019apparition surprenante d\u2019une chouette l\u00e0 o\u00f9 l\u2019on attendait une simple surface minimale<em>.<\/em> Ce genre de surprises explique sans doute ce vers de Lautr\u00e9amont\u00a0:<\/p>\n<p><em>O math\u00e9matiques s\u00e9v\u00e8res, je ne vous ai pas oubli\u00e9es, depuis que vos savantes le\u00e7ons, plus douces que le miel, filtr\u00e8rent dans mon c\u0153ur, comme une onde rafra\u00eechissante.<\/em><\/p>\n<figure id=\"attachment_112\" aria-describedby=\"caption-attachment-112\" style=\"width: 224px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-112 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SM-\u00e0-la-chouette-224x300.jpg\" alt=\"\" width=\"224\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SM-\u00e0-la-chouette-224x300.jpg 224w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/SM-\u00e0-la-chouette.jpg 317w\" sizes=\"auto, (max-width: 224px) 100vw, 224px\" \/><figcaption id=\"caption-attachment-112\" class=\"wp-caption-text\">Surface minimale \u00e0 la chouette \u00a9 Patrice Jeener<\/figcaption><\/figure>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Patrice Jeener est un graveur tomb\u00e9 amoureux des math\u00e9matiques en visitant l\u2019institut Henri Poincar\u00e9 quand il \u00e9tait \u00e9tudiant aux beaux-arts. Il suivait ainsi la trace de Man Ray, qui d\u00e9couvrit les mod\u00e8les de l\u2019institut dans les ann\u00e9es 30 et s\u2019en inspira pour sa s\u00e9rie de tableaux \u00e9quations shakespeariennes comme celui-ci intitul\u00e9 le roi Lear\u00a0: Les &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Les surfaces minimales de Patrice Jeener<\/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":114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[5,12,29],"tags":[57,56,40,30,55],"class_list":["post-108","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts","category-graphismes","category-maths-2","tag-art","tag-gravure","tag-mathematiques","tag-modele-mathematique","tag-patrice-jeener"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Les surfaces minimales de Patrice Jeener, 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\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les surfaces minimales de Patrice Jeener, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Patrice Jeener est un graveur tomb\u00e9 amoureux des math\u00e9matiques en visitant l\u2019institut Henri Poincar\u00e9 quand il \u00e9tait \u00e9tudiant aux beaux-arts. Il suivait ainsi la trace de Man Ray, qui d\u00e9couvrit les mod\u00e8les de l\u2019institut dans les ann\u00e9es 30 et s\u2019en inspira pour sa s\u00e9rie de tableaux \u00e9quations shakespeariennes comme celui-ci intitul\u00e9 le roi Lear\u00a0: Les &hellip; Continuer la lecture de Les surfaces minimales de Patrice Jeener &rarr;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\" \/>\n<meta property=\"og:site_name\" content=\"MATH&#039;MONDE, le blog d&#039;Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-03T10:02:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-05-15T18:00:36+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Jeener-Avant.png\" \/>\n\t<meta property=\"og:image:width\" content=\"709\" \/>\n\t<meta property=\"og:image:height\" content=\"945\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\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=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\",\"name\":\"Les surfaces minimales de Patrice Jeener, par Herv\u00e9 Lehning\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Jeener-Avant.png\",\"datePublished\":\"2018-03-03T10:02:49+00:00\",\"dateModified\":\"2018-05-15T18:00:36+00:00\",\"author\":{\"@id\":\"\"},\"breadcrumb\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/#primaryimage\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Jeener-Avant.png\",\"contentUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Jeener-Avant.png\",\"width\":709,\"height\":945},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/03\/03\/surfaces-minimales-de-patrice-jeener\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Les surfaces minimales de Patrice Jeener\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\",\"name\":\"MATH&#039;MONDE, le blog d&#039;Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\",\"description\":\"Comment comprendre le monde moderne sans culture math\u00e9matique ? 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