575 lines
420 KiB
HTML
575 lines
420 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><head>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1" id="wixDesktopViewport">
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<meta http-equiv="X-UA-Compatible" content="IE=edge">
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<meta name="generator" content="Wix.com Website Builder">
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<link rel="icon" href="favicon.ico" type="image/x-icon">
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<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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<!-- Safari Pinned Tab Icon -->
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<!-- <link rel="mask-icon" href="https://www.wix.com/favicon.ico"> -->
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<!-- Original trials -->
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<!-- Legacy Polyfills -->
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<script nomodule="" src="https://static.parastorage.com/unpkg/core-js-bundle@3.2.1/minified.js"></script>
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<script nomodule="" src="https://static.parastorage.com/unpkg/focus-within-polyfill@5.0.9/dist/focus-within-polyfill.js"></script>
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<script nomodule="" src="https://polyfill.io/v3/polyfill.min.js?features=fetch"></script>
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<!-- Performance API Polyfills -->
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<script>
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(function () {
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var noop = function noop() {};
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if ("performance" in window === false) {
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window.performance = {};
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}
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window.performance.mark = performance.mark || noop;
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window.performance.measure = performance.measure || noop;
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if ("now" in window.performance === false) {
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var nowOffset = Date.now();
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if (performance.timing && performance.timing.navigationStart) {
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nowOffset = performance.timing.navigationStart;
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}
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window.performance.now = function now() {
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return Date.now() - nowOffset;
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};
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}
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})();
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</script>
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<!-- Globals Definitions -->
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<script>
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(function () {
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var now = Date.now()
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window.initialTimestamps = {
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initialTimestamp: now,
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initialRequestTimestamp: Math.round(performance.timeOrigin ? performance.timeOrigin : now - performance.now())
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}
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window.thunderboltTag = "libs-releases-GA-local"
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window.thunderboltVersion = "1.13396.0"
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})();
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</script>
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<!-- sendFedopsLoadStarted.inline -->
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<script type="application/json" id="wix-fedops">{"data":{"site":{"metaSiteId":"ac0ac0d7-9b1b-4bc4-a1e8-09d12ef8f706","userId":"443131ff-8b0c-4753-8513-a7c7c35cffb0","siteId":"e5d7b7fb-7c89-430e-a3f3-7e6a537cc644","externalBaseUrl":"https:\/\/dupontjeanpierre93.wixsite.com\/rapport-d--tonnement","siteRevision":35,"siteType":"UGC","dc":"84","isResponsive":false,"editorName":"Unknown","sessionId":"025f7196-5a1b-4202-aa9d-281da96ea0d6","isSEO":false,"appNameForBiEvents":"thunderbolt"},"rollout":{"siteAssetsVersionsRollout":false,"isDACRollout":0,"isTBRollout":false},"fleetConfig":{"fleetName":"wix-thunderbolt","type":"GA","code":0},"requestUrl":"https:\/\/dupontjeanpierre93.wixsite.com\/rapport-d--tonnement","isInSEO":false,"platformOnSite":true}}</script>
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<script>window.fedops = JSON.parse(document.getElementById('wix-fedops').textContent)</script>
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<script id="sendFedopsLoadStarted">
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</script>
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<!-- Polyfills check -->
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<script>
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if (
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typeof Promise === 'undefined' ||
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typeof Set === 'undefined' ||
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typeof Symbol === 'undefined'
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) {
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// send bi in order to detect the browsers in which polyfills are not working
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window.fedops.phaseStarted('missing_polyfills')
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}
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</script>
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<!-- Essential Viewer Model -->
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<script type="application/json" id="wix-essential-viewer-model">{"fleetConfig":{"fleetName":"wix-thunderbolt","type":"GA","code":0},"mode":{"qa":false,"enableTestApi":false,"debug":false,"ssrIndicator":false,"ssrOnly":false,"siteAssetsFallback":"enable"},"componentsLibrariesTopology":[{"artifactId":"editor-elements","namespace":"wixui","url":"https:\/\/static.parastorage.com\/services\/editor-elements\/1.11634.0"},{"artifactId":"editor-elements","namespace":"dsgnsys","url":"https:\/\/static.parastorage.com\/services\/editor-elements\/1.11634.0"}],"siteFeaturesConfigs":{"sessionManager":{"isRunningInDifferentSiteContext":false}},"language":{"userLanguage":"en"},"siteAssets":{"clientTopology":{"mediaRootUrl":"https:\/\/static.wixstatic.com","staticMediaUrl":"https:\/\/static.wixstatic.com\/media","moduleRepoUrl":"https:\/\/static.parastorage.com\/unpkg","fileRepoUrl":"https:\/\/static.parastorage.com\/services","siteAssetsUrl":"https:\/\/siteassets.parastorage.com","pageJsonServerUrls":["https:\/\/pages.wixstatic.com","https:\/\/staticorigin.wixstatic.com","https:\/\/fallback.wix.com\/wix-html-editor-pages-webapp\/page"],"pathOfTBModulesInFileRepoForFallback":"wix-thunderbolt\/dist\/"}},"siteFeatures":["assetsLoader","businessLogger","captcha","clickHandlerRegistrar","commonConfig","componentsLoader","componentsRegistry","consentPolicy","cyclicTabbing","environmentWixCodeSdk","environment","locationWixCodeSdk","navigationManager","navigationPhases","pages","panorama","renderer","reporter","router","scrollRestoration","seoWixCodeSdk","seo","sessionManager","siteMembersWixCodeSdk","siteMembers","siteScrollBlocker","siteWixCodeSdk","stores","structureApi","thunderboltInitializer","tpaCommons","translations","warmupData","windowMessageRegistrar","windowWixCodeSdk","wixEmbedsApi","componentsReact","platform"],"site":{"externalBaseUrl":"https:\/\/dupontjeanpierre93.wixsite.com\/rapport-d--tonnement","isSEO":false},"media":{"staticMediaUrl":"https:\/\/static.wixstatic.com\/media","mediaRootUrl":"https:\/\/static.wixstatic.com\/","staticVideoUrl":"https:\/\/video.wixstatic.com\/"},"requestUrl":"https:\/\/dupontjeanpierre93.wixsite.com\/rapport-d--tonnement","rollout":{"siteAssetsVersionsRollout":false,"isDACRollout":0,"isTBRollout":false},"commonConfig":{"brand":"wix","host":"VIEWER","bsi":"","consentPolicy":{},"consentPolicyHeader":{}},"interactionSampleRatio":0.01,"dynamicModelUrl":"https:\/\/dupontjeanpierre93.wixsite.com\/rapport-d--tonnement\/_api\/v2\/dynamicmodel","experiments":{"specs.thunderbolt.wowImageRelayout":true}}</script>
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<script>window.viewerModel = JSON.parse(document.getElementById('wix-essential-viewer-model').textContent)</script>
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<script>
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window.fetchDynamicModel = () => (window.viewerModel.siteFeaturesConfigs.sessionManager.isRunningInDifferentSiteContext ? Promise.resolve({}) : fetch(window.viewerModel.dynamicModelUrl, { credentials: 'same-origin' }).then(function(r){if(!r.ok)throw new Error(`[${r.status}]${r.statusText}`);return r.json()}))
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window.dynamicModelPromise = window.fetchDynamicModel()
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window.commonConfig = viewerModel.commonConfig
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</script>
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<!-- initCustomElements -->
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<meta name="wix-dynamic-custom-elements" content="">
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<!-- Initial CSS -->
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<style data-url="https://static.parastorage.com/services/wix-thunderbolt/dist/main.8de0a6ff.min.css">body.device-mobile-optimized{overflow-x:hidden;overflow-y:scroll}body.device-mobile-optimized:not(.responsive) #SITE_CONTAINER{margin-left:auto;margin-right:auto;overflow-x:visible;position:relative;width:320px}body.device-mobile-optimized:not(.responsive):not(.blockSiteScrolling) #SITE_CONTAINER{margin-top:0}body.device-mobile-optimized>*{max-width:100%!important}body.device-mobile-optimized #site-root{overflow-x:hidden;overflow-y:hidden}@supports(overflow:clip){body.device-mobile-optimized #site-root{overflow-x:clip;overflow-y:clip}}body.device-mobile-non-optimized #SITE_CONTAINER #site-root{overflow-x:hidden;overflow-y:auto}body.device-mobile-non-optimized.fullScreenMode{background-color:#5f6360}body.device-mobile-non-optimized.fullScreenMode #MOBILE_ACTIONS_MENU,body.device-mobile-non-optimized.fullScreenMode #SITE_BACKGROUND,body.device-mobile-non-optimized.fullScreenMode #site-root,body.fullScreenMode #WIX_ADS{visibility:hidden}body.fullScreenMode{overflow-x:hidden!important;overflow-y:hidden!important}body.fullScreenMode.device-mobile-optimized #TINY_MENU{opacity:0;pointer-events:none}body.fullScreenMode-scrollable.device-mobile-optimized{overflow-x:hidden!important;overflow-y:auto!important}body.fullScreenMode-scrollable.device-mobile-optimized #masterPage,body.fullScreenMode-scrollable.device-mobile-optimized #site-root{overflow-x:hidden!important;overflow-y:hidden!important}body.fullScreenMode-scrollable.device-mobile-optimized #SITE_BACKGROUND,body.fullScreenMode-scrollable.device-mobile-optimized #masterPage{height:auto!important}body.fullScreenMode-scrollable.device-mobile-optimized #masterPage.mesh-layout{height:0!important}body.device-mobile-optimized.blockSiteScrolling{position:fixed;width:100%}body.device-mobile-optimized.blockSiteScrolling #SITE_CONTAINER{margin-top:calc(var(--blocked-site-scroll-margin-top)*-1)}body.device-mobile-optimized.blockSiteScrolling:not(.responsive) #WIX_ADS{margin-top:var(--blocked-site-scroll-margin-top)}@keyframes slide-horizontal-new{0%{transform:translateX(100%)}}@keyframes slide-horizontal-old{80%{opacity:1}to{opacity:0;transform:translateX(-100%)}}@keyframes slide-vertical-new{0%{transform:translateY(-100%)}}@keyframes slide-vertical-old{80%{opacity:1}to{opacity:0;transform:translateY(100%)}}@keyframes out-in-new{0%{opacity:0}}@keyframes out-in-old{to{opacity:0}}html[data-page-transition=SlideHorizontal]::view-transition-old(page-group){animation:slide-horizontal-old .6s cubic-bezier(.83,0,.17,1) forwards;mix-blend-mode:normal}html[data-page-transition=SlideHorizontal]::view-transition-new(page-group){animation:slide-horizontal-new .6s cubic-bezier(.83,0,.17,1) backwards;mix-blend-mode:normal}html[data-page-transition=SlideVertical]::view-transition-old(page-group){animation:slide-vertical-old .6s cubic-bezier(.83,0,.17,1) forwards;mix-blend-mode:normal}html[data-page-transition=SlideVertical]::view-transition-new(page-group){animation:slide-vertical-new .6s cubic-bezier(.83,0,.17,1) backwards;mix-blend-mode:normal}html[data-page-transition=OutIn]::view-transition-old(page-group){animation:out-in-old .35s cubic-bezier(.64,0,.78,0) forwards}html[data-page-transition=OutIn]::view-transition-new(page-group){animation:out-in-new .35s cubic-bezier(.22,1,.36,1) .35s backwards}@media(prefers-reduced-motion:reduce){::view-transition-group(*),::view-transition-new(*),::view-transition-old(*){animation:none!important}}body,html{background:transparent;border:0;margin:0;outline:0;padding:0;vertical-align:baseline}body{--scrollbar-width:0px;font-family:Arial,Helvetica,sans-serif;font-size:10px}body,html{height:100%}body{overflow-x:auto;overflow-y:scroll}body:not(.responsive) #site-root{min-width:var(--site-width);width:100%}body:not([data-js-loaded]) [data-hide-prejs]{visibility:hidden}#SITE_CONTAINER{position:relative}:root{--one-unit:1vw}@supports(container-type:inline-size){:root{--one-unit:1cqw}}</style>
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<style data-url="https://static.parastorage.com/services/wix-thunderbolt/dist/main.renderer.df786773.min.css">a,abbr,acronym,address,applet,b,big,blockquote,button,caption,center,cite,code,dd,del,dfn,div,dl,dt,em,fieldset,font,footer,form,h1,h2,h3,h4,h5,h6,header,i,iframe,img,ins,kbd,label,legend,li,nav,object,ol,p,pre,q,s,samp,section,small,span,strike,strong,sub,sup,table,tbody,td,tfoot,th,thead,title,tr,tt,u,ul,var{background:transparent;border:0;margin:0;outline:0;padding:0;vertical-align:baseline}input,select,textarea{box-sizing:border-box;font-family:Helvetica,Arial,sans-serif}ol,ul{list-style:none}blockquote,q{quotes:none}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}a{cursor:pointer;text-decoration:none}.testStyles{overflow-y:hidden}.reset-button{-webkit-appearance:none;background:none;border:0;color:inherit;font:inherit;line-height:normal;outline:0;overflow:visible;padding:0;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none}:focus{outline:none}#site-root{margin:0 auto;min-height:100%;position:relative;top:var(--wix-ads-height)}#site-root img:not([src]){visibility:hidden}#site-root svg img:not([src]){visibility:visible}.auto-generated-link{color:inherit}#SCROLL_TO_BOTTOM,#SCROLL_TO_TOP{height:0}.has-click-trigger{cursor:pointer}.fullScreenOverlay{bottom:0;display:flex;justify-content:center;left:0;overflow-y:hidden;position:fixed;right:0;top:-60px;z-index:1005}.fullScreenOverlay>.fullScreenOverlayContent{bottom:0;left:0;margin:0 auto;overflow:hidden;position:absolute;right:0;top:60px;transform:translateZ(0)}[data-mesh-id$=centeredContent],[data-mesh-id$=form],[data-mesh-id$=inlineContent]{pointer-events:none;position:relative}[data-mesh-id$=-gridWrapper],[data-mesh-id$=-rotated-wrapper]{pointer-events:none}[data-mesh-id$=-gridContainer]>*,[data-mesh-id$=-rotated-wrapper]>*,[data-mesh-id$=inlineContent]>:not([data-mesh-id$=-gridContainer]){pointer-events:auto}.device-mobile-optimized #masterPage.mesh-layout #SOSP_CONTAINER_CUSTOM_ID{grid-area:2/1/3/2;-ms-grid-row:2;position:relative}#masterPage.mesh-layout{-ms-grid-rows:max-content max-content min-content max-content;-ms-grid-columns:100%;align-items:start;display:-ms-grid;display:grid;grid-template-columns:100%;grid-template-rows:max-content max-content min-content max-content;justify-content:stretch}#masterPage.mesh-layout #PAGES_CONTAINER,#masterPage.mesh-layout #SITE_FOOTER-placeholder,#masterPage.mesh-layout #SITE_FOOTER_WRAPPER,#masterPage.mesh-layout #SITE_HEADER-placeholder,#masterPage.mesh-layout #SITE_HEADER_WRAPPER,#masterPage.mesh-layout #SOSP_CONTAINER_CUSTOM_ID[data-state~=mobileView],#masterPage.mesh-layout #soapAfterPagesContainer,#masterPage.mesh-layout #soapBeforePagesContainer{-ms-grid-row-align:start;-ms-grid-column-align:start;-ms-grid-column:1}#masterPage.mesh-layout #SITE_HEADER-placeholder,#masterPage.mesh-layout #SITE_HEADER_WRAPPER{grid-area:1/1/2/2;-ms-grid-row:1}#masterPage.mesh-layout #PAGES_CONTAINER,#masterPage.mesh-layout #soapAfterPagesContainer,#masterPage.mesh-layout #soapBeforePagesContainer{grid-area:3/1/4/2;-ms-grid-row:3}#masterPage.mesh-layout #soapAfterPagesContainer,#masterPage.mesh-layout #soapBeforePagesContainer{width:100%}#masterPage.mesh-layout #PAGES_CONTAINER{align-self:stretch}#masterPage.mesh-layout main#PAGES_CONTAINER{display:block}#masterPage.mesh-layout #SITE_FOOTER-placeholder,#masterPage.mesh-layout #SITE_FOOTER_WRAPPER{grid-area:4/1/5/2;-ms-grid-row:4}#masterPage.mesh-layout #SITE_PAGES,#masterPage.mesh-layout [data-mesh-id=PAGES_CONTAINERcenteredContent],#masterPage.mesh-layout [data-mesh-id=PAGES_CONTAINERinlineContent]{height:100%}#masterPage.mesh-layout.desktop>*{width:100%}#masterPage.mesh-layout #PAGES_CONTAINER,#masterPage.mesh-layout #SITE_FOOTER,#masterPage.mesh-layout #SITE_FOOTER_WRAPPER,#masterPage.mesh-layout #SITE_HEADER,#masterPage.mesh-layout #SITE_HEADER_WRAPPER,#masterPage.mesh-layout #SITE_PAGES,#masterPage.mesh-layout #masterPageinlineContent{position:relative}[data-z-counter]{z-index:0}[data-z-counter="0"]{z-index:auto}.wixSiteProperties{-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}</style>
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<meta name="format-detection" content="telephone=no">
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<meta name="skype_toolbar" content="skype_toolbar_parser_compatible">
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<script type="wix/htmlEmbeds" id="pageHtmlEmbeds.head start"></script>
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src: local('Work Sans Bold'), local('WorkSans-Bold'), url("//static.parastorage.com/tag-bundler/api/v1/fonts-cache/googlefont/woff2/s/worksans/v5/QGYpz_wNahGAdqQ43Rh3x4X8lthNy_r-K7mV.woff2") format('woff2');
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unicode-range: U+0100-024F, U+0259, U+1E00-1EFF, U+2020, U+20A0-20AB, U+20AD-20CF, U+2113, U+2C60-2C7F, U+A720-A7FF;
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font-display: block;
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}
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@font-face {
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font-family: 'Work Sans';
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font-style: normal;
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font-weight: 700;
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src: local('Work Sans Bold'), local('WorkSans-Bold'), url("//static.parastorage.com/tag-bundler/api/v1/fonts-cache/googlefont/woff2/s/worksans/v5/QGYpz_wNahGAdqQ43Rh3x4X8mNhNy_r-Kw.woff2") format('woff2');
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unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+2000-206F, U+2074, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
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font-display: block;
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@font-face {
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font-family:"Proxima-N-W01-Reg";
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src:url("//static.parastorage.com/services/third-party/fonts/user-site-fonts/fonts/64017d81-9430-4cba-8219-8f5cc28b923e.woff2") format("woff2"),url("//static.parastorage.com/services/third-party/fonts/user-site-fonts/fonts/e56ecb6d-da41-4bd9-982d-2d295bec9ab0.woff") format("woff");
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font-display: block;
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}
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@font-face{
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font-family:"Proxima-N-W05-Reg";
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src: url("//static.parastorage.com/services/santa-resources/resources/viewer/user-site-fonts/fonts/ProximNova/v1/ProximaNovaW05-Regular.woff2") format("woff2"),
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url("//static.parastorage.com/services/santa-resources/resources/viewer/user-site-fonts/fonts/ProximNova/v1/ProximaNovaW05-Regular.woff") format("woff");
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font-display: block;
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0.00px 5px 0px rgba(0, 0, 0, 0.5);--bg-scrl:var(--color_11);--brwt-scrl:0px;--brd-scrl:var(--color_15);--brwb-scrl:0px;--shd-scrl:0.00px 0.00px 5px 0px rgba(0, 0, 0, 0.5);--alpha-brd:0;--alpha-bg:0.52;--alpha-brd-scrl:1;--alpha-bg-scrl:0;}#SITE_HEADER{left:0;margin-left:0;width:100%;min-width:0;}[data-mesh-id=SITE_HEADERinlineContent]{height:auto;width:100%;}[data-mesh-id=SITE_HEADERinlineContent-gridContainer]{position:static;display:grid;height:auto;width:100%;min-height:auto;grid-template-rows:min-content 1fr;grid-template-columns:100%;}[data-mesh-id=SITE_HEADERinlineContent-gridContainer] > [id="comp-lqybha0r"]{position:relative;margin:30px 0px 0 calc((100% - 980px) * 0.5);left:0px;grid-area:1 / 1 / 2 / 2;justify-self:start;align-self:start;}[data-mesh-id=SITE_HEADERinlineContent-gridContainer] > [id="comp-lqybha0v1"]{position:relative;margin:0px 0px 0px calc((100% - 980px) * 0.5);left:0px;grid-area:2 / 1 / 3 / 2;justify-self:start;align-self:start;}#comp-lqybha0r{margin-left:auto;margin-right:auto;width:calc(100% - 60px - 60px);min-width:980px;}[data-mesh-id=comp-lqybha0sinlineContent]{height:auto;width:100%;position:static;min-height:132px;}[data-mesh-id=comp-lqybha0s1inlineContent]{height:auto;width:100%;}[data-mesh-id=comp-lqybha0s1inlineContent-gridContainer]{position:static;display:grid;height:auto;width:100%;min-height:132px;grid-template-rows:1fr;grid-template-columns:100%;}[data-mesh-id=comp-lqybha0s1inlineContent-gridContainer] > [id="comp-lqybha0t"]{position:relative;margin:21px 0px 10px calc((100% - 432px) * 0.5);left:-123px;grid-area:1 / 1 / 2 / 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[id="comp-lqybhao4"]{position:relative;margin:43px 0px 16px calc((100% - 980px) * 0.5);left:211px;grid-area:1 / 1 / 2 / 2;justify-self:start;align-self:start;}[data-mesh-id=SITE_FOOTERinlineContent-gridContainer] > [id="comp-lqybhao5"]{position:relative;margin:0px 0px 43px calc((100% - 980px) * 0.5);left:435px;grid-area:2 / 1 / 3 / 2;justify-self:start;align-self:start;}[data-mesh-id=SITE_FOOTERinlineContent-gridContainer] > [id="comp-lqybhao51"]{position:relative;margin:0px 0px 31px calc((100% - 980px) * 0.5);left:322px;grid-area:3 / 1 / 4 / 2;justify-self:start;align-self:start;}#comp-lqybhao4{width:557px;height:auto;}#comp-lqybhao5{width:114px;height:auto;}#comp-lqybhao51{width:344px;height:auto;}
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#comp-lqybhao4 { --min-height:29px;height:auto }#comp-lqybhao4 * { text-align:center !important }#comp-lqybhao5 { --min-height:27px;height:auto }#comp-lqybhao51 { --min-height:22px;height:auto }#comp-lqybha0t { --min-height:29px;height:auto }#SITE_HEADER { --shc-mutated-brightness:128,128,128 }#SITE_FOOTER { --shc-mutated-brightness:128,128,128 }#SITE_PAGES { --transition-duration:0ms }#comp-lqybha0r { --bg-overlay-color:transparent;--bg-gradient:none;--padding:0px;--margin:0px;min-width:980px;--firstChildMarginTop:-1px;--lastChildMarginBottom:-1px;--items-direction:row }#comp-lqybha0v1 { --bg-overlay-color:transparent;--bg-gradient:none;--padding:0px;--margin:0px;min-width:980px;--firstChildMarginTop:-1px;--lastChildMarginBottom:-1px;--items-direction:row }#comp-lqybha0s { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:279px;--column-flex:279 }#comp-lqybha0s1 { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:432px;--column-flex:432 }#comp-lqybha0v { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:269px;--column-flex:269 }#comp-lqybha0w { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:20px;--column-flex:20 }#comp-lqybha0w1 { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:940px;--column-flex:940 }#comp-lqybha0x { --bg-overlay-color:transparent;--bg-gradient:none;width:100%;--column-width:20px;--column-flex:20 }#BACKGROUND_GROUP { --transition-duration:0ms }
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font-family:"Avenir-LT-W01_35-Light1475496";
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@font-face {
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font-family: "Avenir-LT-W05_35-Light";
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src: url("//static.parastorage.com/services/santa-resources/resources/viewer/user-site-fonts/fonts/Avenir_Family_Pack/v1/AvenirLTW05-35Light.woff2") format("woff2"),
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url("//static.parastorage.com/services/santa-resources/resources/viewer/user-site-fonts/fonts/Avenir_Family_Pack/v1/AvenirLTW05-35Light.woff") format("woff");
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font-display: block;
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@font-face {
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font-family: "Helvetica-W01-Roman";
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src: url("//static.parastorage.com/services/santa-resources/dist/viewer/user-site-fonts/fonts/Helvetica/v3/HelveticaLTW04-Roman.woff2") format("woff2"),url("//static.parastorage.com/services/third-party/fonts/user-site-fonts/fonts/4021a3b9-f782-438b-aeb4-c008109a8b64.woff") format("woff");
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font-display: block;
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}
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@font-face {
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font-family: "Helvetica-W02-Roman";
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font-display: block;
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}
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@font-face {
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font-family: "Helvetica-LT-W10-Roman";
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font-display: block;
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}
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/**
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* @license
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* Copyright (c) 2016 The Polymer Project Authors. All rights reserved.
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* This code may only be used under the BSD style license found at http://polymer.github.io/LICENSE.txt
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* The complete set of authors may be found at http://polymer.github.io/AUTHORS.txt
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* The complete set of contributors may be found at http://polymer.github.io/CONTRIBUTORS.txt
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* Code distributed by Google as part of the polymer project is also
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* subject to an additional IP rights grant found at http://polymer.github.io/PATENTS.txt
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id="bgLayers_comp-lqybhaxw" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lqybhaxw" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lqybhaxx" class="comp-lqybhaxx YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqybhaxx" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqybhaxx" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqybhaxxinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqybhaxxinlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lqybhaxy" class="comp-lqybhaxy CohWsy wixui-column-strip"><div id="bgLayers_comp-lqybhaxy" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lqybhaxy" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lqybhaxy1" class="comp-lqybhaxy1 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqybhaxy1" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqybhaxy1" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqybhaxy1inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqybhaxy1inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqybk52q" class="comp-lqybk52q SPY_vo"><div data-mesh-id="comp-lqybk52qinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqybk52qinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqybhaxy2" class="KcpHeO tz5f0K comp-lqybhaxy2 wixui-rich-text" data-testid="richTextElement" style="visibility: inherit;" data-angle="0" data-angle-style-location="style" data-screen-in-hide="done"><h1 class="font_2 wixui-rich-text__text" style="font-size:36px; line-height:1.25em; text-align:center;"><span style="text-shadow:rgba(0, 0, 0, 0.4) 0px 4px 5px;" class="wixui-rich-text__text"><span style="font-size:36px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span class="color_45 wixui-rich-text__text"><span style="font-weight:bold;" class="wixui-rich-text__text">Rapport d'étonnement</span></span></span></span></span></h1></div><div id="comp-lqybhaxz" class="KcpHeO tz5f0K comp-lqybhaxz wixui-rich-text" data-testid="richTextElement"><h1 class="font_7 wixui-rich-text__text" style="line-height:1.67em; text-align:center; font-size:18px;"><span style="text-shadow:rgba(0, 0, 0, 0.4) 0px 4px 5px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span class="color_15 wixui-rich-text__text"><span style="font-weight:bold;" class="wixui-rich-text__text">Camilla Schoeser</span></span></span></span></h1></div></div></div></div></div></div></div></div></section><section id="comp-lqybhaxz1" class="comp-lqybhaxz1 CohWsy wixui-column-strip"><div id="bgLayers_comp-lqybhaxz1" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lqybhaxz1" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lqybhaxz2" class="comp-lqybhaxz2 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqybhaxz2" data-hook="bgLayers" class="MW5IWV"><div id="bgMedia_comp-lqybhaxz2" class="VgO9Yg"><wix-video id="videoContainer_comp-lqybhaxz2" 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src="https://video.wixstatic.com/video/11062b_ba2c921477734f8b84ef0c71f64a2562/720p/mp4/file.mp4"></video><wow-image id="comp-lqybhaxz2_img" class="HlRz5e Z_wCwr Jxk_UL bgVideoposter yK6aSC" data-image-info="{"containerId":"comp-lqybhaxz2","alignType":"center","displayMode":"fill","targetWidth":980,"targetHeight":455,"isLQIP":true,"imageData":{"width":1920,"height":1080,"uri":"11062b_ba2c921477734f8b84ef0c71f64a2562f000.jpg","name":"","displayMode":"fill","quality":{"unsharpMask":{"radius":0.33,"amount":1,"threshold":0}},"devicePixelRatio":1}}" data-bg-effect-name="" data-has-ssr-src="" data-src="https://static.wixstatic.com/media/11062b_ba2c921477734f8b84ef0c71f64a2562f000.jpg/v1/fill/w_1120,h_455,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_ba2c921477734f8b84ef0c71f64a2562f000.jpg" style="opacity: 0;"><img src="https://static.wixstatic.com/media/11062b_ba2c921477734f8b84ef0c71f64a2562f000.jpg/v1/fill/w_1120,h_455,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_ba2c921477734f8b84ef0c71f64a2562f000.jpg" alt="" style="width: 1120px; height: 455px; object-fit: cover; object-position: 50% 50%;" width="980" height="455" fetchpriority="high"></wow-image></wix-video></div></div><div data-mesh-id="comp-lqybhaxz2inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqybhaxz2inlineContent-gridContainer" data-testid="mesh-container-content"></div></div></div></div></section></div></div></div></div></section></div></div></section><section id="comp-lqyblosr" tabindex="-1" class="Oqnisf comp-lqyblosr wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lqyblosr" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqyblosr" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqyblosrinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqyblosrinlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lqyblotc" class="comp-lqyblotc CohWsy wixui-column-strip"><div id="bgLayers_comp-lqyblotc" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lqyblotc" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lqyblotl" class="comp-lqyblotl YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqyblotl" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqyblotl" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqyblotlinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqyblotlinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqyblott" class="KcpHeO tz5f0K comp-lqyblott wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:38px; line-height:normal;"><span style="text-shadow:rgba(0, 0, 0, 0.4) 0px 4px 5px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text">Introduction</span></span></span></h2></div></div></div></div><div id="comp-lqyblou2" class="comp-lqyblou2 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqyblou2" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqyblou2" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqyblou2inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqyblou2inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqyblou8" class="KcpHeO tz5f0K comp-lqyblou8 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">L’histoire des mathématiques révèle un voyage captivant à travers les siècles, marqué par des esprits visionnaires et des découvertes révolutionnaires. Elle demeure un domaine en constante évolution, représentant près de 90% des progrès réalisés durant les deux derniers siècles.<br class="wixui-rich-text__text">
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</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">L'impulsion derrière ces avancées mathématiques réside dans divers questionnements :<br class="wixui-rich-text__text">
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Quel était, et quel est encore le moteur des avancées mathématiques ? Quels en sont les buts et les objectifs concrets ?</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><br class="wixui-rich-text__text">
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En outre, comment peut-on assurer la justesse d'une démarche mathématique alors que souvent elle se bâtit sur des hypothèses évolutives, certaines pouvant être confirmées ou réfutées ultérieurement ?</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span class="wixGuard wixui-rich-text__text"></span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">La diffusion des découvertes mathématiques à travers différents pays constitue un autre enjeu à explorer. Comment ces connaissances se sont-elles propagées à travers les frontières, traversant les barrières linguistiques et culturelles pour enrichir les connaissances mondiales en mathématiques ?</p></div></div></div></div></div></section></div></div></section><section id="comp-lqycezpd" tabindex="-1" class="Oqnisf comp-lqycezpd wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lqycezpd" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqycezpd" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqycezpdinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqycezpdinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqycezru" class="KcpHeO tz5f0K comp-lqycezru wixui-rich-text" data-testid="richTextElement"><h2 class="font_0 wixui-rich-text__text" style="font-size:56px; line-height:normal;"><span style="text-shadow:rgba(0, 0, 0, 0.4) 0px 4px 5px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:56px;" class="wixui-rich-text__text">Articles étudiés </span></span></span></h2></div><div id="comp-lqycezs5" class="KcpHeO tz5f0K comp-lqycezs5 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="font-size:16px;" class="wixui-rich-text__text">Les articles que j’ai étudiés sont tirés du site « <span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://imagesdev.math.cnrs.fr/tag/histoire-des-mathematiques/" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text">Images des mathématiques</a></span> ».</span></p></div><section id="comp-lqycezsb" class="comp-lqycezsb CohWsy wixui-column-strip"><div id="bgLayers_comp-lqycezsb" data-hook="bgLayers" class="if7Vw2" style="opacity: 1; transform: translate3d(0px, 0px, 0px); visibility: inherit;"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><wix-bg-media id="bgMedia_comp-lqycezsb" class="rWP3Gv" data-container-id="comp-lqycezsb" data-container-size="0, 0" data-page-id="z1agc" data-bg-effect-name="BgFadeIn" style="width: 1200px; height: 828.933px; left: 0px; top: 0px;"></wix-bg-media></div><div data-testid="columns" class="V5AUxf"><div id="comp-lqycezt4" class="comp-lqycezt4 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lqycezt4" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqycezt4" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqycezt4inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqycezt4inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqyceztc" class="KcpHeO tz5f0K comp-lqyceztc wixui-rich-text" data-testid="richTextElement" style="visibility: inherit;" data-angle="0" data-angle-style-location="style" data-screen-in-hide="done"><h3 class="font_2 wixui-rich-text__text" style="font-size:38px; line-height:normal;"><span style="text-shadow:rgba(0, 0, 0, 0.4) 0px 4px 5px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text">Synthèse rapide des articles</span></span></span></h3></div><div id="comp-lqycezti" class="KcpHeO tz5f0K comp-lqycezti wixui-rich-text" data-testid="richTextElement"><h4 class="font_5 wixui-rich-text__text" style="font-size:16px; line-height:normal;"><span style="font-style:italic;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Le triangle analytique, un outil pour tracer les courbes algébriques aux XVIIIe et XIXe siècles </span></span></span></h4></div><div id="comp-lqycezto" class="KcpHeO tz5f0K comp-lqycezto wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://images.math.cnrs.fr/Le-triangle-analytique-un-outil-pour-tracer-les-courbes-algebriques-aux-XVIIIe.html" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">lien</span></span></a></span></p></div><div id="comp-lqyceztz" class="KcpHeO tz5f0K comp-lqyceztz wixui-rich-text" data-testid="richTextElement"><h4 class="font_5 wixui-rich-text__text" style="font-size:16px; line-height:normal;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text"><span style="font-style:italic;" class="wixui-rich-text__text">« Hermann Minkowski : des formes quadratiques à la géométrie des nombres </span></span></span></h4></div><div id="comp-lqycezu6" class="KcpHeO tz5f0K comp-lqycezu6 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://images.math.cnrs.fr/Hermann-Minkowski-des-formes-quadratiques-a-la-geometrie-des-nombres.html" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">lien</span></span></a></span></p></div><div id="comp-lqycezui" class="KcpHeO tz5f0K comp-lqycezui wixui-rich-text" data-testid="richTextElement"><h4 class="font_5 wixui-rich-text__text" style="font-size:16px; line-height:normal;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text"><span style="font-style:italic;" class="wixui-rich-text__text">« Le rang des courbes elliptiques </span></span></span></h4></div><div id="comp-lqycezuo" class="KcpHeO tz5f0K comp-lqycezuo wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://images.math.cnrs.fr/Le-rang-des-courbes-elliptiques.html#nh13" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">lien</span></span></a></span></p></div><div id="comp-lqyculoy" class="KcpHeO tz5f0K comp-lqyculoy wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Cet article présente un outil du 18e siècle qui permet de tracer des courbes algébriques, à l’époque où le traçage des courbes se fait point par point et sans l’aide d’outil numérique.</span></span></p></div><div id="comp-lqycezuc" class="KcpHeO tz5f0K comp-lqycezuc wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Cet article présente un théorème d’Hermann Minkowski (1864-1909), théorème géométrique utilisé initialement pour étudier l’arithmétique.</span></span></p></div><div id="comp-lqycezuu" class="KcpHeO tz5f0K comp-lqycezuu wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Cet article présente des théorèmes arithmétiques de Pierre de Fernat (17e siècle) qui permettent de trouver des résultats sur les courbes elliptiques et les équations diophantiennes (concept découvert par Diophante, 3e siècle après J.C.).</span></span></p></div><div id="comp-lqycy8sr" class="KcpHeO tz5f0K comp-lqycy8sr wixui-rich-text" data-testid="richTextElement"><h4 class="font_5 wixui-rich-text__text" style="font-size:16px; line-height:normal;"><span style="font-style:italic;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Fonctions fuchsiennes ou schwarziennes ? Mieux poincaréennes ! (II) </span></span></span></h4></div><div id="comp-lqycyfmp" class="KcpHeO tz5f0K comp-lqycyfmp wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://images.math.cnrs.fr/Fonctions-fuchsiennes-ou-schwarziennes-Mieux-poincareennes-II.html" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">lien</span></span></a></span></p></div><div id="comp-lqyceztu" class="KcpHeO tz5f0K comp-lqyceztu wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text">Enfin, cet article présente une révolution amenée par Poincaré (1854-1912), qui décide d’étudier la géométrie hyperbolique (non-euclidienne) pour résoudre un certain type d’équations différentielles.</span></span></p></div><div id="comp-lr3s08ik" class="KcpHeO tz5f0K comp-lr3s08ik wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px;"><span class="wixGuard wixui-rich-text__text"></span>Ces articles sont une très étroite fenêtre sur l’avancée des mathématiques entre le 17e et le 19e siècle. Ils vont me permettre d’élaborer une réflexion sur le moteur des avancées mathématiques.</p></div></div></div></div></div></section></div></div></section><section id="comp-lqybz4n2" tabindex="-1" class="Oqnisf comp-lqybz4n2 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lqybz4n2" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lqybz4n2" class="VgO9Yg"></div></div><div data-mesh-id="comp-lqybz4n2inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqybz4n2inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lqybz4pf" class="KcpHeO tz5f0K comp-lqybz4pf wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:38px; line-height:normal;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text">Points communs et différences entre les articles</span></span></h2></div><div id="comp-lqybz4pn" class="comp-lqybz4pn aVng1S wixui-horizontal-line"></div><div id="comp-lqybz4q3" class="KcpHeO tz5f0K comp-lqybz4q3 wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text">Chaque article aborde le coté historique de la découverte ou de l’énoncé du théorème par le savant, en révélant l’origine, le contexte, et en exposant les acteurs majeurs en lien, des extraits de volumes, des citations des savants, la propagation et enfin le devenir de la découverte.</span></span></p></div><div id="comp-lr3wstpf" class="KcpHeO tz5f0K comp-lr3wstpf wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text"><span class="wixGuard wixui-rich-text__text"></span>Cependant, les trois premiers articles explicitent en plus le raisonnement mathématique et la démonstration aboutissant au théorème, afin que le lecteur puisse le comprendre et s’en imprégner, au lieu de seulement accepter son énoncé. En comprenant les aspects mathématiques, il peut, en mon opinion, mieux s’imprégner des aspects historiques de la découverte.</span></span></p></div><div id="comp-lr3y2lnh" class="KcpHeO tz5f0K comp-lr3y2lnh wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text">Le 4e article, sur le nouvel outil de Poincaré, ne présente pas de théorème mathématique, mais plutôt le cheminement historique de son idée, qui est plus large qu’un simple théorème.</span></span></p></div></div></div></section><section id="comp-lr3zd2n2" tabindex="-1" class="Oqnisf comp-lr3zd2n2 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr3zd2n2" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr3zd2n2" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr3zd2n2inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr3zd2n2inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr3zgdln" class="oYv3_8 comp-lr3zgdln wixui-video-box" data-audio="off" data-has-play="" data-no-audio="" data-playing="" data-can-play=""><div class="F9nckB" tabindex="0" role="button" aria-label=" Play video" aria-pressed="true"><div id="bgLayers_comp-lr3zgdln" data-hook="bgLayers" class="MW5IWV wmoHxw"><div id="bgMedia_comp-lr3zgdln" class="VgO9Yg"><wix-video id="videoContainer_comp-lr3zgdln" data-video-info="{"fittingType":"fill","alignType":"center","hasBgScrollEffect":"","bgEffectName":"","videoId":"11062b_1c881d9de2f24d04a97b1fce733e1599","videoWidth":1920,"videoHeight":1080,"qualities":[{"quality":"360p","size":230400,"url":"video/11062b_1c881d9de2f24d04a97b1fce733e1599/360p/mp4/file.mp4"},{"quality":"480p","size":409920,"url":"video/11062b_1c881d9de2f24d04a97b1fce733e1599/480p/mp4/file.mp4"},{"quality":"720p","size":921600,"url":"video/11062b_1c881d9de2f24d04a97b1fce733e1599/720p/mp4/file.mp4"},{"quality":"1080p","size":2073600,"url":"video/11062b_1c881d9de2f24d04a97b1fce733e1599/1080p/mp4/file.mp4"}],"isVideoDataExists":"1","videoFormat":"mp4","playbackRate":1,"autoPlay":true,"containerId":"comp-lr3zgdln","animatePoster":"none"}" class="bX9O_S bgVideo yK6aSC"><video id="comp-lr3zgdln_video" class="K8MSra" role="presentation" crossorigin="anonymous" playsinline="" preload="auto" muted="" loop="" tabindex="-1" autoplay="" style="height: 100%; width: 100%; object-fit: cover; object-position: center center; opacity: 1;" src="https://video.wixstatic.com/video/11062b_1c881d9de2f24d04a97b1fce733e1599/1080p/mp4/file.mp4"></video><wow-image id="comp-lr3zgdln_img" class="HlRz5e Z_wCwr Jxk_UL bgVideoposter yK6aSC" data-image-info="{"containerId":"comp-lr3zgdln","alignType":"center","displayMode":"fill","targetWidth":1322,"targetHeight":743,"isLQIP":true,"imageData":{"width":2560,"height":1440,"uri":"11062b_1c881d9de2f24d04a97b1fce733e1599f000.jpg","name":"","displayMode":"fill","quality":{"unsharpMask":{"radius":0.33,"amount":1,"threshold":0}},"devicePixelRatio":1}}" data-bg-effect-name="" data-has-ssr-src="" style="opacity: 0;" data-src="https://static.wixstatic.com/media/11062b_1c881d9de2f24d04a97b1fce733e1599f000.jpg/v1/fill/w_1322,h_743,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_1c881d9de2f24d04a97b1fce733e1599f000.jpg"><img src="https://static.wixstatic.com/media/11062b_1c881d9de2f24d04a97b1fce733e1599f000.jpg/v1/fill/w_1322,h_743,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_1c881d9de2f24d04a97b1fce733e1599f000.jpg" alt="" style="width: 1322px; height: 743px; object-fit: cover; object-position: 50% 50%;" width="1322" height="743" fetchpriority="high"></wow-image></wix-video></div></div></div><div data-mesh-id="comp-lr3zgdlninlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr3zgdlninlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr3zgdoq"><div id="play-comp-lr3zgdoq" class="Xh82G7 wixui-vector-image"><div data-testid="svgRoot-play-comp-lr3zgdoq" class="aizuI7 TcoJIb Xh82G7"><!--?xml version="1.0" encoding="UTF-8"?-->
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</div></div></div><div data-mesh-id="comp-lr3zgdlninlineContent-wedge-3"></div></div></div></div><div id="comp-lr3zowy5" class="tI1Qp6 comp-lr3zowy5"><div class="xPEAfP wixui-box" data-testid="container-bg"></div><div data-mesh-id="comp-lr3zowy5inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr3zowy5inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr3zd2p0" class="KcpHeO tz5f0K comp-lr3zd2p0 wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:38px; line-height:normal;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text">Liens entre les domaines mathématiques</span></span></h2></div><div id="comp-lr3zd2p8" class="comp-lr3zd2p8 aVng1S wixui-horizontal-line"></div><div id="comp-lr3zd2pw1" class="KcpHeO tz5f0K comp-lr3zd2pw1 wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text">Dans les articles « Formes quadratiques » et « Le rang des courbes elliptiques », on observe que les découvertes mathématiques, à l’origine arithmétiques, ont des applications majeures en géométrie. Un domaine d’application mathématique peut être un outil pour en étudier un autre, et les différents secteurs en mathématiques sont en fait étroitement reliés entre eux.</span></span></span></p></div><div id="comp-lr3zi6z4" class="KcpHeO tz5f0K comp-lr3zi6z4 wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text">On peut étendre ce constat à d’autres disciplines : si les mathématiques ont des applications en physique, c’est qu’ils sont intrinsèquement liés. Ce ne sont pas des domaines distincts et séparés, il y a continuité entre eux.</span></span></span></p></div></div></div></div></div></div></section><section id="comp-lr6hho9e" tabindex="-1" class="Oqnisf comp-lr6hho9e wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6hho9e" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6hho9e" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6hho9einlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6hho9einlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6hhobg" class="KcpHeO tz5f0K comp-lr6hhobg wixui-rich-text" data-testid="richTextElement"><h2 class="font_2 wixui-rich-text__text" style="font-size:38px; line-height:normal; text-align:center;"><span style="color:#000000;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text"><span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://images.math.cnrs.fr/Le-triangle-analytique-un-outil-pour-tracer-les-courbes-algebriques-aux-XVIIIe.html" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text">Le triangle analytique, un outil pour tracer les courbes algébriques (18e-19e siècle)</a></span></span></span></span></h2></div><div id="comp-lr6hhoby1" class="KcpHeO tz5f0K comp-lr6hhoby1 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">L’introduction de cet article sur les courbes algébriques peut soulever plusieurs questions.</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Tout d’abord, si les courbes algébriques pouvaient être difficilement représentées, alors comment le concept de courbe algébrique a pu émerger dès l’Antiquité ? Quelles ont donc été les sources de ce domaine mathématique ?</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Ensuite, comment les mathématiciens depuis l’Antiquité ont-ils pu étudier les courbes arithmétiques, alors qu’ils ne pouvaient pas forcément les visualiser ? Que signifie « étudier » dans ce cas ?</span></p></div><div id="comp-lr6hm0qa" class="KcpHeO tz5f0K comp-lr6hm0qa wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Ces questions seront laissées en suspens mais pourrons trouver des éléments de réponses.<br class="wixui-rich-text__text">
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Par exemple, il est intéressant de noter que les problèmes étaient formulés différemment comme on peut le voir <span style="text-decoration:underline;" class="wixui-rich-text__text"><a href="https://www.maths-et-tiques.fr/index.php/histoire-des-maths/nombres/histoire-de-l-algebre" target="_blank" rel="noreferrer noopener" class="wixui-rich-text__text">ici</a></span>, et que l’algébrisation n’est apparue que plus tard. On peut également trouver des informations intéressante sur l’évolution des mathématiques dans le livre de Michel Garcia : Mathématiques à travers les siècles (Tome 1): Géométrie et arithmétique de l'Antiquité à nos jours.</span></p></div></div></div></section><section id="comp-lr6hq0je" tabindex="-1" class="Oqnisf comp-lr6hq0je wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6hq0je" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6hq0je" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6hq0jeinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6hq0jeinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6hq0lh1" class="KcpHeO tz5f0K comp-lr6hq0lh1 wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span class="color_37 wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text"><span class="wixGuard wixui-rich-text__text"></span>Le premier article, sur le triangle analytique, est fortement intéressant car il permet de prendre du recul sur les outils mathématiques de l’époque, et donc les moyens avec lesquels les recherches sont menées.<br class="wixui-rich-text__text">
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En effet, la technologie de nos jours permet de réaliser des opérations et des tâches d’une manière fluide et efficace qui peut nous faire oublier que de tels outils n’existaient pas il y a quelques siècles (et même décennies), et qu’il fallait utiliser d’autres méthodes, à la fois plus longues et moins fiables. Une question très intéressante est de savoir comment les courbes algébriques complexes pouvaient être tracées sans l’utilisation de logiciels informatiques.</span></span></span></p></div><div id="comp-lr6hruep" class="KcpHeO tz5f0K comp-lr6hruep wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:16px;">De manière évidente, le traçage d’une courbe algébrique doit se faire point par point. Mais pour y parvenir, il faut pouvoir tracer y en fonction de x. Seulement, certaines expressions de courbes comme \[ y^{4}+x^{2}y^{2}+2y^{3}-x^{3}=0 \] ne permettent pas d’avoir y en fonction de x.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:16px;">Concrètement, le problème à l’époque était le suivant : comment tracer des courbes algébriques lorsqu'on ne peut pas avoir une expression directe de y en fonction de x ? Pour résoudre ce problème, soit on a recours à quelques astuces mathématiques quand la forme des fonctions le permet, ce qui est détaillé au début de l’article.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:16px;">Ou alors on utilise un outil basé sur la simplification de termes par rapport à d’autres. De ce fait, le triangle analytique, méthode créée par le Genevois Gabriel Cramer (1704-1752), permet de déterminer quelles sont les composantes d’une fonction que l'on peut négliger par rapport à d’autres lors du tracer de la courbe, selon les valeurs de x ou y. Cet outil permet dans une première étape de déterminer les branches infinies, puis dans une 2e étape, les points singuliers.</p></div></div></div></section><section id="comp-lr6ib2tb" tabindex="-1" class="Oqnisf comp-lr6ib2tb wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6ib2tb" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6ib2tb" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6ib2tbinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6ib2tbinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6icygx" class="KcpHeO tz5f0K comp-lr6icygx wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Si la méthode du parallélogramme de Newton, précurseur de cette méthode, a été démontrée : « [la règle] du parallélogramme analytique due à Newton et que Lagrange a démontrée » ; l’article ne fait pas part de démonstration concernant la méthode du triangle analytique.</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">(Au passage, nous pouvons signaler que Newton ne publie pas les démonstrations de ses résultats :</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">« Comme souvent, Newton publie ses résultats sans démonstration, ce qui oblige ses successeurs à reconstituer les méthodes utilisées pour obtenir ces résultats, et qui fera dire à Gabriel Crameren préface de son propre ouvrage : « Il est facheux que Mr. NEWTON se soit contenté d’étaler ses découvertes sans y joindre les Démonstrations, & qu’il ait préféré le plaisir de se faire admirer à celui d’instruire » : Gabriel Cramer, Introduction à l'analyse des lignes courbes algébriques.)</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><br class="wixui-rich-text__text">
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<span style="color:#000000;" class="wixui-rich-text__text">Si nous revenons au triangle analytique, nous pouvons remarquer par ailleurs que l’utilisation de cet outil se base sur des approximations, donc une démonstration par rapport à son exactitude peut sembler un peu délicat.</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">De façon générale, comment faire pour savoir si une découverte ou une méthode mathématique est fiable ? Comment faire pour qu’une méthode le soit ?</span></p></div></div></div></section><section id="comp-lr6ih7vd" tabindex="-1" class="Oqnisf comp-lr6ih7vd wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6ih7vd" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6ih7vd" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6ih7vdinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6ih7vdinlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lr6ih7xi" class="comp-lr6ih7xi CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6ih7xi" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6ih7xi" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6ih7y3" class="comp-lr6ih7y3 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6ih7y3" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6ih7y3" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6ih7y3inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6ih7y3inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6ih7ya" class="KcpHeO tz5f0K comp-lr6ih7ya wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:18px; line-height:normal;"><span style="font-size:18px;" class="wixui-rich-text__text"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text">Les théorèmes peuvent être démontrés (et les démonstrations doivent être fiables)</span></span></span></span></h2></div></div></div></div><div id="comp-lr6ih7yg1" class="comp-lr6ih7yg1 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6ih7yg1" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6ih7yg1" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6ih7yg1inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6ih7yg1inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6ih7ym" class="KcpHeO tz5f0K comp-lr6ih7ym wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">Les démonstrations mathématiques se basent sur des relations, des théorèmes supposés vrais ou vérifiés.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Une démonstration est un raisonnement qui prouve la vérité de sa conclusion par déduction et d'une manière évidente et convaincante. La démonstration se démontre d’elle-même : chaque étape est compréhensible (si on y passe le temps nécessaire) et peut donc être aisément vérifiée. Et si on peut vérifier chaque étape, et si chaque étape s’enchaine logiquement, alors on peut finalement admettre la démonstration entière.</p></div><div id="comp-lr6ilipl" class="KcpHeO tz5f0K comp-lr6ilipl wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">Cependant j’ai été surprise de constater que certaines démonstrations, au lieu d’utiliser des égalités facilement déductibles, utilisent plutôt des astuces savamment trouvées.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Par exemple, dans la démonstration que la courbe \[ C : x^{3}+y^{3}=9 \] est elliptique, l’auteur utilise un enchainement d’égalités logiques qui sont après coup compréhensibles, mais que quelqu’un d’autre aurait difficilement imaginé au départ.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Ou encore, la démonstration de Minkowski a attiré mon attention. Voici l’énoncé de son théorème :</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="font-style:italic;" class="wixui-rich-text__text">On considère, dans le plan, un repère orthonormé d’origine O. Soit le réseau L des nombres entiers et R une partie centrée en O (cela signifie que R admet O comme centre de symétrie), convexe et dont l’aire est plus grande que 4. Minkowski établit alors qu’<span style="font-weight:bold;" class="wixui-rich-text__text">il</span><span style="font-weight:bold;" class="wixui-rich-text__text"> y a au moins un point du réseau L, différent de l’origine O, qui se trouve à l’intérieur de R ou sur son bord</span>.</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Pour prouver cela, Minkowski décide de prendre le quart R0 des parties R, de paver un espace de largeur n, de l’agrandir de 2d … pour finalement tomber sur une égalité arithmétique.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Comment en a-t-il eu l’idée ? Cet exemple m’a fait réfléchir de façon générale et m’a amenée à cet étonnement : Comment les savants ont-ils l’intuition pour trouver des raisonnements qui semblent s’éloigner de l’objectif de départ, mais répondant tout de même au problème posé ?<br class="wixui-rich-text__text">
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<br class="wixui-rich-text__text">
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<br class="wixui-rich-text__text">
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Les savants utilisent leur intuition, et parfois de façon plus large :</p></div></div></div></div></div></section></div></div></section><section id="comp-lr6iq1za" tabindex="-1" class="Oqnisf comp-lr6iq1za wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6iq1za" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iq1za" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iq1zainlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iq1zainlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lr6iq21s" class="comp-lr6iq21s CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6iq21s" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6iq21s" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6iq21y" class="comp-lr6iq21y YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6iq21y" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iq21y" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iq21yinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iq21yinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6iq224" class="KcpHeO tz5f0K comp-lr6iq224 wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:18px; line-height:normal;"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text">Pressentir une vérité</span></span></span></span></h2></div></div></div></div><div id="comp-lr6iq22b" class="comp-lr6iq22b YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6iq22b" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iq22b" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iq22binlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iq22binlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6iq22g" class="KcpHeO tz5f0K comp-lr6iq22g wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">Les scientifiques peuvent parfois pressentir une vérité, tandis que la démonstration n’arrive que plus tard.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">On peut citer comme exemple cet extrait de l’article « le rang des courbes elliptiques » :</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">« Le rang est un invariant fondamental, dont l’importance avait été pressentie par Poincaré en 1901 » ; ou encore : « On obtient alors le résultat suivant, pressenti par Fermat : ».</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">L’avancée mathématique peut se baser sur des pressentiments, des intuitions, qui sont conjecturés même s’ils ne sont prouvés que par la suite.</p></div></div></div></div></div></section><div id="comp-lr6itum9" class="KcpHeO tz5f0K comp-lr6itum9 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">La progression mathématique peut également se baser sur des éléments déjà existants, comme le parallélogramme de Newton a inspiré le triangle de Cramer.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Et ces outils sont devenus désuets par la suite, dépassés par d’autres méthodes plus efficaces : calcul différentiel pour l’étude des courbes, ou la géométrie synthétique.<br class="wixui-rich-text__text">
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La progression mathématique améliore les outils existants, avant de les remplacer par des outils plus performants, plus fiables, ou simplement qui semblent plus exacts.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">J’ai été surprise de constater que les recherches mathématiques sur des sujets datant d’il y a plusieurs siècles, continuent encore de nos jours. Par exemple, l’article sur les courbes elliptiques mentionne la découverte en 2006 d’une courbe elliptique de rang >= 28 ; ainsi qu’un théorème sur leur hauteur en 2020…</p></div></div></div></section><section id="comp-lr6iy9y5" tabindex="-1" class="Oqnisf comp-lr6iy9y5 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6iy9y5" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iy9y5" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iy9y5inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iy9y5inlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lr6iya03" class="comp-lr6iya03 CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6iya03" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6iya03" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6iya0b" class="comp-lr6iya0b YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6iya0b" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iya0b" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iya0binlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iya0binlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6iya0l" class="KcpHeO tz5f0K comp-lr6iya0l wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:18px; line-height:normal;"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text">… ou parfois amener des révolutions !</span></span></span></span></h2></div></div></div></div><div id="comp-lr6iya1l1" class="comp-lr6iya1l1 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6iya1l1" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6iya1l1" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6iya1l1inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6iya1l1inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6iya1r" class="KcpHeO tz5f0K comp-lr6iya1r wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:18px;" class="wixui-rich-text__text">Dans certains cas, les mathématiciens peuvent amener une révolution, en utilisant une nouvelle façon de penser, en élargissant le cadre des possibles pour résoudre les problèmes.<br class="wixui-rich-text__text">
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Le 4e article présente la « révolution » de Poincaré dans la résolution d’un certain type d’équations, les équations fuchsiennes.</span></span></p></div><div id="comp-lr6j08b9" class="KcpHeO tz5f0K comp-lr6j08b9 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="text-decoration:underline;" class="wixui-rich-text__text">Petite explication par rapport à la géométrie :</span> la géométrie euclidienne (dont le précurseur est Euclide) s’étudie dans un espace euclidien, c’est-à-dire un espace « plat » lorsqu’on est en 2 dimensions.<br class="wixui-rich-text__text">
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La géométrie non-euclidienne ou hyperbolique, au contraire, étudie la géométrie dans un espace « courbe », où les lois de la géométrie euclidienne ne sont pas forcément valables. Par exemple, dans un espace euclidien, la somme des angles d’un triangle fera toujours 180°, ce qui n’est pas le cas dans un espace hyperbolique.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Poincaré réussit à faire le lien entre équations fuchsiennes et géométrie hyperbolique.<br class="wixui-rich-text__text">
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Par ailleurs, on peut parler de révolution car avant Poincaré, peu de mathématiciens s’étaient penchés sur la géométrie hyperbolique. Tandis que par la suite, la géométrie non-euclidienne a pu devenir un véritable outil mathématique.</p></div></div></div></div></div></section></div></div></section><section id="comp-lr6jbj48" tabindex="-1" class="Oqnisf comp-lr6jbj48 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6jbj48" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jbj48" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jbj48inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jbj48inlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lr6jbj71" class="comp-lr6jbj71 CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6jbj71" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6jbj71" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6jbj77" class="comp-lr6jbj77 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6jbj77" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jbj77" class="VgO9Yg"><wow-image id="img_comp-lr6jbj77" class="HlRz5e Kv1aVt dLPlxY mNGsUM bgImage" data-image-info="{"containerId":"comp-lr6jbj77","alignType":"center","displayMode":"fill","targetWidth":620,"targetHeight":362,"isLQIP":true,"imageData":{"width":6784,"height":4000,"uri":"a3c153_56669e38ce904a728a6246879d546efe~mv2.jpg","name":"","displayMode":"fill"}}" data-bg-effect-name="" data-has-ssr-src="" data-src="https://static.wixstatic.com/media/a3c153_56669e38ce904a728a6246879d546efe~mv2.jpg/v1/fill/w_1064,h_543,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/a3c153_56669e38ce904a728a6246879d546efe~mv2.jpg"><img src="https://static.wixstatic.com/media/a3c153_56669e38ce904a728a6246879d546efe~mv2.jpg/v1/fill/w_1064,h_543,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/a3c153_56669e38ce904a728a6246879d546efe~mv2.jpg" alt="" style="width: 709px; height: 362px; object-fit: cover; object-position: 50% 50%;" width="620" height="362" fetchpriority="high"></wow-image></div></div><div data-mesh-id="comp-lr6jbj77inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jbj77inlineContent-gridContainer" data-testid="mesh-container-content"></div></div></div><div id="comp-lr6jbj7q" class="comp-lr6jbj7q YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6jbj7q" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jbj7q" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jbj7qinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jbj7qinlineContent-gridContainer" data-testid="mesh-container-content"></div></div></div></div></section><section id="comp-lr6jbj7y" class="comp-lr6jbj7y CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6jbj7y" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6jbj7y" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6jbj84" class="comp-lr6jbj84 YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6jbj84" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jbj84" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jbj84inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jbj84inlineContent-gridContainer" data-testid="mesh-container-content"></div></div></div><div id="comp-lr6jbj8a" class="comp-lr6jbj8a YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6jbj8a" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jbj8a" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jbj8ainlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jbj8ainlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6jbj8h" class="KcpHeO tz5f0K comp-lr6jbj8h wixui-rich-text" data-testid="richTextElement"><h2 class="font_0 wixui-rich-text__text" style="font-size:56px; line-height:normal;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:56px;" class="wixui-rich-text__text"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text">Diffusion </span></span></span></span></h2></div><div id="comp-lr6jbj8m1" class="KcpHeO tz5f0K comp-lr6jbj8m1 wixui-rich-text" data-testid="richTextElement"><h2 class="font_8 wixui-rich-text__text" style="font-size:16px; line-height:1.8em;"><span style="letter-spacing:normal;" class="wixui-rich-text__text"><span style="font-size:16px;" class="wixui-rich-text__text"><span class="wixGuard wixui-rich-text__text"></span>Si on prend l’exemple du triangle analytique, cette méthode obtient une certaine postérité dans les pays germanophones et anglophones. On peut se demander comment Cramer a pu faire connaitre son outil, à tel point qu’il a été utilisé et cité des décennies plus tard ? Plus généralement, comment se propageaient les outils mathématiques à travers les pays ?</span></span></h2></div></div></div></div></div></section></div></div></section><section id="comp-lqyd9m03" tabindex="-1" class="Oqnisf comp-lqyd9m03 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lqyd9m03" data-hook="bgLayers" class="MW5IWV"><div id="bgMedia_comp-lqyd9m03" class="VgO9Yg"><wix-video id="videoContainer_comp-lqyd9m03" data-video-info="{"fittingType":"fill","alignType":"center","hasBgScrollEffect":"","bgEffectName":"","videoId":"11062b_2c0e918b0b1d4a95a7dd0e799202470c","videoWidth":1280,"videoHeight":720,"qualities":[{"quality":"480p","size":409920,"url":"video/11062b_2c0e918b0b1d4a95a7dd0e799202470c/480p/mp4/file.mp4"},{"quality":"720p","size":921600,"url":"video/11062b_2c0e918b0b1d4a95a7dd0e799202470c/720p/mp4/file.mp4"}],"isVideoDataExists":"1","videoFormat":"mp4","playbackRate":1,"autoPlay":true,"containerId":"comp-lqyd9m03","animatePoster":"none"}" class="bX9O_S bgVideo yK6aSC"><video id="comp-lqyd9m03_video" class="K8MSra" role="presentation" crossorigin="anonymous" playsinline="" preload="auto" muted="" loop="" tabindex="-1" autoplay="" style="height: 100%; width: 100%; object-fit: cover; object-position: center center; opacity: 1;" src="https://video.wixstatic.com/video/11062b_2c0e918b0b1d4a95a7dd0e799202470c/720p/mp4/file.mp4"></video><wow-image id="comp-lqyd9m03_img" class="HlRz5e Z_wCwr Jxk_UL bgVideoposter yK6aSC" data-image-info="{"containerId":"comp-lqyd9m03","alignType":"center","displayMode":"fill","targetWidth":980,"targetHeight":823,"isLQIP":true,"imageData":{"width":1280,"height":720,"uri":"11062b_2c0e918b0b1d4a95a7dd0e799202470cf000.jpg","name":"","displayMode":"fill","quality":{"unsharpMask":{"radius":0.33,"amount":1,"threshold":0}},"devicePixelRatio":1}}" data-bg-effect-name="" data-has-ssr-src="" style="opacity: 0;" data-src="https://static.wixstatic.com/media/11062b_2c0e918b0b1d4a95a7dd0e799202470cf000.jpg/v1/fill/w_1120,h_720,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_2c0e918b0b1d4a95a7dd0e799202470cf000.jpg"><img src="https://static.wixstatic.com/media/11062b_2c0e918b0b1d4a95a7dd0e799202470cf000.jpg/v1/fill/w_1120,h_720,al_c,q_85,usm_0.33_1.00_0.00,enc_auto/11062b_2c0e918b0b1d4a95a7dd0e799202470cf000.jpg" alt="" style="width: 1280px; height: 823px; object-fit: cover; object-position: 50% 50%;" width="980" height="823" fetchpriority="high"></wow-image></wix-video></div></div><div data-mesh-id="comp-lqyd9m03inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lqyd9m03inlineContent-gridContainer" data-testid="mesh-container-content"><section id="comp-lr6jdkgx" class="comp-lr6jdkgx CohWsy wixui-column-strip"><div id="bgLayers_comp-lr6jdkgx" data-hook="bgLayers" class="if7Vw2"><div data-testid="colorUnderlay" class="tcElKx i1tH8h"></div><div id="bgMedia_comp-lr6jdkgx" class="wG8dni"></div></div><div data-testid="columns" class="V5AUxf"><div id="comp-lr6jdkhq" class="comp-lr6jdkhq YzqVVZ wixui-column-strip__column"><div id="bgLayers_comp-lr6jdkhq" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jdkhq" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jdkhqinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jdkhqinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6jefbp" class="KcpHeO tz5f0K comp-lr6jefbp wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;">Nous pouvons trouver quelques pistes dans les articles étudiés.<br class="wixui-rich-text__text">
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En premier lieu, les mathématiciens publiaient des ouvrages, comme Cramer a écrit un ouvrage contenant sa méthode du triangle analytique.</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Ensuite, l’article mentionne que la méthode de Cramer a été citée dans différents traités, dans le dictionnaire de mathématiques de l’Encyclopédie méthodique (1784-1789), dans l’Encyclopédie d’Yverdon, et la partie Mathématiques de l’Encyclopédie méthodique, qui sont des ouvrages de diffusion scientifique. Ces ouvrages connaissent une très bonne propagation en Europe continentale, notamment en France et en Suisse, où elles sont éditées et imprimées, mais également en Europe du Nord (Hollande, Danemark et Allemagne).</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Dans l’article sur Poincaré, on apprend que ses découvertes sont publiées dans la « prestigieuse revue suédoise dirigée par Gösta Mittag-Leffler » : il s’agit de Acta Mathematica, « quʼon qualifie souvent de première revue de caractère international en mathématiques ».</p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;">Ainsi les découvertes mathématiques sont publiées à large échelle dans différents types d’ouvrages, ceci permet donc aux scientifiques d’appuyer leurs recherches sur des théorèmes et observations déjà existants, afin de se fonder sur des résultats déjà existants, et ne pas prendre du temps à chercher un résultat qui a déjà été démontré.</p></div></div></div></div></div></section></div></div></section><section id="comp-lr6k0wb6" tabindex="-1" class="Oqnisf comp-lr6k0wb6 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6k0wb6" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6k0wb6" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6k0wb6inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6k0wb6inlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6k0wc0" class="KcpHeO tz5f0K comp-lr6k0wc0 wixui-rich-text" data-testid="richTextElement"><h2 class="font_3 wixui-rich-text__text" style="font-size:38px; line-height:normal;"><span style="font-size:38px;" class="wixui-rich-text__text"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text">Une autre dimension des mathématiques </span></span></span></span></h2></div><div id="comp-lr6k0wcb1" class="KcpHeO tz5f0K comp-lr6k0wcb1 wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Dans l’article « fonctions poincaréennes », on trouve une citation de Vito Volterra (1860-1940, mathématicien et physicien italien) :</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">« On a demandé plusieurs fois : les fonctions fuchsiennes ont-elles des applications ? Mais on peut répliquer : qu’est-ce que signifie pour une théorie avoir des applications ? La pierre de touche d’une théorie consiste-t-elle dans son emploi en mécanique et en physique ? La théorie des coniques, que les Grecs ont élevée à un si haut degré de perfection, a-t-elle eu sa place d’honneur dans la géométrie le jour seulement où l’on a cru que ces courbes étaient les orbites des planètes ? Ne constituait-elle pas un monument artistique superbe, même en dehors de toute idée pratique ? »</span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"> </p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="color:#000000;" class="wixui-rich-text__text">Cet auteur souligne que la beauté des mathématiques n’est pas seulement présente lorsque ceux-ci possèdent des applications concrètes dans d’autres domaines, mais qu’elle existe déjà dans la perfection d’une idée ou d’une théorie mathématique.</span></p></div><div id="comp-lr6k4ihk" class="KcpHeO tz5f0K comp-lr6k4ihk wixui-rich-text" data-testid="richTextElement"><h2 class="font_2 wixui-rich-text__text" style="font-size:38px;"><span style="font-weight:bold;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text"><span style="font-size:38px;" class="wixui-rich-text__text">… la beauté mathématique</span></span></span></h2></div><div id="comp-lr6k5yoo" class="KcpHeO tz5f0K comp-lr6k5yoo wixui-rich-text" data-testid="richTextElement"><p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="font-size:18px;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text">Cette idée de beauté mathématique est également soulignée dans l’article sur les courbes elliptiques :</span></span></p>
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<p class="font_8 wixui-rich-text__text" style="font-size:18px;"><span style="font-size:18px;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text">« Il est tout à fait remarquable qu’un ensemble a priori « désordonné » de solutions d’une équation soit en fait muni d’une structure aussi belle que celle d’un groupe ! »</span></span><br class="wixui-rich-text__text">
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<span style="font-size:18px;" class="wixui-rich-text__text"><span style="color:#000000;" class="wixui-rich-text__text">Ainsi que dans l’article sur Minkowski : « Dans un discours prononcé à la mort de Minkowski en 1909, Hilbert note la richesse de ses applications et parle, au sujet de la démonstration, de « perle de l’art heuristique de Minkowski ».</span></span></p></div></div></div></section><section id="comp-lr6k8fkq" tabindex="-1" class="Oqnisf comp-lr6k8fkq wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6k8fkq" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6k8fkq" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6k8fkqinlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6k8fkqinlineContent-gridContainer" data-testid="mesh-container-content"><div id="comp-lr6k8fol1" class="KcpHeO tz5f0K comp-lr6k8fol1 wixui-rich-text" data-testid="richTextElement"><h2 class="font_0 wixui-rich-text__text" style="font-size:38px; line-height:normal; text-align:center;"><span style="font-size:38px;" class="wixui-rich-text__text"><span style="letter-spacing:normal;" class="wixui-rich-text__text">Ouverture</span></span></h2></div><div id="comp-lr6k9ut3" class="KcpHeO tz5f0K comp-lr6k9ut3 wixui-rich-text" data-testid="richTextElement"><p class="font_7 wixui-rich-text__text" style="font-size:18px;">Les découvertes mathématiques trouvent ou trouveront-elles toujours des applications concrètes ? Ou certains domaines sont-ils voués à être étudiés juste pour le plaisir d’explorer, la beauté des mathématiques et l’admiration d’un infini insaisissable ?</p></div></div></div></section><section id="comp-lr6jvti8" tabindex="-1" class="Oqnisf comp-lr6jvti8 wixui-section" data-block-level-container="ClassicSection"><div id="bgLayers_comp-lr6jvti8" data-hook="bgLayers" class="MW5IWV"><div data-testid="colorUnderlay" class="LWbAav Kv1aVt"></div><div id="bgMedia_comp-lr6jvti8" class="VgO9Yg"></div></div><div data-mesh-id="comp-lr6jvti8inlineContent" data-testid="inline-content" class=""><div data-mesh-id="comp-lr6jvti8inlineContent-gridContainer" data-testid="mesh-container-content"></div></div></section>
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