{"id":309268,"date":"2026-10-27T13:49:04","date_gmt":"2026-10-27T12:49:04","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=309268"},"modified":"2026-10-27T13:52:05","modified_gmt":"2026-10-27T12:52:05","slug":"topologie","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/topologie\/","title":{"rendered":"Topologie : les myst\u00e8res de cette branche des maths \ud83e\udde9"},"content":{"rendered":"<section class=\"you-know\"><div class=\"you-know__title\"><p>\ud83e\udde0 \u00c0 retenir :<\/p><\/div><div class=\"you-know__text\"><ul>\n<li>La topologie est une branche des math\u00e9matiques qui explore les propri\u00e9t\u00e9s et les structures invariantes par d\u00e9formation continue.<\/li>\n<li>Elle repose sur des notions cl\u00e9s comme l\u2019espace topologique, les ensembles ouverts et ferm\u00e9s, la continuit\u00e9 et l\u2019hom\u00e9omorphisme.<\/li>\n<li>Ses applications couvrent la g\u00e9om\u00e9trie, les r\u00e9seaux et l\u2019informatique th\u00e9orique, ainsi que l\u2019analyse de donn\u00e9es par l\u2019homologie persistante.<\/li>\n<li>Des exemples concrets comme les anneaux borrom\u00e9ens et le ruban de M\u00f6bius illustrent des ph\u00e9nom\u00e8nes topologiques et des d\u00e9formations utiles en robotique.<\/li>\n<\/ul><\/div><\/section>\n\n<p>La <strong>topologie<\/strong> est une <a href=\"https:\/\/sherpas.com\/cours\/maths\">branche des math\u00e9matiques<\/a> qui explore les propri\u00e9t\u00e9s et les structures invariantes par d\u00e9formation continue. Cette discipline analyse les espaces, les situations et les syst\u00e8mes pour comprendre comment ils peuvent \u00eatre transform\u00e9s sans alt\u00e9rer leurs caract\u00e9ristiques essentielles. Ce domaine se distingue par sa capacit\u00e9 \u00e0 traiter des concepts tels que la <strong>continuit\u00e9<\/strong>, les <strong>fonctions<\/strong> et les <strong>limites<\/strong>, offrant ainsi un cadre th\u00e9orique puissant utilis\u00e9 dans diverses applications pratiques.<\/p>\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udccc En bref<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p>La topologie est la branche des math\u00e9matiques qui \u00e9tudie les propri\u00e9t\u00e9s d\u2019une forme conserv\u00e9es par d\u00e9formation continue, sans d\u00e9chirer ni recoller. Elle repose sur les notions d\u2019ouvert, de voisinage et de continuit\u00e9. Un espace topologique est un ensemble muni d\u2019une famille d\u2019ouverts qui contient le vide et l\u2019espace entier, stable par union quelconque et par intersection finie. Une tasse et un donut ont la m\u00eame forme topologique : un hom\u00e9omorphisme passe de l\u2019une \u00e0 l\u2019autre. On l\u2019\u00e9tudie en pr\u00e9pa, avec la topologie des espaces vectoriels norm\u00e9s, puis en licence de maths, avec la topologie g\u00e9n\u00e9rale et les espaces m\u00e9triques.<\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"definitions-et-concepts-fondamentaux-de-la-topologie\">D\u00e9finitions et concepts fondamentaux de la topologie<\/h2>\n\n\n<p>Pour mieux appr\u00e9hender la topologie, il est indispensable de conna\u00eetre certains concepts cl\u00e9s qui constituent la trame de cette discipline. Ces notions permettent de dresser un portrait d\u2019ensemble des id\u00e9es majeures et des outils utilis\u00e9s en topologie.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"que-veut-dire-topologie\">Que veut dire topologie ?<\/h3>\n\n\n\n<p>Le mot topologie vient du grec topos, le lieu, et logos, le discours. Listing l\u2019emploie en 1847, mais le premier probl\u00e8me de topologie date d\u2019Euler, avec les sept ponts de K\u00f6nigsberg (1735-1736). Poincar\u00e9 pose ensuite les bases de la topologie alg\u00e9brique avec Analysis situs (1895), puis Hausdorff d\u00e9finit les espaces topologiques par des axiomes en 1914.<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" data-banner=\"2\" data-name=\"CPM1 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div 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      xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                    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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     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          class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Pierre2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Pierre<\/p>                          <p class=\"push__teachers-school\">ESSEC<\/p>                                                     <div 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  class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            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xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Jade2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Jade<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                 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       <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Besoin d&rsquo;un <span style=\"color: #4cc583;\">prof particulier<\/span> de maths ? <span role=\"image\" aria-label=\"\u2728\">\u2728<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos Sherpas sont l\u00e0 pour t&rsquo;aider \u00e0 progresser et prendre confiance en toi !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS OFFERT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"espace-topologique\">Espace topologique<\/h3>\n\n\n<p>L\u2019<strong>espace topologique<\/strong> est la notion centrale de la topologie. Un espace topologique est constitu\u00e9 d\u2019un ensemble de points, appel\u00e9 espace, accompagn\u00e9 d\u2019une collection de sous-ensembles appel\u00e9e topologie. Ces sous-ensembles, appel\u00e9s ouverts, permettent de d\u00e9finir le voisinage d\u2019un point et la continuit\u00e9 d\u2019une fonction. Un espace topologique se doit de satisfaire certaines propri\u00e9t\u00e9s telles que l\u2019inclusion de l\u2019ensemble vide et de l\u2019espace entier, ainsi que la stabilit\u00e9 par union quelconque et par intersection finie.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"ouvert-et-ferme\">Ouvert et ferm\u00e9<\/h3>\n\n\n<p>Les <strong>ensembles ouverts<\/strong> et les <strong>ensembles ferm\u00e9s<\/strong> sont des entit\u00e9s cruciales dans un espace topologique. Un ensemble ouvert ne contient pas ses points fronti\u00e8res, tandis qu\u2019un ensemble ferm\u00e9 les inclut. Comprendre ces diff\u00e9rences permet de cerner comment l\u2019information circule \u00e0 travers des r\u00e9seaux et comment les circuits complexes se comportent dans diff\u00e9rentes r\u00e9gions de l\u2019espace.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"continuite-et-homeomorphisme\">Continuit\u00e9 et hom\u00e9omorphisme<\/h3>\n\n\n<p>Deux notions importantes en topologie sont la <strong>continuit\u00e9<\/strong> et l\u2019<strong>hom\u00e9omorphisme<\/strong>. Une fonction continue pr\u00e9serve la proximit\u00e9 des points, ce qui signifie qu\u2019une petite modification de l\u2019entr\u00e9e entra\u00eene une petite modification de la sortie. L\u2019hom\u00e9omorphisme est une application bijective continue dont l\u2019inverse est \u00e9galement continu ; il \u00e9tablit une \u00e9quivalence entre deux espaces topologiques, signifiant qu\u2019ils partagent les m\u00eames propri\u00e9t\u00e9s topologiques m\u00eame s\u2019ils diff\u00e8rent g\u00e9om\u00e9triquement.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"base-dune-topologie\">Base d\u2019une topologie<\/h3>\n\n\n<p>Une <strong>base d\u2019une topologie<\/strong> est une collection sp\u00e9cifique d\u2019ouverts capables de g\u00e9n\u00e9rer toute la topologie par unions quelconques. Cette base offre un moyen efficace de visualiser et de manipuler des espaces complexes, facilitant ainsi des processus d\u2019optimisation en minimisant le nombre de composants n\u00e9cessaires pour constituer la topologie compl\u00e8te.<\/p>\n\n<div style=\"position:relative;overflow:hidden;padding-top:56.25%\"><iframe style=\"position:absolute;top:0;left:0;width:95%;height:100%;border:0\" src=\"https:\/\/www.youtube.com\/embed\/h_5zSlvIcvE?si=4fvg-MWKP6y0LzgS&#038;controls=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"applications-et-implications-pratiques-de-la-topologie\">Applications et implications pratiques de la topologie<\/h2>\n\n\n<p>La topologie, bien que th\u00e9orique, trouve des applications dans divers domaines pratiques. Des ing\u00e9nieurs en r\u00e9seau aux artistes num\u00e9riques, de nombreux professionnels tirent avantage des concepts topologiques.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"topologie-et-geometrie\">Topologie et g\u00e9om\u00e9trie<\/h3>\n\n\n<p>En g\u00e9om\u00e9trie, la topologie aide \u00e0 \u00e9tudier les figures ind\u00e9pendamment de leurs formes pr\u00e9cises. Par exemple, dans l\u2019analyse des surfaces ou objets tridimensionnels, la topologie fournit des outils permettant de naviguer et de mod\u00e9liser leur structure complexe sans tenir compte de mesures exactes. Cela rev\u00eat une importance capitale dans la conception et l\u2019optimisation de structures architecturales ou m\u00e9caniques.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"topologie-des-reseaux\">Topologie des r\u00e9seaux<\/h3>\n\n\n<p>Dans le contexte des r\u00e9seaux informatiques et des syst\u00e8mes de communication, la topologie joue un r\u00f4le crucial en influen\u00e7ant la mani\u00e8re dont les informations circulent. Diff\u00e9rentes configurations comme les <strong>topologies en \u00e9toile, en anneau ou en maillage<\/strong> d\u00e9crivent les interconnexions entre n\u0153uds et impactent directement l\u2019efficacit\u00e9 et la robustesse du syst\u00e8me. Analyser la topologie des r\u00e9seaux offre donc des perspectives pour am\u00e9liorer la fiabilit\u00e9 et la performance des communications.<\/p>\n\n<ul>\n  <li>Topologie en \u00e9toile<\/li>\n  <li>Topologie en anneau<\/li>\n  <li>Topologie en maillage<\/li>\n <\/ul>\n\n\n<h3 class=\"wp-block-heading\" id=\"topologie-algebrique\">Topologie alg\u00e9brique<\/h3>\n\n\n<p>La <strong>topologie alg\u00e9brique<\/strong> utilise des m\u00e9thodes alg\u00e9briques pour \u00e9tudier les espaces topologiques. En assignant des invariants alg\u00e9briques aux espaces, elle permet de comparer et classifier diff\u00e9rents espaces sur la base de leurs propri\u00e9t\u00e9s int\u00e9rieures, telles que les <strong>groupes de cohomologie<\/strong> ou les <strong>groupes d\u2019homotopie<\/strong>. Ces invariants fournissent des solutions \u00e9l\u00e9gantes \u00e0 des probl\u00e8mes tels que le calcul des chemins dans les circuits \u00e9lectroniques.<\/p>\n\n<div style=\"justify-content:center;align-items:center;margin-top:5px;margin-bottom:5px\"><img decoding=\"async\" src=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/p\/files\/photos\/maths\/topologie-2.webp?w=640&#038;q=95\" alt=\"Image qui repr\u00e9sente la Topologie\" width=\"640\" height=\"400\" style=\"width:100%;max-width:500px;height:auto;margin:0.9rem 0 0.9rem 0\" loading=\"lazy\"><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"analyse-des-donnees-et-intelligence-artificielle\">Analyse des donn\u00e9es et intelligence artificielle<\/h3>\n\n\n<p>La topologie est utilis\u00e9e dans l\u2019<strong>analyse de grandes bases de donn\u00e9es<\/strong> via des algorithmes d\u2019homologie persistante. Elle aide \u00e0 r\u00e9v\u00e9ler des structures cach\u00e9es et des patterns dans des sets de donn\u00e9es complexes, contribuant ainsi aux avanc\u00e9es en intelligence artificielle et apprentissage machine. Cette approche permet une interpr\u00e9tation plus intuitive et visuelle des corr\u00e9lations entre les donn\u00e9es recueillies.<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"exemples-et-cas-pratiques\">Exemples et cas pratiques<\/h2>\n\n\n<p>Naviguer \u00e0 travers une s\u00e9rie d\u2019exemples concrets peut rendre la compr\u00e9hension de la topologie plus accessible. Voici quelques illustrations pratiques pour mettre en lumi\u00e8re la puissance de cette branche des math\u00e9matiques.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"illustration-par-les-anneaux-borromeens\">Illustration par les anneaux borrom\u00e9ens<\/h3>\n\n\n<p>Les <strong>anneaux borrom\u00e9ens<\/strong> illustrent joliment certains principes topologiques. Trois anneaux imbriqu\u00e9s forment un tout ins\u00e9cable, mais si l\u2019on retire un seul anneau, les deux autres se s\u00e9parent. Cet exemple d\u00e9montre comment des structures complexes peuvent exister alors m\u00eame que chaque composant individuel reste simple. C\u2019est une belle d\u00e9monstration du pouvoir des liens topologiques au sein des r\u00e9seaux interconnect\u00e9s.<\/p>\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" data-banner=\"2\" data-name=\"CPM2 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Antoine2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Antoine<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Pierre2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Pierre<\/p>                          <p class=\"push__teachers-school\">ESSEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">16\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Emma2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Emma<\/p>                          <p class=\"push__teachers-school\">Dauphine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">15\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Thibault2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Thibault<\/p>                          <p class=\"push__teachers-school\">ENS Paris Ulm<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Martin2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Martin<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">23\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Agathe2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Agathe<\/p>                          <p class=\"push__teachers-school\">ENS Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Fabien2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fabien<\/p>                          <p class=\"push__teachers-school\">T\u00e9l\u00e9com Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Ton premier <span style=\"color: #4cc483;\">cours particulier<\/span> de maths est <span style=\"color: #4cc483;\">offert<\/span> ! <span role=\"image\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Tous nos profs sont pass\u00e9s par les meilleures \u00e9coles de France !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        J\u2019EN PROFITE !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n<div style=\"position:relative;overflow:hidden;padding-top:56.25%\"><iframe style=\"position:absolute;top:0;left:0;width:95%;height:100%;border:0\" src=\"https:\/\/www.youtube.com\/embed\/hE_1_MSOjt0?si=IUsurc-AaLqV2pp2&#038;controls=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"le-ruban-de-mobius\">Le ruban de M\u00f6bius<\/h3>\n\n\n<p>Le <strong>ruban de M\u00f6bius<\/strong> est une surface avec une seule face et un seul bord. En le d\u00e9coupant par le milieu, dans le sens de la longueur, on obtient un seul ruban et non deux. Le ruban de M\u00f6bius est l\u2019exemple type d\u2019une surface non orientable. Voil\u00e0 un exemple frappant des ph\u00e9nom\u00e8nes contre-intuitifs explor\u00e9s gr\u00e2ce \u00e0 la topologie, impliquant non seulement les math\u00e9maticiens mais aussi des artistes fascin\u00e9s par cet \u00e9trange concept g\u00e9om\u00e9trique.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"homotopies-et-deformations-continues\">Homotopies et d\u00e9formations continues<\/h3>\n\n\n<p>Un exemple pratique de l\u2019utilisation des <strong>homotopies<\/strong> r\u00e9side dans la robotique, o\u00f9 les trajets robotiques doivent souvent \u00eatre ajust\u00e9s pour \u00e9viter des obstacles sans casser la continuit\u00e9 du mouvement. Les homotopies guident ces mouvements optimis\u00e9s reliant des points dans un espace configur\u00e9 de mani\u00e8re syst\u00e9matique et fluide.<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"topologie-et-autres-disciplines-scientifiques\">Topologie et autres disciplines scientifiques<\/h2>\n\n\n<p>En tant que champ transversal, la topologie influence de nombreuses autres disciplines scientifiques, r\u00e9v\u00e9lant son interconnexion avec des secteurs vari\u00e9s tels que la physique, la biologie et la science informatique.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"physique-theorique\">Physique th\u00e9orique<\/h3>\n\n\n<p>En physique th\u00e9orique, notamment dans la <strong>th\u00e9orie quantique des champs<\/strong>, la topologie \u00e9claire des questions fondamentales comme la nature de l\u2019univers. La classification des particules \u00e9l\u00e9mentaires b\u00e9n\u00e9ficie de l\u2019application des concepts topologiques, en particulier lors de la manipulation d\u2019espaces de dimension sup\u00e9rieure et de l\u2019\u00e9tude des singularit\u00e9s. L\u2019impact des structures topologiques y est donc significatif pour comprendre et mod\u00e9liser le cosmos.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"biologie-et-dynamiques-des-populations\">Biologie et dynamiques des populations<\/h3>\n\n\n<p>Les mod\u00e8les dynamiques en <strong>biologie<\/strong> servent \u00e0 observer les comportements des populations biologiques bas\u00e9s sur des r\u00e9seaux de pr\u00e9dation et d\u2019alimentation. La topologie met en \u00e9vidence les routes critiques dans ces r\u00e9seaux \u00e9cologiques, facilitant l\u2019\u00e9tablissement de strat\u00e9gies pour la conservation des esp\u00e8ces et la gestion des environnements naturels.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"cerveau-et-neurosciences\">Cerveau et neurosciences<\/h3>\n\n\n<p>Les <strong>neurosciences<\/strong> font appel \u00e0 la topologie pour cartographier le cerveau et analyser les circuits neuronaux. Les chercheurs utilisent des <a href=\"https:\/\/sherpas.com\/blog\/theorie-des-graphes\/\">graphes topologiques<\/a> et l\u2019homologie persistante afin d\u2019\u00e9tudier les modes de communication neuronale et d\u00e9tecter des anomalies pouvant mener \u00e0 des troubles cognitifs. Cela conduit \u00e0 une meilleure compr\u00e9hension des fonctions c\u00e9r\u00e9brales, ouvrant des portes pour de nouvelles th\u00e9rapeutiques neurologiques.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"informatique-theorique\">Informatique th\u00e9orique<\/h3>\n\n\n<p>La topologie joue un r\u00f4le crucial dans l\u2019<strong>informatique th\u00e9orique<\/strong>, particuli\u00e8rement dans la conception d\u2019algorithmes distribu\u00e9s et la v\u00e9rification de syst\u00e8mes complexes. L\u2019id\u00e9e de continuit\u00e9 et de transformation appliqu\u00e9e aux espaces infiniment divisibles sert \u00e0 \u00e9laborer des preuves rigoureuses concernant le comportement des programmes informatiques, garantissant ainsi leur pr\u00e9cision et efficacit\u00e9.<\/p>\n\n<div style=\"line-height:1.7;margin-top:0.75rem;margin-bottom:0.25rem;letter-spacing:-0.01em\">Nos autres articles sur <a href=\"https:\/\/sherpas.com\/blog\/exploration-geometrie-topologie\/\">la g\u00e9om\u00e9trie et la topologie<\/a> :<br><ul>\n<li><a href=\"https:\/\/sherpas.com\/blog\/geometrie-algebrique\/\">G\u00e9om\u00e9trie Alg\u00e9brique<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/geometrie-differentielle\/\">G\u00e9om\u00e9trie Diff\u00e9rentielle<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/geometrie-non-euclidienne\/\">G\u00e9om\u00e9trie Non Euclidienne<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/geometrie-hyperbolique\/\">G\u00e9om\u00e9trie Hyperbolique<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/geometrie-spherique\/\">G\u00e9om\u00e9trie Sph\u00e9rique<\/a><\/li>\n<\/ul><\/div>\n\n<section class=\"faq\">\n    <div class=\"container\" itemscope itemtype=\"http:\/\/schema.org\/FAQPage\">\n        <div class=\"faq__title\">\n                        <h2 id=\"faq\">FAQ \u2705<\/h2>\n                    <\/div>\n         <div class=\"faq__questions\">\n                                                                             <div class=\"faq__questions--item \" itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n                <div class=\"faq__questions--title  collapsed\">\n                    <p class=\"h4\" itemprop=\"name\">Qu\u2019est-ce que la topologie logique ?<\/p>\n                    <svg>\n                        <use\n                        xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#chevron-right\"\/>\n                    <\/svg>\n                <\/div>\n                <div class=\"faq__questions--content\" style=\"max-height: 0px\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                    <div itemprop=\"text\"><p>La topologie logique d\u2019un r\u00e9seau informatique d\u00e9crit le chemin suivi par les donn\u00e9es entre les appareils, alors que la topologie physique d\u00e9crit la disposition des c\u00e2bles et des \u00e9quipements.<\/p>\n<\/div>\n                <\/div>\n             <\/div>\n                                                                 <div class=\"faq__questions--item \" itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n                <div class=\"faq__questions--title  collapsed\">\n                    <p class=\"h4\" itemprop=\"name\">Quelle est la diff\u00e9rence entre topologie et topographie ?<\/p>\n                    <svg>\n                        <use\n                        xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#chevron-right\"\/>\n                    <\/svg>\n                <\/div>\n                <div class=\"faq__questions--content\" style=\"max-height: 0px\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                    <div itemprop=\"text\"><p>La topographie mesure le relief d\u2019un terrain (altitudes, distances), alors que la topologie ignore les mesures et ne garde que les propri\u00e9t\u00e9s qui r\u00e9sistent aux d\u00e9formations, comme le nombre de trous.<\/p>\n<\/div>\n                <\/div>\n             <\/div>\n                                <\/div>\n    <\/div>\n<\/section>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;309268&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;2&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;5&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;5\\\/5 - (2 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Topologie : les myst\u00e8res de cette branche des maths \ud83e\udde9&quot;,&quot;width&quot;:&quot;142.5&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 142.5px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            5\/5 - (2 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>\ud83e\udde0 \u00c0 retenir : La topologie est une branche des math\u00e9matiques qui explore les propri\u00e9t\u00e9s et les structures (&#8230;)<\/p>\n","protected":false},"author":326,"featured_media":309122,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[],"class_list":["post-309268","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/309268","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/326"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=309268"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/309268\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/309122"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=309268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=309268"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=309268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}