{"id":90,"date":"2023-07-30T20:20:08","date_gmt":"2023-07-30T18:20:08","guid":{"rendered":"https:\/\/www.arnold-artiste.be\/?p=90"},"modified":"2023-08-06T20:17:35","modified_gmt":"2023-08-06T18:17:35","slug":"la-boucle","status":"publish","type":"post","link":"https:\/\/www.arnold-artiste.be\/index.php\/2023\/07\/30\/la-boucle\/","title":{"rendered":"La boucle"},"content":{"rendered":"\n

Une boucle ferm\u00e9e. Si on tire sur les extr\u00e9mit\u00e9s, obtient-on un n\u0153ud ou pas\u00a0?\u00a0<\/p>\n\n\n\n

La topologie est l\u2019\u00e9tude des propri\u00e9t\u00e9s invariantes dans la d\u00e9formation g\u00e9om\u00e9trique des objets et dans les transformations continues appliqu\u00e9es \u00e0 des \u00eatres math\u00e9matiques.<\/p>\n\n\n\n

La\u00a0th\u00e9orie\u00a0des\u00a0n\u0153uds<\/a>\u00a0est une branche de la\u00a0topologie\u00a0qui consiste en l\u2019\u00e9tude math\u00e9matique de courbes pr\u00e9sentant des liaisons avec elles-m\u00eames, un \u00ab\u00a0bout de ficelle\u00a0\u00bb id\u00e9alis\u00e9 en\u00a0lacets. La th\u00e9orie des n\u0153uds a commenc\u00e9 vers 1860\u00a0avec des travaux de\u00a0Carl Friedrich Gauss<\/a>\u00a0li\u00e9s \u00e0 l\u2019\u00e9lectromagn\u00e9tisme. <\/p>\n\n\n\n

Nous y voil\u00e0.<\/p>\n\n\n\n

La th\u00e9orie des n\u0153uds est tr\u00e8s proche de la\u00a0th\u00e9orie des tresses<\/a>\u00a0qui comporte plusieurs\u00a0chemins\u00a0ou \u00ab\u00a0bouts de ficelle\u00a0\u00bb. Les tresses ont une structure de\u00a0groupe\u00a0naturelle, et poss\u00e8dent des liens profonds avec des domaines divers des\u00a0math\u00e9matiques\u00a0notamment en\u00a0topologie,\u00a0th\u00e9orie des n\u0153uds\u00a0et\u00a0combinatoire alg\u00e9brique. Cette th\u00e9orie trouve des applications en\u00a0physique statistique, en\u00a0m\u00e9canique quantique\u00a0ainsi qu\u2019en\u00a0informatique th\u00e9orique, par exemple en\u00a0cryptographie.<\/p>\n\n\n

\n
\"\"<\/a>
La boucle \u2013 Encre sur papier \u2013 Juin 2013<\/figcaption><\/figure>\n<\/div>\n\n\n

Caract\u00e9ristiques<\/h2>\n\n\n\n

Encre sur papier, juin 2013, A4<\/p>\n","protected":false},"excerpt":{"rendered":"

Une boucle ferm\u00e9e. Si on tire sur les extr\u00e9mit\u00e9s, obtient-on un n\u0153ud ou pas\u00a0?\u00a0 La topologie est l\u2019\u00e9tude des propri\u00e9t\u00e9s invariantes dans la d\u00e9formation g\u00e9om\u00e9trique…<\/p>\n

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