{"id":13443,"date":"2025-01-26T10:00:00","date_gmt":"2025-01-26T10:00:00","guid":{"rendered":"https:\/\/modernsciences.org\/staging\/4414\/?p=13443"},"modified":"2025-01-08T07:54:56","modified_gmt":"2025-01-08T07:54:56","slug":"geometry-topology-hand-in-hand-inscribed-square-problem-january-2025","status":"publish","type":"post","link":"https:\/\/modernsciences.org\/staging\/4414\/geometry-topology-hand-in-hand-inscribed-square-problem-january-2025\/","title":{"rendered":"Geometry and Topology Go Hand In Hand"},"content":{"rendered":"\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"This open problem taught me what topology is\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/IQqtsm-bBRU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"\">The <em>Inscribed Square Problem<\/em>, posed by Otto Toeplitz in 1911, asks whether every closed continuous loop contains four points forming the vertices of a square. While the problem remains unsolved, it has inspired deep exploration into topology and geometry.<\/p>\n","protected":false},"excerpt":{"rendered":"The Inscribed Square Problem, posed by Otto Toeplitz in 1911, asks whether every closed continuous loop contains four&hellip;\n","protected":false},"author":4,"featured_media":13445,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"nf_dc_page":"","fifu_image_url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d0\/Topology_joke.jpg\/2560px-Topology_joke.jpg","fifu_image_alt":"","footnotes":""},"categories":[17],"tags":[283,3772,3775,3769,1106,3763,3764,3770,3774,3771,3773,3767,3766,3768,416,3765,189],"class_list":{"0":"post-13443","1":"post","2":"type-post","3":"status-publish","4":"format-video","5":"has-post-thumbnail","7":"category-math-and-the-sciences","8":"tag-3blue1brown","9":"tag-abstract-shapes","10":"tag-boundaries-of-possibility","11":"tag-continuous-loops","12":"tag-geometry","13":"tag-inscribed-rectangles","14":"tag-inscribed-square-problem","15":"tag-klein-bottle","16":"tag-logical-deduction","17":"tag-mathematical-exploration","18":"tag-mathematical-puzzles","19":"tag-mobius-strip","20":"tag-otto-toeplitz","21":"tag-problem-solving","22":"tag-topology","23":"tag-topology-and-geometry-connection","24":"tag-youtube","25":"post_format-post-format-video","26":"cs-entry","27":"cs-video-wrap"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/13443","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/comments?post=13443"}],"version-history":[{"count":1,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/13443\/revisions"}],"predecessor-version":[{"id":13444,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/13443\/revisions\/13444"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/media\/13445"}],"wp:attachment":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/media?parent=13443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/categories?post=13443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/tags?post=13443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}