{"id":31,"date":"2022-02-17T01:34:08","date_gmt":"2022-02-17T01:34:08","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=31"},"modified":"2022-02-17T21:39:23","modified_gmt":"2022-02-17T21:39:23","slug":"paper-triangles-in-a-circle-maximising-area","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/02\/17\/paper-triangles-in-a-circle-maximising-area\/","title":{"rendered":"Paper Triangles in a Circle Maximising Area"},"content":{"rendered":"\n<p>Three equal right-angled triangles are inscribed in a circle. They are positioned around an equilateral triangle which stabilises the construction. The triangles are cut from paper, with dimensions noted. The right-angled triangles are 7\u2033 x 9\u201d = 17.8 cm x 22.3 cm, and the equilateral triangle has side length 2.46\u2033 = 6.24 cm. The six outermost points are equidistant from the centre of the equilateral triangle, thus lying on a circle, which is not shown. Iterative modelling with Geogebra found that this construction maximises the area of the circle covered by the three right-angled triangles. The ratio 7:9 of side lengths is a rational approximation to a numerical value found experimentally.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-1024x768.jpg\" alt=\"\" class=\"wp-image-32\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-1024x768.jpg 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-300x225.jpg 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-768x576.jpg 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-1536x1152.jpg 1536w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/02\/ThreeRightTrianglesInCirclePaper4-2048x1536.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Three equal right-angled triangles are inscribed in a circle. They are positioned around an equilateral triangle which stabilises the construction. The triangles are cut from paper,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-31","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/31","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=31"}],"version-history":[{"count":2,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/31\/revisions"}],"predecessor-version":[{"id":46,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/31\/revisions\/46"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=31"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=31"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=31"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}