{"id":76,"date":"2022-04-11T20:46:06","date_gmt":"2022-04-11T20:46:06","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=76"},"modified":"2022-04-12T17:22:33","modified_gmt":"2022-04-12T17:22:33","slug":"three-equal-squares-in-a-semicircle","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/11\/three-equal-squares-in-a-semicircle\/","title":{"rendered":"Three Equal Squares in a Semicircle"},"content":{"rendered":"\n<p>In this construction three unit squares are butted up together inside a semicircle. Each square has a vertex that touches the circumference, and the vertices of two of the squares lie on the diameter shown. The vertical diagonal of the middle square is in line with the circle\u2019s centre, so everything looks quite symmetrical. Can you find the exact value of the radius of the circle? I constructed this arrangement experimentally using Geogebra. I thank Ed Staples for this concise statement of the problem.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"590\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-1024x590.png\" alt=\"\" class=\"wp-image-79\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-1024x590.png 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-300x173.png 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-768x442.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-1536x885.png 1536w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/three-equal-squares-in-a-semicircle-1-2048x1180.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>This problem was shared on LinkedIn, where it was solved by St\u00e9phane Jaubert who calculated the radius as r=13.sqrt(2)\/10. His work is attached below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"966\" height=\"707\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/StephaneJaubertSolutionOfThreeEqualSquares.jpg\" alt=\"\" class=\"wp-image-85\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/StephaneJaubertSolutionOfThreeEqualSquares.jpg 966w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/StephaneJaubertSolutionOfThreeEqualSquares-300x220.jpg 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/StephaneJaubertSolutionOfThreeEqualSquares-768x562.jpg 768w\" sizes=\"auto, (max-width: 966px) 100vw, 966px\" \/><figcaption>Problem solution<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In this construction three unit squares are butted up together inside a semicircle. Each square has a vertex that touches the circumference, and the vertices of&#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-76","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/76","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=76"}],"version-history":[{"count":3,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/76\/revisions"}],"predecessor-version":[{"id":86,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/76\/revisions\/86"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=76"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=76"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}