{"id":87,"date":"2022-04-12T17:47:35","date_gmt":"2022-04-12T17:47:35","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=87"},"modified":"2022-04-12T18:25:17","modified_gmt":"2022-04-12T18:25:17","slug":"solution-of-two-unit-squares-in-a-semicircle","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/12\/solution-of-two-unit-squares-in-a-semicircle\/","title":{"rendered":"Solution of Two Unit Squares in a Semicircle"},"content":{"rendered":"\n<p>As usual, my online colleague Ed Staples has provided a succinct solution to this problem. I attach his diagram and result below. You can see that he began by bisecting the chord AB and drawing the perpendicular bisector MC. He calculated the radius of the circle as an exact expression involving square roots, which has an approximate numeric value of 1.5213. This is in agreement with the value I found experimentally when using Geogebra to create the problem. The problem statement is here:  <a href=\"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/11\/two-unit-squares-in-a-semicircle\/\">https:\/\/convexabacus.xyz\/index.php\/2022\/04\/11\/two-unit-squares-in-a-semicircle\/<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"787\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/ed-soln-45-deg-square-1024x787.jpeg\" alt=\"\" class=\"wp-image-88\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/ed-soln-45-deg-square-1024x787.jpeg 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/ed-soln-45-deg-square-300x230.jpeg 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/ed-soln-45-deg-square-768x590.jpeg 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/ed-soln-45-deg-square.jpeg 1148w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>The problem was shared on LinkedIn where it was solved by Mohamad Saleh. He took a different approach using coordinate geometry and simultaneous equations. I attach his work below in two images.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"559\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution1of2.png\" alt=\"\" class=\"wp-image-91\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution1of2.png 634w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution1of2-300x265.png 300w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/figure>\n\n\n\n<p>Diagram (above) and solution (below) by Mohamad Saleh.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"918\" height=\"631\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution2of2.png\" alt=\"\" class=\"wp-image-92\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution2of2.png 918w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution2of2-300x206.png 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/Mohamad_SALEH_solution2of2-768x528.png 768w\" sizes=\"auto, (max-width: 918px) 100vw, 918px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>As usual, my online colleague Ed Staples has provided a succinct solution to this problem. I attach his diagram and result below. You can see that&#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-87","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/87","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=87"}],"version-history":[{"count":2,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/87\/revisions"}],"predecessor-version":[{"id":93,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/87\/revisions\/93"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=87"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=87"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=87"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}