{"id":58,"date":"2022-03-13T00:28:15","date_gmt":"2022-03-13T00:28:15","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=58"},"modified":"2022-03-13T00:29:17","modified_gmt":"2022-03-13T00:29:17","slug":"more-golden-rectangles-in-the-3-4-5-right-angled-triangle","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/03\/13\/more-golden-rectangles-in-the-3-4-5-right-angled-triangle\/","title":{"rendered":"More Golden Rectangles in the 3-4-5 Right-Angled Triangle"},"content":{"rendered":"\n<p>In my previous post <a href=\"https:\/\/convexabacus.xyz\/index.php\/2022\/02\/17\/golden-rectangles-in-a-right-triangle\/\">Golden Rectangles in a Right Triangle<\/a> I constructed three golden rectangles in the right-angled triangle with sides of length 3, 4, and 5. I continue this construction by drawing lines through existing points, then marking new points at the intersections of perpendicular lines. This results in two more golden rectangles being identified, these each being flush with one of the perpendicular sides of the triangle and with each other. Their dimensions are 1 x \u03c6 and 2 x 2\/\u03c6, where \u03c6 is the golden ratio. They are shaded in the diagram. A <a href=\"https:\/\/convexabacus.xyz\/index.php\/2022\/02\/20\/proof-that-the-golden-ratio-is-in-the-3-4-5-right-triangle\/\">trigonometric proof by Ed Staples<\/a> shows that \u03c6 is indeed key to this construction.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"985\" height=\"1024\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-985x1024.png\" alt=\"\" class=\"wp-image-60\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-985x1024.png 985w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-289x300.png 289w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-768x798.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-1478x1536.png 1478w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/03\/more-golden-rectangles-in-the-345-right-triangle-1970x2048.png 1970w\" sizes=\"auto, (max-width: 985px) 100vw, 985px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In my previous post Golden Rectangles in a Right Triangle I constructed three golden rectangles in the right-angled triangle with sides of length 3, 4, and&#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-58","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/58","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=58"}],"version-history":[{"count":2,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/58\/revisions"}],"predecessor-version":[{"id":61,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/58\/revisions\/61"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=58"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=58"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=58"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}