{"id":589,"date":"2019-01-04T11:36:04","date_gmt":"2019-01-04T03:36:04","guid":{"rendered":"https:\/\/squarez.motd.org\/?p=589"},"modified":"2020-02-09T12:34:59","modified_gmt":"2020-02-09T04:34:59","slug":"pythagoras-and-agrippa","status":"publish","type":"post","link":"https:\/\/squarez.motd.org\/?p=589","title":{"rendered":"Pythagoras and Agrippa"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Of right triangles and odd squares<\/p><cite>If we look at the center of the odd sized squares in Agrippa&#8217;s magic squares (Saturn, Mars, Mercury, Moon), we can spot lengths of the sides of right triangles. By extension, this holds for all odd sized squares built in the same way.<br><br><em>3\u00b2 + 4\u00b2 = 5\u00b2<\/em> <br>5\u00b2 + 12\u00b2 = 13\u00b2<br>7\u00b2 + 24\u00b2 = 25\u00b2<br>9\u00b2 + 40\u00b2 = 41\u00b2<br>&#8230;<br>27\u00b2 + 364\u00b2 = 365\u00b2<br>&#8230;<\/cite><\/blockquote>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"939\" height=\"644\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2019\/01\/Squares-and-Triangles.png\" alt=\"\" class=\"wp-image-590\" srcset=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2019\/01\/Squares-and-Triangles.png 939w, https:\/\/squarez.motd.org\/wp-content\/uploads\/2019\/01\/Squares-and-Triangles-300x206.png 300w, https:\/\/squarez.motd.org\/wp-content\/uploads\/2019\/01\/Squares-and-Triangles-768x527.png 768w\" sizes=\"auto, (max-width: 939px) 100vw, 939px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Of magic triangles<\/p><cite>Now if we consider the associated right triangles sides length (Saturn, Mars, Mercury &amp; Venus triangles).<br><br>3\u00b2 = 4 + 5<br>5\u00b2 = 12 + 13<br>7\u00b2 = 24 + 25<br>9\u00b2 = 40 + 41<br>&#8230;<br>27\u00b2 = 364 + 365<br>&#8230;<\/cite><\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Of squares summed<\/p><cite>Then looking at the center square of each odd sized squares, we can see that they can be written as sum of two squares.<br><br>  5 = 1 \u00b2 + 2 \u00b2 <br>13 = 2 \u00b2+ 3 \u00b2 <br>25 = 3 \u00b2+ 4 \u00b2 <br>41 = 4 \u00b2+ 5 \u00b2 <br>&#8230;<br>365 = 13 \u00b2 + 14 \u00b2 <br>&#8230;<\/cite><\/blockquote>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Of right triangles and odd squares If we look at the center of the odd sized squares in Agrippa&#8217;s magic squares (Saturn, Mars, Mercury, Moon), we can spot lengths of the sides of right triangles. By extension, this holds for &hellip; <a href=\"https:\/\/squarez.motd.org\/?p=589\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-589","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/589","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=589"}],"version-history":[{"count":7,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/589\/revisions"}],"predecessor-version":[{"id":693,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/589\/revisions\/693"}],"wp:attachment":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}