{"id":675,"date":"2014-03-07T08:41:02","date_gmt":"2014-03-07T14:41:02","guid":{"rendered":"http:\/\/daylateanddollarshort.com\/bloog\/?p=675"},"modified":"2014-03-07T08:41:02","modified_gmt":"2014-03-07T14:41:02","slug":"proof-without-words-pi-from-squareroots","status":"publish","type":"post","link":"http:\/\/daylateanddollarshort.com\/bloog\/proof-without-words-pi-from-squareroots\/","title":{"rendered":"Proof without words: Pi from Square(root)s"},"content":{"rendered":"<p><br \/>\n$$ \\huge \\sqrt{2} + \\sqrt{3} \\;\\approx\\; \\pi $$<\/p>\n<p><center><br \/>\n<a href=\"http:\/\/daylateanddollarshort.com\/bloog\/wp-content\/uploads\/2014\/03\/pidentity-small1.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/daylateanddollarshort.com\/bloog\/wp-content\/uploads\/2014\/03\/pidentity-small1-300x277.png\" alt=\"pidentity-small\" width=\"300\" height=\"277\" class=\"alignnone size-medium wp-image-686\" srcset=\"http:\/\/daylateanddollarshort.com\/bloog\/wp-content\/uploads\/2014\/03\/pidentity-small1-300x277.png 300w, http:\/\/daylateanddollarshort.com\/bloog\/wp-content\/uploads\/2014\/03\/pidentity-small1.png 360w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/center><\/p>\n<p>$$\\large \\begin{align}<br \/>\n\\sqrt{2} + \\sqrt{3} &#038;= |\\overline{AB}| + |\\overline{CD}| \\\\<br \/>\n&#038;= |\\widehat{AB^\\prime}| + |\\widehat{CD^\\prime}| \\\\<br \/>\n&#038;\\approx |\\stackrel{\\frown}{AB^\\prime}| + |\\stackrel{\\frown}{CD^\\prime}| \\\\<br \/>\n&#038;\\approx |\\stackrel{\\frown}{AC}| \\\\[6pt]<br \/>\n&#038;= \\pi<br \/>\n\\end{align}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>$$ \\huge \\sqrt{2} + \\sqrt{3} \\;\\approx\\; \\pi $$ $$\\large \\begin{align} \\sqrt{2} + \\sqrt{3} &#038;= |\\overline{AB}| + |\\overline{CD}| \\\\ &#038;= |\\widehat{AB^\\prime}| + |\\widehat{CD^\\prime}| \\\\ &#038;\\approx |\\stackrel{\\frown}{AB^\\prime}| + |\\stackrel{\\frown}{CD^\\prime}| \\\\ &#038;\\approx |\\stackrel{\\frown}{AC}| \\\\[6pt] &#038;= \\pi \\end{align}$$<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-675","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/675","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/comments?post=675"}],"version-history":[{"count":10,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/675\/revisions"}],"predecessor-version":[{"id":701,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/675\/revisions\/701"}],"wp:attachment":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/media?parent=675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/categories?post=675"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/tags?post=675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}