{"id":223,"date":"2016-03-14T01:21:44","date_gmt":"2016-03-14T06:21:44","guid":{"rendered":"https:\/\/trigonography.com\/?p=223"},"modified":"2022-06-25T04:24:11","modified_gmt":"2022-06-25T09:24:11","slug":"nearly-pi-from-square-roots-2","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=223","title":{"rendered":"(Nearly-)Pi from Square Roots"},"content":{"rendered":"\n<p class=\"has-text-align-center\" style=\"font-size:16px\">A little something for Pi Day.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/03\/trigonograph-sqrt2sqrt3pi@2x.png\" rel=\"attachment wp-att-177\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/03\/trigonograph-sqrt2sqrt3pi@2x.png\" alt=\"trigonograph-sqrt2+sqrt3=pi@2x\" class=\"wp-image-177\" width=\"640\" height=\"640\"\/><\/a><\/figure>\n<\/div>\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt\">$$\\begin{align}<br>\\sqrt{2} + \\sqrt{3} &amp;\\;=\\; |\\overline{AB}| + |\\overline{CD}| \\\\[6pt]<br>\\large &amp;\\;=\\; |\\widehat{AB^\\prime}| + |\\widehat{CD^\\prime}| \\\\[4pt]<br>\\large &amp;\\;\\approx\\; |\\stackrel{\\frown}{AB^\\prime}| + |\\stackrel{\\frown}{CD^\\prime}| \\\\[4pt]<br>\\large &amp;\\;\\approx\\; |\\stackrel{\\frown}{AC}| \\\\[4pt]<br>\\large &amp;\\;=\\; \\pi<br>\\end{align}<br>$$<\/div>\n\n\n\n<div style=\"text-align:center;font-size:12pt;margin-top:40px;\"><b>Get the t-shirt!<\/b><br>\n<a href=\"https:\/\/inspired-by-math.creator-spring.com\/listing\/approx-pi\"><img decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2022\/06\/tmock-approxpi.jpg\" width=\"360\" style=\"margin-top:12px\" \/><\/a>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A little something for Pi Day. $$\\begin{align}\\sqrt{2} + \\sqrt{3} &amp;\\;=\\; |\\overline{AB}| + |\\overline{CD}| \\\\[6pt]\\large &amp;\\;=\\; |\\widehat{AB^\\prime}| + |\\widehat{CD^\\prime}| \\\\[4pt]\\large &amp;\\;\\approx\\; |\\stackrel{\\frown}{AB^\\prime}| + |\\stackrel{\\frown}{CD^\\prime}| \\\\[4pt]\\large &amp;\\;\\approx\\; |\\stackrel{\\frown}{AC}| \\\\[4pt]\\large &amp;\\;=\\; \\pi\\end{align}$$ Get the t-shirt!<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-223","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=223"}],"version-history":[{"count":7,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/223\/revisions"}],"predecessor-version":[{"id":1246,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/223\/revisions\/1246"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}