{"id":321,"date":"2019-06-26T23:35:19","date_gmt":"2019-06-26T23:35:19","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=321"},"modified":"2019-11-18T21:49:39","modified_gmt":"2019-11-18T21:49:39","slug":"area-of-a-hyperbolic-wedge","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/area-of-a-hyperbolic-wedge\/","title":{"rendered":"Area of a Hyperbolic Wedge"},"content":{"rendered":"\n<p>The unit circle can be parametrized by (cos w, sin w). Given a point on it, the region cut out by this circle, the x-axis, and the ray from the origin to this point has area w\/2.<\/p>\n\n\n\n<p>As you may know, the hyperbolic cosine and hyperbolic sine functions are similar to the usual cosine and sine; they obey similar properties. Here&#8217;s a cool fact that is parallel to the one above.<\/p>\n\n\n\n<p>The parametrization (cosh w, sinh w) parametrizes a hyperbola. Given a point on it, the region cut out by this hyperbola, the x-axis, and the ray to from the origin to this point also has area w\/2!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Draw a picture!<\/p>\n\n\n\n<p><strong>The&nbsp;Math&nbsp;Behind&nbsp;the&nbsp;Fact:<\/strong><br>The above fact can be verified by integration in&nbsp;polar coordinates.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong><br>Su, Francis E., et al. &#8220;Area of a Hyperbolic Wedge.&#8221;\u00a0<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:<\/strong><br>Lesley Ward<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The unit circle can be parametrized by (cos w, sin w). Given a point on it, the region cut out&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[56,3,130,8,75],"class_list":["post-321","page","type-page","status-publish","hentry","tag-analytic-geometry","tag-easy","tag-functions","tag-geometry","tag-unit-circle"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/321","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=321"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/321\/revisions"}],"predecessor-version":[{"id":1348,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/321\/revisions\/1348"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=321"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}