{"id":431,"date":"2019-06-27T17:44:52","date_gmt":"2019-06-27T17:44:52","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=431"},"modified":"2019-12-09T22:18:26","modified_gmt":"2019-12-09T22:18:26","slug":"one-two-three-pi","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/one-two-three-pi\/","title":{"rendered":"One, Two, Three, Pi"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Here’s an interesting formula:<\/p>\n\n\n\n

Arctan(1) + Arctan(2) + Arctan(3) = Pi.<\/p>\n\n\n\n

(Everything’s in radians, of course). <\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
Challenge students to prove this fact.<\/p>\n\n\n\n

The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong>
The Figure contains a hint; check that the angles of the three\u00a0triangles\u00a0at their common vertex add to Pi. Can you find a similar proof for the following equation?
Arctan(1\/2)+Arctan(1\/3) = Pi\/4.<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “One, Two, Three, Pi.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

References:<\/strong>
R. Nelsen, Proofs without Words<\/a><\/em>. p.39.
R. Vakil, A Mathematical Mosaic<\/a><\/em>, 1996. p.86.<\/p>\n\n\n\n

Fun Fact suggested by: <\/strong>
Stan Wagon<\/p>\n","protected":false},"excerpt":{"rendered":"

Here’s an interesting formula: Arctan(1) + Arctan(2) + Arctan(3) = Pi. (Everything’s in radians, of course). Presentation Suggestions:Challenge students to prove...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[8,4,144],"class_list":["post-431","page","type-page","status-publish","hentry","tag-geometry","tag-medium","tag-trigonometry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/431","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=431"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/431\/revisions"}],"predecessor-version":[{"id":1555,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/431\/revisions\/1555"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=431"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}