Here’s a fun\u00a0formula for Pi\u00a0involving an infinite product, known as Wallis’ Formula:<\/p>\n\n\n\n
(Pi\/2) = (2*2)(4*4)(6*6)\/(1*3)(3*5)(5*7)<\/p>\n\n\n\n
It is somewhat surprising that when you pull out every other pair of terms, you get a completely different kind of number!<\/p>\n\n\n\n
Sqrt[2] = (2*2)(6*6)(10*10)\/(1*3)(5*7)(9*11)<\/p>\n\n\n\n
Presentation Suggestions:<\/strong> The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong> How to Cite this Page:<\/strong> References:<\/strong> Fun Fact suggested by: <\/strong> Here’s a fun\u00a0formula for Pi\u00a0involving an infinite product, known as Wallis’ Formula: (Pi\/2) = (2*2)(4*4)(6*6)\/(1*3)(3*5)(5*7) It is somewhat surprising that...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[20,7,3,10,12,30],"class_list":["post-244","page","type-page","status-publish","hentry","tag-analysis","tag-calculus","tag-easy","tag-numtheory","tag-other","tag-pi-formula"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/244","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=244"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/244\/revisions"}],"predecessor-version":[{"id":1699,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/244\/revisions\/1699"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
You can also start with the infinite product, and ask if student can guess what it converges to, before you tell them the answer.<\/p>\n\n\n\n
There is an infinite product formula for the sine function which yields Wallis’ formula as a consequence. Infinite products are defined as the\u00a0limit\u00a0of the partial products, which are finite. This is similar to the way we define\u00a0infinite sums!<\/p>\n\n\n\n
Su, Francis E., et al. “Wallis’ Formula.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
S. Vandervelde, Mathematics and Informatics Quarterly<\/em>, 9 (1999), pp. 64-69.<\/p>\n\n\n\n
Sam Vandervelde <\/p>\n","protected":false},"excerpt":{"rendered":"