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The Wallis Formula For π

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Channel: MindYourDecisions
Categories: Math  
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Description

Start with the pair of fractions (2/1)(2/3). Now increment each number by 2 to get the pair of fractions (4/3)(4/5). Repeat this to get the next pair, and repeat this infinitely many times. If you then multiply all the fractions, you get a marvelous value: it is equal to pi divided by 2. The Wallis product formula for pi was described in 1655. This video explains some of the historical motivation and then gives a modern proof using calculus of why the formula is true.

My blog post for this video
http://wp.me/p6aMk-4U7

Factorial of 1/2 video
https://youtu.be/QhDDpSju3uY

Wallis product
https://en.wikipedia.org/wiki/Wallis_product

Wallis product historical motivation
https://www2.bc.edu/~reederma/105WallisGauss.pdf

Wallis pi and quantum theorem
http://www.intmath.com/blog/mathematics/wallis-pi-and-quantum-theory-10494

Geometric intuition of Wallis product
http://commonsensequantum.blogspot.com/2010/03/exhaustion-of-nested-squares-and-wallis.html

Wallis's original book "Arithmetica Infinitorum"
https://archive.org/details/ArithmeticaInfinitorum

Another proof of the Wallis product
Wästlund, Johan. "An Elementary Proof of the Wallis Product Formula for Pi." The American Mathematical Monthly 114.10 (2007): 914-17. Web. http://www.jstor.org/stable/27642364

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