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The Wallis Formula For π

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Channel: MindYourDecisions
Categories: Math  
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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

Factorial of 1/2 video

Wallis product

Wallis product historical motivation

Wallis pi and quantum theorem

Geometric intuition of Wallis product

Wallis's original book "Arithmetica Infinitorum"

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.

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