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/mark-reeder/1103WG(4-22).pdf

Wallis pi and quantum theorem
http://www.intmath.com/blog/ma....thematics/wallis-pi-

Geometric intuition of Wallis product
http://commonsensequantum.blog....spot.com/2010/03/exh

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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My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

"Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/

"Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/