# The Wallis Formula For π

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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

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/

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Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

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/

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

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/

Twitter: http://twitter.com/preshtalwalkar

Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965

Google+: https://plus.google.com/108336608566588374147/posts

Pinterest: https://www.pinterest.com/preshtalwalkar/

Tumblr: http://preshtalwalkar.tumblr.com/

Instagram: https://instagram.com/preshtalwalkar/

Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

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/

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