The Magical Fraction 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999

Math
The number 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 has the Fibonacci numbers in order for every group of 24 decimals. This video explains why the pattern emerges. (sources, proofs, and links below)

Via Futility Closet: http://www.futilitycloset.com/2015/06/28/made-to-order-4/

WolframAlpha verification: http://www.wolframalpha.com/input/?i=1%2F999%2C999%2C999%2C999%2C999%2C999%2C999%2C998%2C999%2C999%2C999%2C999%2C999%2C999%2C999%2C999+to+2784+decimal+places

Pingala described the Fibonacci sequence 1,000 before: https://www.youtube.com/watch?v=gTQeVlDsAi0

Blog post: http://mindyourdecisions.com/blog/2015/07/08/why-does-this-fraction-generate-the-fibonacci-numbers-in-order/#.VZyYiflVhBc

“A Magic Trick from Fibonacci” by James Smoak and Thomas J. Osler. This academic paper explains why the fraction and related fractions have the Fibonacci numbers. http://www.rowan.edu/open/depts/math/osler/fibonoaccifractionsfinalversioncmj.pdf

The polynomial x/(1-x-x^2) is a generating function for the Fibonacci sequence. Here are some proofs.
http://math.stackexchange.com/questions/338740/the-generating-function-for-the-fibonacci-numbers
http://austinrochford.com/posts/2013-11-01-generating-functions-and-fibonacci-numbers.html
http://www.cut-the-knot.org/blue/GeneratingFunctionsFromRecurrences.shtml

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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/

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