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 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/