I couldn't believe the answer when I solved this one!

Start with a unit square (a rectangle with both sides equal to 1, call it R1). Attach a rectangle of area 1 to its right side, then attach a rectangle of area 1 to its top. The border of this new shape is another rectangle, call it R2. We can repeat the process with R2 to create a new rectangle R3, and then repeat again, and so on. What is the ratio of the length to the width of Rn, as n goes to infinity? The answer is surprising!

My blog post for this puzzle
http://wp.me/p6aMk-4TK

Proof of final formula (this spoils the answer, so watch the video first)
https://youtu.be/EZSiQv_G9HM

Thanks to Patrons!
Kyle
Brian M. Mooney
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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/