Can You Solve The HARD Rectangle Ratio Puzzle? A SURPRISING Appearance Of Pi (π)
- 6 years ago
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!\r
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My blog post for this puzzle\r
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Proof of final formula (this spoils the answer, so watch the video first)\r
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Thanks to Patrons!\r
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Brian M. Mooney\r
Shrihari Puranik\r
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The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
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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) \r
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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. \r
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Math Puzzles Volume 2 is a sequel book with more great problems. \r
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Math Puzzles Volume 3 is the third in the . \r
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40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) \r
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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) \r
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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)
\r
My blog post for this puzzle\r
\r
\r
Proof of final formula (this spoils the answer, so watch the video first)\r
\r
\r
Thanks to Patrons!\r
Kyle\r
Brian M. Mooney\r
Shrihari Puranik\r
\r
If you like my videos, you can support me at Patreon: \r
\r
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.\r
\r
My Blog: \r
Twitter: \r
Facebook: \r
Google+: \r
Pinterest: \r
Tumblr: \r
Instagram: \r
Patreon: \r
\r
Newsletter (sent about 2 times a year): \r
\r
My Books\r
\r
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
\r
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) \r
\r
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. \r
\r
Math Puzzles Volume 2 is a sequel book with more great problems. \r
\r
Math Puzzles Volume 3 is the third in the . \r
\r
40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) \r
\r
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) \r
\r
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)