Counter-Intuitive Probability: Buffon's Needle Problem. Pi (π) From Probability!
A needle of length 1 is randomly dropped on a floor with horizontal lines 2 units apart. What is the probability the needle intersects one of the horizontal lines? The answer might surprise you--it involves the constant π!
This is known as Buffon's Needle Problem. In this video I present the common proof that uses trigonometry and calculus. I also show a clever proof from Barbier's (I read about this in "Proofs from THE BOOK" which is a collection of elegant proofs).
If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions
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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/
Видео Counter-Intuitive Probability: Buffon's Needle Problem. Pi (π) From Probability! канала MindYourDecisions
This is known as Buffon's Needle Problem. In this video I present the common proof that uses trigonometry and calculus. I also show a clever proof from Barbier's (I read about this in "Proofs from THE BOOK" which is a collection of elegant proofs).
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/
Видео Counter-Intuitive Probability: Buffon's Needle Problem. Pi (π) From Probability! канала MindYourDecisions
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