VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square?
What is the average distance between two randomly chosen points in a square with a side length 1? The video presents how to estimate the answer and also derives the exact answer using integrals. Per suggestions in the comments, I have modified the title to indicate the difficulty level is VERY HARD (a college level calculus course and probability theory course are necessary background).
Blog post
http://wp.me/p6aMk-4FA
Simulation
https://docs.google.com/spreadsheets/d/1ZPnDOQlncgPZsLKeYXqKDNL93-RUFTqypot4EY9h61w/edit?usp=sharing
Sources and further reading
Quadruple integral
http://math.stackexchange.com/questions/1254129/average-distance-between-two-random-points-in-a-square
Difference of two uniform variables
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/StandarduniformStandardtriangular.pdf
Difference of two uniform variables and solving the double integral
https://www.quora.com/How-can-I-calculate-the-mean-distance-of-two-points-placed-at-random-in-a-unit-square
Solving the double integral
http://math.stackexchange.com/questions/1294800/average-distance-between-two-randomly-chosen-points-in-unit-square-without-calc
Mean distance polar coordinates change
http://www.mathpages.com/home/kmath324/kmath324.htm
Integral secant cubed
https://en.wikipedia.org/wiki/Integral_of_secant_cubed
Mean distance square
http://mathworld.wolfram.com/SquareLinePicking.html
Cleve Moler's blog post
https://blogs.mathworks.com/cleve/2017/09/25/how-far-apart-are-two-random-points-in-a-square/
Thanks to Patrons! A video like this takes a lot of research and you guys make it possible.
Kyle
Alberto Nishikawa
Brian M. Mooney
If you like my videos, you can support me at Patreon:
https://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: https://mindyourdecisions.com/blog/
Twitter: https://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: https://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: https://www.patreon.com/mindyourdecisions
Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r
If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.
My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 32 reviews)
http://amzn.to/1uQvA20
"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 4.6/5 stars on 3 reviews)
http://amzn.to/1o3FaAg
"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 4.4/5 stars on 13 reviews.
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews)
http://amzn.to/1NKbGlp
"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
http://amzn.to/1LOCI4U
"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 4 reviews)
http://amzn.to/18maAdo
"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 3 reviews)
http://amzn.to/XRm7M4
Видео VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square? канала MindYourDecisions
Blog post
http://wp.me/p6aMk-4FA
Simulation
https://docs.google.com/spreadsheets/d/1ZPnDOQlncgPZsLKeYXqKDNL93-RUFTqypot4EY9h61w/edit?usp=sharing
Sources and further reading
Quadruple integral
http://math.stackexchange.com/questions/1254129/average-distance-between-two-random-points-in-a-square
Difference of two uniform variables
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/StandarduniformStandardtriangular.pdf
Difference of two uniform variables and solving the double integral
https://www.quora.com/How-can-I-calculate-the-mean-distance-of-two-points-placed-at-random-in-a-unit-square
Solving the double integral
http://math.stackexchange.com/questions/1294800/average-distance-between-two-randomly-chosen-points-in-unit-square-without-calc
Mean distance polar coordinates change
http://www.mathpages.com/home/kmath324/kmath324.htm
Integral secant cubed
https://en.wikipedia.org/wiki/Integral_of_secant_cubed
Mean distance square
http://mathworld.wolfram.com/SquareLinePicking.html
Cleve Moler's blog post
https://blogs.mathworks.com/cleve/2017/09/25/how-far-apart-are-two-random-points-in-a-square/
Thanks to Patrons! A video like this takes a lot of research and you guys make it possible.
Kyle
Alberto Nishikawa
Brian M. Mooney
If you like my videos, you can support me at Patreon:
https://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: https://mindyourdecisions.com/blog/
Twitter: https://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: https://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: https://www.patreon.com/mindyourdecisions
Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r
If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.
My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 32 reviews)
http://amzn.to/1uQvA20
"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 4.6/5 stars on 3 reviews)
http://amzn.to/1o3FaAg
"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 4.4/5 stars on 13 reviews.
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews)
http://amzn.to/1NKbGlp
"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
http://amzn.to/1LOCI4U
"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 4 reviews)
http://amzn.to/18maAdo
"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 3 reviews)
http://amzn.to/XRm7M4
Видео VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square? канала MindYourDecisions
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
Killer Math Problem With An Unbelievably Elegant SolutionBut why is a sphere's surface area four times its shadow?How To Solve Google's 25 Horses Interview QuestionWhat is the average distance of two points in a disc? (PART 1)What Is The Average Distance Of Two Points On A Circle?How To Solve The Hiding Cat Puzzle. HARD Logic RiddleCan you solve this tricky interview question? The rectangle in a triangle problemAdults Stumped By Geometry Problems For 10 Year Olds. Can You Solve Them?The ladder and box problem - a classic challenge!HARD Geometry Problem: Can You Solve The Horse Grazing Puzzle?The REAL Answer To The Viral Chinese Math Problem "How Old Is The Captain?""Only Geniuses Can Solve" The Viral 11x11 = 4 Puzzle. The Correct Answer Explained"Impossible" Math Problem Leaves 15 Year Olds In Tears - New Zealand (Parabola Question)How To Solve Amazon's Hanging Cable Interview QuestionSolving An Insanely Hard Problem For High School StudentsWhat Positive Number Doubles When The Last Digit Moves To The First Digit? Riddle For "Geniuses"How To Solve For The Area. Viral Homework Problem From ChinaWhy did everyone miss this SAT Math question?A very challenging question about fractionsCan You Solve A REALLY HARD 8th Grade Math Problem From Russia?