# Math

Johnny Ball discusses Archimedes and the volume of a sphere. Check out https://www.kiwico.com/Numberphile and get 50% off your first month of any subscription (sponsor) More links & stuff in full description below ↓↓↓ Johnny Ball: https://johnnyball.co.uk More Numberphile videos with Johnny Ball: http://bit.ly/Johnny_Ball Johnny Ball books: https://amzn.to/3v8Xxqx Numberphile is supported by the Mathematical Sciences Research

Matt Parker shows off his Magic Square party trick (unlike magicians, mathematicians often reveal their secrets). More links & stuff in full description below ↓↓↓ More Magic Square videos: http://bit.ly/MagicSquareVideos Rubik’s Cube videos: http://bit.ly/rubiksvids More Matt on Numberphile: http://bit.ly/Matt_Videos A little extra bit for this video: https://youtu.be/zhB2AUNcsx0 Parker Square: https://youtu.be/aOT_bG-vWyg Parker Square T-Shirt: http://bit.ly/ParkerSquareTshirt Support

Three chords are drawn in a circle, spaced 30 degrees apart from the same vertex. If the left chord is 10, and the right chord is 12, what is the length of the middle chord? Wow! The channel “Freedom Mathematics” did a general case of the chord progression puzzle. The general problem is quite complicated!

Thanks to Devesh from India for the suggestion! A version of this problem was given in an Olympiad qualifying test. Socratic https://socratic.org/questions/a-root-a-b-root-b-183-a-root-b-b-root-a-182-find-9-5-a-b Math StackExchange https://math.stackexchange.com/questions/2405256/find-the-value-of-frac95ab-given-that-a-sqrtab-sqrtb-183-and-a Brainly https://brainly.in/question/3901575 Quora https://www.quora.com/Suppose-a-b-are-positive-real-numbers-such-that-a%E2%88%9Aa-+-b%E2%88%9Ab-183-a%E2%88%9Ab-+-b%E2%88%9Aa-182-How-do-we-find-9-5-a-+-b Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy

Langton’s Ant – starring Katie Steckles (and Audrey). More links & stuff in full description below ↓↓↓ Extra footage: https://youtu.be/oTssNuDEkSc The 104-steps: https://youtu.be/xU072T4V12A John Conway videos: http://bit.ly/ConwayNumberphile Support us on Patreon: http://www.patreon.com/numberphile Katie Steckles website: http://bit.ly/stecks_web Audrey: https://www.facebook.com/AudreyAdorable One of many online simulators: http://rossscrivener.co.uk/projects/langtons-ants/ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:

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

Can you solve this incredibly difficult calculus question? I had a lot of fun solving this one! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari. Robert Zarnke, Fiona Harper. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from Comment from discussion PhysicsHelpBernoulli’s comment from discussion "[12th grade math] What number would n have

Can you solve this geometry brain teaser? Note: I was emailed a similar problem but I am unable to locate the original source. It seems to be in the style of Bright Side quizzes, but often those are based on problems circulating. Please let me know if can identify the original source and I will

Can you solve this interesting geometry problem? References Solution by “WAY TO GOVT JOB” on YouTube Stretched length of band https://www.thestudentroom.co.uk/showthread.php?t=1936482 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a

15-year old Joseph Rosenfeld thought he spotted an error in the Boston Museum of Science. The exhibit Mathematica has a sign that says the golden ratio is (√5 – 1)/2. He remembered and checked online that the golden ratio is supposed to have a positive symbol, (√5 + 1)/2. He left a note for the

Can you solve for the area of the square and the length of the tangent line? Special thanks this month to Fiona Harper, Kyle, Mike Robertson, Michael Anvari, Robert Zarnke. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from a puzzle by Twitter @Cshearer41 (Catriona Agg) A semicircle and quarter circle inside a square. How

A compilation of Numberphile sound checks – Brady typically asks “what did you have for breakfast” so he can monitor audio levels. More links & stuff in full description below ↓↓↓ Previous sound checks with scientists here: http://youtu.be/4anqDfgQneA Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub

Professor Ron Graham discusses the famed Happy Ending Problem and Ramsey Theory. More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ An extra little bit at: http://youtu.be/hnIBiIcuudU Graham’s Number: http://youtu.be/XTeJ64KD5cg Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported

I had a lot of fun solving this one, and I think you will too! 0:00 Problem 0:49 Hints 4:12 Solution Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a

Partitions are a major part of the Ramanujan story (as shown in the new film about his life) – but what are they? More links & stuff in full description below ↓↓↓ Dr James Grime tackles the issue. Extra footage: https://youtu.be/ksHqQW94KlE More James Grime on Numberphile: http://bit.ly/grimevideos Young Tableau: https://youtu.be/vgZhrEs4tuk Shuffling: https://youtu.be/AxJubaijQbI James discusses Good

This problem is adapted from the first round of the 2017 Dutch Maths Olympiad. Special thanks this month to: Robert Zarnke, Marq Short, Kyle, Mike Robertson, Michael Anvari. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Reddit Math Riddles Simple square puzzle from mathriddles Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many

Tadashi Tokieda is back. This time talking about stability, instability and train wheels. More Tadashi videos: http://bit.ly/tadashi_vids Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile

Asha and Lata are two sisters with mathematically interesting ages. If you write Lata’s age after Asha’s, you get a 4 digit perfect square. Amazingly the same thing happens if you repeat the exercise in 11 years. How old are Asha and Lata currently? 0:00 Problem 1:09 Difference of squares 2:25 Solution Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send

James Maynard on discoveries about large gaps between prime numbers. More links & stuff in full description below ↓↓↓ More Maynard videos: http://bit.ly/JamesMaynard Prime Playlist: http://bit.ly/primevids The 20 August paper: https://arxiv.org/abs/1408.4505 The 21 August paper: https://arxiv.org/abs/1408.5110 Terry Tao interview: https://youtu.be/MXJ-zpJeY3E Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported

Thanks to Thinh for suggesting this problem! What is the area of a single square? A version of this was given to 12-13 year olds in Vietnam. I admit I didn’t see the trick, but it is a fun one! VN Express (in Vietnamese) https://vnexpress.net/bai-toan-cau-kinh-7-o-vuong-4169822.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end

The Prisoner’s Dilemma is the most famous problem in game theory, as it shows that individuals who make rational decisions might end up in an outcome that’s worse for everyone in the group. In other words, individual rationality does not imply group rationality. Watch a higher quality version of this video: https://www.youtube.com/watch?v=TJCGTNIwmv8 You can also

Can you solve this equation? Thanks to Hrigved for the suggestion! Reference https://math.stackexchange.com/questions/438452/find-all-real-numbers-such-that-sqrtx-frac1x-sqrt1-frac1x Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I

This is a nice little logic puzzle from Terry Stickels! Books by Terry Stickels (including “Contemporary Brainteasers”) http://www.terrystickels.com/books.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on

Can you solve this fun little geometry puzzle? Thanks to Roman for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an Amazon Associate

See more links about the dice in the full description below… More links & stuff in full description below ↓↓↓ Extra footage at Numberphile2: https://youtu.be/pCCtcqyazOE Check Henry’s book about 3D printing math: http://amzn.to/2cWhY3R More about dice designs: http://bit.ly/AboutDice Buy these dice and others at: http://bit.ly/DiceLabDice Some dice are also available from our UK friends at

Thanks to George Tan for suggesting this problem! It is from the 2019 SPM paper in Malaysia. Many students cried after taking the exam, and many teachers found the problems to be very challenging as well. (This means the problems were hard given the syllabus and expectations of the exam–no need to let us know

Tadashi’s back (for the final video in this mini series) demonstrating the Kendama and some angular momentum. More links & stuff in full description below ↓↓↓ Tadashi Tokieda will be back on Numberphile soon. Here’s a playlist of his videos: http://bit.ly/tadashi_vids Kendama also known as bilboquet or boliche or bolero. Video by Brady Haran and

Two boats make a round trip from opposite shores of a lake. They meet and pass at 500 units from the left shore, then at 300 units from the right shore. The boats move at a constant speed and turn around instantly from the shores. What is the distance between the shores? What is the

Neil Sloane discusses peaceable queens and chess. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Learn more at the OEIS entry (loads of links): https://oeis.org/A250000 References: Ainley, Stephen. Mathematical Puzzles. London: G Bell & Sons, 1977. Yukun Yao and Doron Zeilberger, Numerical and

Matt Parker talks about numbers – as he often does. His book “Humble Pi” is at: http://bit.ly/Humble_Pi More links & stuff in full description below ↓↓↓ The book on Amazon: https://amzn.to/2NKposg Numberphile podcast is on your podcast player. Or the website is: https://www.numberphile.com/podcast And it’s on YouTube too: http://bit.ly/Numberphile_Pod_Playlist The Knight’s Tour T-Shirt is in

This is a fun algebra problem. Can you figure it out? Thanks to Aslah from India for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for

Can you solve this geometry problem? Thanks to Lucas from Brazil for the suggestion! Kangaroo Maths 2020 https://www.matematica.pt/en/docs/kangaroo/enunciados/2020/2020_Grade9-10.pdf Proof of inscribed angle theorem https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/inscribed-and-central-angles-proof Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I

Is 1 a prime number? Apparently not. Dr James Grime explains. More links & stuff in full description below ↓↓↓ James Grime’s website is: http://singingbanana.com/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady’s videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady’s latest videos across all channels: http://www.bradyharanblog.com/ Sign

Can you solve this tricky math problem? Thanks to Asad for the suggestion! Art of Problem Solving 2019 AIME Problem 3 (there are many solution methods) https://artofproblemsolving.com/wiki/index.php/2019_AIME_I_Problems/Problem_3 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I cannot reply to everyone but I consider all ideas! Like many YouTubers I use popular software to

Extended math version: http://youtu.be/ugbWqWCcxrg?t=2m32s A version for Dummies: https://youtu.be/7u6kFlWZOWg More links & stuff in full description below ↓↓↓ This video features Lisa Goldberg, an adjunct professor in the Department of Statistics at University of California, Berkeley. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is

Happy #PiDay! When two of the hardest tests in the world cover the same problem, you know it’s a big deal. References Wikipedia article https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80 Putnam exam 1968 A1 https://prase.cz/kalva/putnam/putn68.html JEE Advanced 2010 Paper Solutions Part-1 | IIT-JEE | Strategy, Tips, & Tricks | Paper Discussion (see around 55:30) Proving 22/7 is greater than PI

In the past 5 months, all of Mark Rober’s videos have been #1 trending on YouTube. He put his success in perspective by analogy to a statistical experiment of flipping coins. Some people pointed out the calculation wasn’t quite correct, so I thought it would be a great topic for a video. Mark Rober tweet

Can you solve this challenging problem from the Mathematical Olympiad of Singapore? Thanks to Truong from Vietnam for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I cannot reply to everyone but I consider all ideas! Like many YouTubers I use popular software to prepare my videos. You can search for

Can you solve this challenging Valentine’s Day problem? Thanks to Stéphane from Belgium for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an

Can you solve this “coffin” problem? Thanks to Rahul for the suggestion! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from problem 4 of Jewish Problems by Tanya Khovanova, Alexey Radul https://arxiv.org/abs/1110.1556v2 Coffin Problem ft. blackpenredpen: Cube and Cube Root (Mu Prime Math) Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1

This was asked to students in Indonesia. Can you figure it out? Special thanks this month to: Michael Anvari, Kyle, Mike Robertson. Thanks to all supporters on Patreon! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I cannot reply to everyone but I consider all ideas! Like many YouTubers I use popular software

The Dynamical Uniform Boundedness Conjecture with Dr Holly Krieger. Extra from this interview: https://youtu.be/v4LWFzTyhpU Dr Krieger on the Numberphile Podcast: https://youtu.be/QmfQQzjpdpM More links & stuff in full description below ↓↓↓ More videos with Holly: http://bit.ly/HollyKrieger Holly’s website: https://www.dpmms.cam.ac.uk/~hk439/ She is the Corfield Lecturer at the University of Cambridge as well as a Fellow at Murray

Happy Pi Day! At 3/14/15 at 9:26 the time will be accurate to pi for 7 decimal places. What’s your favorite fact about pi? Links to proofs and more below in the description. 1. The definition 00:10 Related: the area of circle intuitive explanation 2. Pi is irrational 00:47 Proof (video) Proof (blog post) http://mindyourdecisions.com/blog/2013/11/08/proving-pi-is-irrational-a-step-by-step-guide-to-a-simple-proof/

A little extra trick based on some of the Mobius cutting videos we recently published. Featuring Tadashi Tokieda. More links & stuff in full description below ↓↓↓ MORE: http://bit.ly/tadashi_vids Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute

What fraction of the entire circle is shaded? Special thanks this month to: Michael Anvari, Kyle, Mike Robertson. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Jobbings, A. (2011). The Mathematical Gazette https://www.cambridge.org/core/journals/mathematical-gazette/article/9564-two-semicircles-fill-half-a-circle/6365F0D492DF2E682E71A891C782CAF6 The chalice problem Azimuth Project (John Carlos Baez) Geometry Puzzles Folding proof by Greg Egan http://math.ucr.edu/home/baez/mathematical/semicircle_puzzle_egan.gif Cut The Knot https://www.cut-the-knot.org/proofs/Semicircles.shtml Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send

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