# Math

Our Pi Playlist (more videos): http://bit.ly/PiPlaylist Pi is famously calculated to trillions of digits – but Dr James Grime says 39 is probably enough. More links & stuff in full description below ↓↓↓ An extra note from Dr Grime: “Since pi39 ends in 0, you may think we could use pi38 instead – which has

This video gives a method to convert decimal numbers to binary numbers quickly. This is a variation of the remainder system that is typically taught in courses. I like this method because it gives the answer in the correct order from left to right. Proof of why it works: http://math.stackexchange.com/questions/86207/converting-decimalbase-10-numbers-to-binary-by-repeatedly-dividing-by-2 I also give a proof

Dividing by zero, zero divided by zero and zero to the power of zero – all pose problems! More links & stuff in full description below ↓↓↓ This video features Matt Parker and James Grime – https://twitter.com/standupmaths and https://twitter.com/jamesgrime 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

Thanks to Surjadi from Indonesia for the suggestion! Twitter Cshearer41 A square is split into five rectangles with equal areas. What’s the area of the square? pic.twitter.com/wtuEjxMASI — Catriona Agg (@Cshearer41) July 11, 2020 solution by @birkhofyan pic.twitter.com/3EIij7DjaU — Birkan Yıldız (@birkhofyan) July 11, 2020 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video).

Tadashi explores a special set of dice… And has a powerful lesson. More links & stuff in full description below ↓↓↓ Subscribe to Numberphile: http://bit.ly/Numberphile_Sub More dice videos: http://bit.ly/Dice_Videos Playlist of Tadashi Tokieda videos: http://bit.ly/tadashi_vids Want to buy some dice like this – our friends at Maths Gear have some: http://bit.ly/MathsGearDice Discuss this video on

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

How do we know there are an infinite number of primes? More links & stuff in full description below ↓↓↓ Dr James Grime explains, with a bit of help from Euclid. Follow James at https://twitter.com/jamesgrime 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

This one stumped me! This problem is part of the AIME, a qualifying test for the US Mathematical Olympiad team. The talented students who take the AIME only average about 20 percent–it’s a hard test! Plus no calculators are allowed. Can you figure out this problem from the 1987 test? Learn the trick which results

We now have a Tumblr: Tumblr: http://numberphile.tumblr.com This paper on ebay: http://www.ebay.co.uk/itm/221197137799? More links & stuff in full description below ↓↓↓ Just how hard was the second problem cracked by Will in Good Will Hunting? Matt Damon! And who doesn’t love Homeomorphically Irreducible Trees? This video features Dr James Grime – http://singingbanana.com/ Music by Alan

Who can solve this one? 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 YouTube to learn how to make videos. Be prepared–animation is time consuming and

The AKS Test has been a major break-through in the search for Prime Numbers. More links & stuff in full description below ↓↓↓ See the previous video about Fermat’s Prime Test at: http://youtu.be/jbiaz_aHHUQ The video features Dr James Grime – http://singingbanana.com The AKS Test paper: http://bit.ly/primetest Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile

What is the height of the red bar? This puzzle was posted on Math StackExchange by a Math PhD candidate, so I did not feel bad when I was unable to solve it! (Though I suspect some people will even find it “easy.”) Math StackExchange (see solution by Eric Duminil). It was posted by a

Catch David on the Numberphile podcast: https://youtu.be/9y1BGvnTyQA Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be “ready” to crack. More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/O2_h3z1YgEU Prof Eisenbud’s 17-gon: https://youtu.be/87uo2TPrsl8 Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on

This problem went viral because even teachers had trouble solving it. It even got covered in television news! Can you figure it out? References BlackPenRedPen Twitter Find A, B, C, D, E. This was a 4th-grade math problem in Taiwan that made the news! I remember my friend gave this problem to me from her

Henry Segerman (mathematician and 3D printing guru) discusses how to make three gears work together. More links & stuff in full description below ↓↓↓ Skew dice: https://youtu.be/uAnCL3vhVIs Check Henry’s book about 3D printing math: http://amzn.to/2cWhY3R Prime Numbers Playlist: http://bit.ly/primevids Prime Machine: https://youtu.be/8UqCyepX3AI You can buy the gears from Henry at Shapeways: http://bit.ly/HenryGears Support us on

This is a pretty tricky problem. Can you solve for the angle? Watch the video for the solution. I thank Barry, and I thank Akshay Dhivare from India for suggesting the problem via email. Sources https://gogeometry.blogspot.com/2008/05/elearn-geometry-problem-10.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics

Marcus du Sautoy discusses Gödel’s Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy’s book as mentioned… In

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

Featuring Neil Sloane… Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Trapped Knight T-Shirt: https://teespring.com/en-GB/numberphile-trapped-knight Neil Sloane is creator of the On-Line Encyclopedia of Integer Sequences: https://oeis.org For more on the sequences and diagrams in this video, you can start at: https://oeis.org/A316667

This is a tricky geometry problem with an elegant solution! Sources Adapted from past SEAMO problem (emailed to me) Cut The Knot similar problem https://www.cut-the-knot.org/proofs/swivel.shtml Quote A Technique is Just a Trick That Went Viral 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! Why are

Featuring Professor Edward Frenkel. Here is the biggest (?) unsolved problem in maths… The Riemann Hypothesis. More links & stuff in full description below ↓↓↓ Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat’s Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel’s book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley – http://edwardfrenkel.com

Can you solve for the shaded area? 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 YouTube to learn how to make videos. Be prepared–animation is time

A bit about zero – including a discussion of its even-ness!? More links & stuff in full description below ↓↓↓ Featuring Dr James Grime (https://twitter.com/jamesgrime) and Professor Roger Bowley (University of Nottingham). 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

The Prisoner’s Dilemma is the most famous problem in game theory. Here I give a quick introduction to the problem. 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

See our other Graham’s Number videos: http://bit.ly/G_Number More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ The magnitude of Graham’s Number is difficult to fathom – Ron Graham himself attempts to explain. WHAT IS the number: http://youtu.be/HX8bihEe3nA Extra footage: http://youtu.be/rGWuimr5CGQ Our original Graham’s Number video: http://youtu.be/XTeJ64KD5cg Any errors in this

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

Numbers like e and Pi cannot be made using normal algebra. Featuring Australia’s Numeracy Ambassador, Simon Pampena. Extra footage: http://youtu.be/dzerDfN2E7U More links & stuff in full description below ↓↓↓ Discussing transendental numbers, algebraic numbers, pi, e and other stuff. Simon’s website: http://www.numbercrunch.com.au/ Root 2: http://www.youtube.com/watch?v=5sKah3pJnHI Pi Playlist: http://www.youtube.com/playlist?list=PL4870492ACBDC2E7C NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile

Olympiad problems are challenging for most of us. But this one was considered “easy” for the students taking the test! (The oldest students are in high school, but have also been 13 year old students who have taken the test and gotten a gold medal). Thanks to all patrons! Special thanks to: Michael Anvari, Richard

Professor Tony Padilla on the epic number, TREE(3). Continues at: https://youtu.be/IihcNa9YAPk More links & stuff in full description below ↓↓↓ Graham’s Number: http://bit.ly/G_Number 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

The quadratic formula is really useful, but its derivation is confusing to many. Like what is the point of “completing the square” anyway? In this video, I show how “completing the square” has a geometric interpretation–you are actually making the areas of two squares equal to each other! Blog post (text/image summary): http://wp.me/p6aMk-4kG You can

Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY More links & stuff in full description below ↓↓↓ 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

This problem stumped me! But it has a pretty nice solution. Thanks to all patrons! Special thanks this month to Kyle, Michael Anvari, Richard Ohnemus, Shrihari Puranik. Source Emailed to me about 2 years ago, traced to the Australian Intermediate Olympiad given in 2013. Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send

Free trial at The Great Courses Plus: http://ow.ly/tKWt306Gg7a Dr James Grime discusses “e” – the famed Euler’s Number. More links & stuff in full description below ↓↓↓ A bit extra from this video: https://youtu.be/uawO3-tjP1c More James Grime videos from Numberphile: http://bit.ly/grimevideos 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:

Many people requested this one. It was asked to 9th grade students in India who had only learned geometry, so you are supposed to solve it without using trigonometry. I thank Anand Gautam for discovering the incredible solution! Polish translation credit: Tłumaczenie: Przemyslav Znajdź mnie tutaj: https://forum.cdaction.pl/blogs/blog/64401-ma%C5%82a-wie%C5%9B-po%C5%9Brodku-niczego/ You can also solve the problem with trigonometry.

Dr James Grime discusses a couple of clever formulas which are pandigital – using all the numbers from 1-9. More links & stuff in full description below ↓↓↓ More on pandigital numbers: https://youtu.be/gaVMrqzb91w More on e: https://youtu.be/AuA2EAgAegE More James Grime videos: http://bit.ly/grimevideos Book James for a talk: http://jamesgrime.com The contest which gave us these formulas:

What is the area of the square? Thanks to Papa in India for the suggestion! This puzzle is half of of problem 21 in the 2017 AMC 10A. https://artofproblemsolving.com/wiki/index.php/2017_AMC_10A_Problems/Problem_21 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

A million digits of Pi on one piece of paper (1.05 miles). More links & stuff in full description below ↓↓↓ More about how and why: http://youtu.be/99Welatppzk More Pi videos from Numberphile: http://bit.ly/PiPlaylist Film by Brady Haran Our thanks to HP and HSA Systems. Extra special thanks to Hugh McPartlan, Torben Dam Jensen, Jesper Hyldager

Can you estimate the log of 3 to the base of 2 without using a calculator? This kind of skill is actually pretty important in university mathematics. Watch the video to learn how to solve it! Source https://www.quora.com/How-do-you-solve-this-question-from-Oxfords-Math-Admissions-Test-No-calculators 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

Simon Singh on Fermat’s Last Theorem. Simpsons book: http://amzn.to/1fKe4Yo Fermat book: http://amzn.to/1jWqMTa More links & stuff in full description below ↓↓↓ EXTRA FOOTAGE: http://youtu.be/FXbsIbRVios FERMAT IN SIMPSONS:http://youtu.be/ReOQ300AcSU Interview with Ken Ribet, who played a big role: https://youtu.be/nUN4NDVIfVI Wiles’ proof: http://bit.ly/FermatProof 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

Why squaring the circle – the old-fashioned way – was found to be impossible? Numblr: http://numberphile.tumblr.com/ More links & stuff in full description below ↓↓↓ This video featuring Dr James Grime: https://twitter.com/jamesgrime The paper from this video on ebay – http://bit.ly/brownpapers 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

Some people say this is “how the Japanese multiply.” Others say this is “Vedic Math.” I’m not sure of the origin, but this is a visual way to multiply two numbers and it does work. The video also shows how to use the same method to multiply algebraic expressions like (x + 2)(x + 3).

Ron Graham explains the number which takes his name… See our other Graham’s Number videos: http://bit.ly/G_Number More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ Graham’s Number (Numberphile T-Shirt): http://bit.ly/Grahams_T-Shirt See him discuss how big it is: http://youtu.be/GuigptwlVHo Extra footage here: http://youtu.be/rGWuimr5CGQ And our original Graham’s Number video: http://youtu.be/XTeJ64KD5cg Support

This problem is baffling many people on Facebook and Twitter. Can you figure it out? I thank everyone who emailed it to me, with a special thanks to the first two people: Riadh Temala from Tunisia; and Shivam Varma from India. Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only

Our Pi Playlist (more videos): http://bit.ly/PiPlaylist The State of Indiana nearly passed a law which would have made Pi equal 3.2 – strange but true. More links & stuff in full description below ↓↓↓ More Pi videos from Numberphile: http://bit.ly/W4oDN1 This video features Dr James Grime – https://twitter.com/jamesgrime The video about squaring circles: https://www.youtube.com/watch?v=CMP9a2J4Bqw A