Matt Parker on Stern-Brocot numbers, fractions and rational numbers. More links & stuff in full description below ↓↓↓ Matt’s book on Amazon US: http://bit.ly/Matt_4D_US Amazon UK: http://bit.ly/Matt_4D_UK Signed: http://bit.ly/Matt_Signed Poster: http://bit.ly/NumberPoster EXTRA FOOTAGE: http://youtu.be/zv5M9zuZiXo 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
Math
This is a fun little geometry problem! DataGenetics http://datagenetics.com/blog/november22016/index.html How to solve the shape-shifting triangle 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 some comments before the video is published? Get early access and support the channel on Patreon https://www.patreon.com/mindyourdecisions If you buy
Tadashi Tokieda cuts various combinations of loops and Mobius loops – with surprising results. More links & stuff in full description below ↓↓↓ Part 2: https://youtu.be/mh3eMt09EAs And 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
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
Why number 1 is the “leading digit” more often than you may expect? More links & stuff in full description below ↓↓↓ See us test the law using Brady’s YouTube viewing figures at: http://youtu.be/VbtNy54ya9A Blog about all this at: http://bit.ly/benfordslaw Brown Paper from this video on ebay: http://bit.ly/brownpapers This video features Steve Mould: http://www.stevemould.com/ and
Many tests around the world include a problem like this. How can you calculate this quickly, without making any mistakes? Thanks to all patrons! Special thanks to: Ertugrul Oruç, Michael Anvari, Richard Ohnemus, Shrihari Puranik, Kyle. Source https://twitter.com/thebapex/status/1149020375189270528 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
Brady Numbers T-Shirt: http://bit.ly/T-Shirt-BN Part One of Golden Ratio Trilogy More links & stuff in full description below ↓↓↓ The new “Brady Sequence” demonstrates why Fibonacci Numbers are not so special. Featuring Matt Parker. Next in the trilogy: http://youtu.be/dTWKKvlZB08 Matt’s signed book (& extra goodies): http://bit.ly/Matt_Signed Amazon (UK): http://bit.ly/Matt_4D_UK Amazon (US): http://bit.ly/Matt_4D_US Discuss this video
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
Part Two of Golden Ratio Trilogy Proof that an infinite number of sequences have that “golden ratio” property – not just the Fibonacci Numbers. More links & stuff in full description below ↓↓↓ Next in the trilogy: http://youtu.be/PeUbRXnbmms Matt’s signed book (& extra goodies): http://bit.ly/Matt_Signed Amazon (UK): http://bit.ly/Matt_4D_UK Amazon (US): http://bit.ly/Matt_4D_US All links to videos
This is the higher quality version of how to multiply numbers by drawing lines. Get the Multiply By Lines Book! http://amzn.to/XRm7M4 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
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
Thanks to Hriden for the suggestion! A version of this problem was given to class 8 students in India (~13 years old). Can you solve for the area of ABCD? Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video).
First in a series of videos about knots. Here we have Carlo H. Séquin from UC Berkeley. More links & stuff in full description below ↓↓↓ More videos to come at: http://bit.ly/Knot-a-Phile Edit and animation by Pete McPartlan. Film and interview by Brady Haran With thanks to Rob Scharein for the use of his software
The 80/20 rule or Pareto principle comes up a lot in economics and business. But why does this pattern emerge? I show why using a paper clip experiment. Note: VSauce later made a video about Zipf’s law that uses this same experiment but does the math incorrectly. The long tail should be for the single
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
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
The Josephus Problem, featuring Daniel Erman from University of Wisconsin-Madison. Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k More links & stuff in full description below ↓↓↓ Correction: Around 9:40 that should be L less than 2^a NOT 2a — Sorry, typo in editing! But you got the point hopefully. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website:
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
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
In 1911, Srinivasa Ramanujan posed this problem involving an infinite nested radical (a never-ending expression that has square roots inside of square roots). Can you figure out how to simplify the equation? The video presents an intuitive solution. Technically it is necessary to prove the equation has a solution (the nested radical converges) because crazy
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
Thanks to Taka for the suggestion! This is a fun and challenging geometry problem. Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Source https://twitter.com/panbtc/status/1232235184335908864 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
Dr James Grime is back and talking about tortoises. More links & stuff in full description below ↓↓↓ In many ways this video follows on from http://www.youtube.com/watch?v=bFNjA9LOPsg and then http://www.youtube.com/watch?v=CMP9a2J4Bqw 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
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 byu/Irratix inmathriddles Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many
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
This is a really fun geometry problem. It comes from the UKMT, a test which is part of forming the Olympiad team in the UK. Thanks to Liam for sending it to me! Can you figure it out? 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
Banks, Facebook, Twitter and Google use epic numbers – based on prime factors – to keep our Internet secrets. This is RSA public-key encryption. More links & stuff in full description below ↓↓↓ Gold Vault: https://youtu.be/CTtf5s2HFkA This video features Dr James Grime (http://singingbanana.com/). Message from James: “Thanks to Dr Chris Hughes of the University of
Some students in Finland missed out on 1000 euros because they missed this problem! Sources for problem https://old.reddit.com/r/math/comments/cy7u04/a_very_simple_but_tricky_question_from_finnish/ @rizka commented with a link to the 2014 exam (in Finnish). It is question 4: https://yle.fi/progressive/fynd/oppiminen/oppiminen.yle.fi/yo-kokeet/matematiikka_pitka.pdf Quadratic equation history (Brahmagupta) https://www-history.mcs.st-and.ac.uk/HistTopics/Quadratic_etc_equations.html https://en.wikipedia.org/wiki/Quadratic_equation#History Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?Subscribe https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Click to watch all
Thanks to http://www.audible.com/numberphile More links & stuff in full description below ↓↓↓ Here’s the paper Dr Grime discusses: http://arxiv.org/pdf/1101.4470.pdf OEIS: http://oeis.org Dr Grime: http://singingbanana.com 1729: http://youtu.be/LzjaDKVC4iY 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/
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
The Prime Number Theorem shows that primes are like weeds, popping up everywhere! Dr James Grime explains — Little bit extra cut from this video: http://youtu.be/TMRZYSQGAcw More links & stuff in full description below ↓↓↓ Our prime number video collection: http://bit.ly/primevids Follow James on Twitter at: https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile
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
Infographics are not new.. in 1862 Charles Joseph Minard created a much-praised infographic depicting Napoleon’s invasion of Russia in 1812. More links & stuff in full description below ↓↓↓ This video features Dr James Grime – http://singingbanana.com More of James on Numberphile: http://bit.ly/grimevideos Here is the info graphic: http://en.wikipedia.org/wiki/File:Minard.png A book coming soon about the
The problem is a little bit complex, but the answer is delightfully sur-pi-sing! 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 some comments before the video is published? Get early access and support the channel on Patreon https://www.patreon.com/mindyourdecisions If you buy from the
Patreon: http://www.patreon.com/numberphile More links & stuff in full description below ↓↓↓ Tony Padilla is an associate professor of physics at the University of Nottingham. Here he discusses the zeta function and Apéry’s Constant. More Tony videos: http://bit.ly/Padilla_Numberphile Tony’s Tweet: https://twitter.com/DrTonyPadilla/status/828527018081918976 Roger Apéry pics courtesy of François Apéry Numberphile is supported by the Mathematical Sciences Research
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
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
To complete a job, it takes: Alice and Bob 2 hours, Alice and Charlie 3 hours, and Bob and Charlie 4 hours. How long will the job take if all 3 work together? Many, many US college students set up the equations incorrectly and get the wrong answer. Can you solve it? Watch the video
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
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 https://twitter.com/blackpenredpen/status/1284719356799115264 BlackPenRedPen video (English) BlackPenRedPen video (Chinese) China Times News 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
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
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