L-Functions are likely to play a key role in proving the Riemann Hypothesis, says Professor Jon Keating from the University of Bristol. More links & stuff in full description below ↓↓↓ L-Function & Modular Form database: http://www.lmfdb.org Prime Number and Riemann Hypothesis playlist: http://bit.ly/primevids Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:
Math
This is adapted from a problem given to 14-16 year old students. Watch the video to learn how to solve it! Source (in Spanish) http://mimosa.pntic.mec.es/jcolon/pjanteriores3.html http://mimosa.pntic.mec.es/jcolon/soluciones3.html#3-14p27 “Learn Right, Not Rote.” Kalid Azad, BetterExplained (https://betterexplained.com/) 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
Another pass at the Monty Hall Problem – see the last video and a new “express explanation” at: http://bit.ly/MontyHallProb 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 (MSRI):
Photomath can’t solve this, and neither can Mathway, Symbolab, or Desmos. Can you? I explain how you can. A similar problem was given to high school students in Massachusetts, and you really have to know what you’re doing to figure it out. Thanks to all patrons! Special thanks this month to: Shrihari Puranik Richard Ohnemus
Prime numbers, Ulam Spirals and other cool numbery stuff with Dr James Grime. More links & stuff in full description below ↓↓↓ James Clewett on spirals at: http://youtu.be/3K-12i0jclM And more to come soon… * subscribing to numberphile does not really change your physical appearance! And “golden line” in this context was made up by Brady!
This is a fun one! Sources National Museum of Mathematics tweet Can you solve this #math problem for #MathMonday? We will reveal the answer in 24 hours! Suppose there is a square ABCD with a point E on edge BC and a point F on edge CD such that the area of triangle ABE is
When is n² + 45 equal to a perfect square, for n a positive integer? I received this MathCounts problem by email from Bill by email. Can you figure it out? Watch the video for a solution. My blog post for this video https://wp.me/p6aMk-5i0 If you like my videos, you can support me at Patreon:
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
Catch a more in-depth interview with Ben Sparks on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile More links & stuff in full description below ↓↓↓ Golden seeds limited edition T-Shirt: https://teespring.com/NP-Seeds More Golden Ratio stuff: http://bit.ly/Golden_Ratio More Ben Sparks Numberphile videos: http://bit.ly/Sparks_Playlist Ben’s Twitter: https://twitter.com/SparksMaths Ben’s website: www.bensparks.co.uk
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
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
The harmonic series and the elusive Euler–Mascheroni constant. More links & stuff in full description below ↓↓↓ Featuring Dr Tony Padilla. Audible: http://www.audible.com/numberphile Extra footage: https://youtu.be/eRGN8ThZfhU Videos about -1/12: http://bit.ly/minus_twelfth Tony at the LHC: https://youtu.be/sVYUqMRolaA (via Sixty Symbols, our physics channel) 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:
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
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
A semicircle contains an inscribed semicircle dividing its diameter into two lengths a and b. Can you find the formula for the inscribed semicircle’s diameter in terms of the lengths a and b? What is the locus of the center of the inscribed semicircle? Thanks to Nick from Greece for the suggestion! Special thanks this
Thanks to Lucas for suggesting this problem! It comes from a Belgian Olympiad problem for 16 to 18 year old students. 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
This is a fun little geometry puzzle! adapted from a puzzle by @Cshearer41 What’s the area of the toppled square? pic.twitter.com/77yHacED5Y — Catriona Agg (@Cshearer41) August 7, 2018 solution 1- area multiplication right squares: 3*4 = 12 and 3*9 = 27, that means *2 and *3 for the sides. 2- roots for sides: √3, 2√3
Solve this to get into Oxford! 2021 Oxford MAT Questions https://www.maths.ox.ac.uk/system/files/attachments/test21.pdf 2021 Oxford MAT Solutions https://www.maths.ox.ac.uk/system/files/attachments/websolutions21.pdf 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
Hannah Fry on parallels between the game “rock paper scissors” and lizards in nature. PART ONE: http://youtu.be/rudzYPHuewc More links & stuff in full description below ↓↓↓ EXTRA FOOTAGE: http://youtu.be/ygHwBxWyI6E Lizards by Pete McPartlan 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
Alex’s book: http://amzn.to/1l0yX46 The Curta is a pocket-sized, mechanical, digital calculator!!! It was invented by Curt Herzstark. More links & stuff in full description below ↓↓↓ Shown here by Alex Bellos, author of Alex’s Adventures in Numberland. More about our contributors, including Alex, at http://www.numberphile.com/team/index.html NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile
These are the answers to the previous video with 3 matchstick puzzlers. 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
Featuring Professor Hannah Fry – more details on her work below. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Hannah Fry: https://hannahfry.co.uk Hannah’s books: https://amzn.to/3ArNEaA Her latest is Rutherford and Fry’s Complete Guide to Absolutely Everything: https://amzn.to/3tSvYDN More Hannah Fry on Numberphile: http://bit.ly/hannah_vids
How do you measure the length of a spiral on a cylinder? There is a neat trick! 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
Google asked this problem as an interview question. If the probability of seeing a car on the highway in 30 minutes is 0.95, what is the probability of seeing a car on the highway in 10 minutes? (assume a constant default probability) The video presents a solution. Blog post: http://wp.me/p6aMk-4Qk Sources http://www.impactinterview.com/2009/10/140-google-interview-questions/ http://www.businessinsider.com/answers-to-15-more-google-interview-questions-that-will-make-you-feel-stupid-2010-11#if-the-probability-of-observing-a-car-in-30-minutes-on-a-highway-is-095-what-is-the-probability-of-observing-a-car-in-10-minutes-assuming-constant-default-probability-2 If you
What is the radius of each sphere? Reference http://puzzling.stackexchange.com/questions/41952/nine-identical-spheres-fit-exactly-into-a-cube 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
Squarespace: http://www.squarespace.com/numberphile This video features Hannah Fry – https://twitter.com/fryrsquared More links & stuff in full description below ↓↓↓ More on this topic (and lizards): http://youtu.be/Z8lv2vy5vco And even more on this topic: http://youtu.be/ygHwBxWyI6E The paper: http://bit.ly/RPSpaper Reddit for this video: http://redd.it/2tq25k Art and animation by Pete McPartlan Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile
This is a delightful problem. Find the area of the triangle defined by the four squares. It seems impossible but it can be solved with the right perspective. Can you figure it out? Sources Puzzle by Catriona Shearer The area of the bottom left square is 5. What’s the area of the blue triangle? pic.twitter.com/nBR32b760x
Can you solve this geometry puzzle? Thanks to Robson for the suggestion! 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/ 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
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
Thanks to Umesh for the suggestion! If the large circle has a radius equal to 1, what is the radius of each small circle? 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
A gigantic pie is shared with 100 guests, and each guest gets an increasing percentage of the remaining pie. Who gets the largest piece? Sources https://www.theguardian.com/science/2017/jun/19/did-you-solve-it-pythagorass-best-puzzles https://puzzling.stackexchange.com/questions/52787/who-get-the-biggest-piece 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 suggested by people around the world. Support on Patreon
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) Proving
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:
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
I bet this one will give many adults a good challenge too. Thanks to Pett for the suggestion! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari, Daniel Lewis, Robert Zarnke. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Singapore International Math Olympiad Challenge (SIMOC) 2015 – Primary 5 Paper, problem 24. Sample Papers Subscribe:
More links & stuff in full description below ↓↓↓ Brady’s Movember Page: http://bit.ly/BradyMo See full description for list of Connect 4 links. John Tromp’s page: http://bit.ly/TrompNumberphile James Allen’s Connect Four book: http://bit.ly/AllenBook James Allen: http://james.fabpedigree.com/ OEIS: https://oeis.org/A212693 Victor Allis paper: http://bit.ly/AllisPaper 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
What is 7×8? This video teaches how you can use your hands to multiply two numbers between 6 and 10 using your fingers. Here’s the reason the method works: https://www.youtube.com/watch?v=eEao6-F7fz8 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
Johnny Ball on the “often missed” Hippocrates of Chios. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk See Johnny discuss Russian multiplication: https://youtu.be/HJ_PP5rqLg0 Numberphile is supported by the Mathematical Sciences Research Institute
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
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
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
Thanks to Jumar for the suggestion! Can you solve this interesting geometry problem? 0:00 Problem 1:10 Similar triangles 2:29 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 commission
If a semicircle and its flipped copy are placed side by side, how much distance do they span from end to end? This is a neat problem adapted from a Mathematical Olympiad Qualifying Test in the Philippines. Can you figure it out? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos).
Professor Tony Padilla is back with another epic number. Our Big Number playlist of previous videos: http://bit.ly/Big_Numbers More links & stuff in full description below ↓↓↓ Busy Beavers on Computerphile: https://youtu.be/CE8UhcyJS0I With thanks to Agustín Rayo himself. Read more from Prof Rayo at: http://web.mit.edu/arayo/www/bignums.html And see his website at: https://arayo.scripts.mit.edu/home/ Tony Padilla: https://twitter.com/DrTonyPadilla Numberphile is
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