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
Math
Thanks to Ryan from India for the suggestion! Two candles of equal height but different thickness are lit. The first burns off in 8 hours and the second in 10 hours. When will the first candle be half the height of the second? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many
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
Thanks to Amit from India for the suggestion! A circle is tangent on the exterior of a side of a triangle and tangent to the lines through the other two sides. The tangent side length 7, and the other side lengths are 8 and 9. What is the radius of the circle? 0:00 Problem 1:22
17 is the minimum number of clues required to give a unique sudoku solution – but how did mathematicians prove this? Featuring James Grime. More links & stuff in full description below ↓↓↓ Dr James Grime discusses a recent paper which cracked the problem. The paper being discussed by McGuire and others is at http://arxiv.org/abs/1201.0749
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
Matt Parker explores the work of William Shanks – and boots up the ShanksBot. More links & stuff in full description below ↓↓↓ Matt Parker’s 2022 Pi Day Video: https://youtu.be/dtiLxLrzjOQ Discussing William Shanks on Objectivity: https://youtu.be/7yTXMeiVBCc Prime Number playlist: https://bit.ly/PrimePlaylist Pi playlist: http://bit.ly/PiPlaylist Matt Parker website: https://standupmaths.com Numberphile is supported by the Mathematical Sciences Research
Our Pi Playlist (more videos): http://bit.ly/PiPlaylist How accurately can we calculate Pi using hundreds of REAL pies? More links & stuff in full description below ↓↓↓ Extended version of this video (director’s slice) at http://www.youtube.com/watch?v=x4kyFKyCMv0 This video features Matt Parker: https://twitter.com/standupmaths Matt believes this is the world’s most accurate pie-based Pi calculation. More Pi videos:
Thanks to Victor for the suggestion! A version of this problem appeared on a Kangaroo math competition for 12-13 year olds. Can you figure it out? Special thanks this month to: Michael Anvari, Daniel Lewis, Robert Zarnke, Kyle, Mike Robertson. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Original Math Kangaroo question on YouTube Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1
A 6’28” version of our “Pi with Pies” calculation. More links & stuff in full description below ↓↓↓ Videos features Matt Parker who tweets at https://twitter.com/standupmaths The Pi-inspired music in the video explained: http://periodicvideos.blogspot.co.uk/2013/03/pimusic.html Our full collection of Pi videos at http://bit.ly/W4oDN1 While the pies are usually delicious, this batch was not for consumption (even
People often email me that my videos helped them get a tech or finance job, which is really awesome, and I want to do more to help! So in this video I’m sharing a problem based on an interview question asked at Facebook. Source https://www.glassdoor.com/Interview/You-re-about-to-get-on-a-plane-to-Seattle-You-want-to-know-if-you-should-bring-an-umbrella-You-call-3-random-friends-of-y-QTN_519262.htm (Note: I re-uploaded this video with corrections. The original calculations
Our Pi Playlist (more videos): http://bit.ly/PiPlaylist Steve Mould (tau) and Matt Parker (pi) go head-to-head. More links & stuff in full description below ↓↓↓ See our tau video: http://www.youtube.com/watch?v=83ofi_L6eAo And check our Pi videos: http://www.youtube.com/playlist?list=PL4870492ACBDC2E7C Matt Parker: http://www.standupmaths.com/ Steve Mould: http://www.stevemould.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
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:
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
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU Cliff Stoll discusses a “Remarkable Theorem”, Gaussian curvature and pizza. More links & stuff in full description below ↓↓↓ Postscript note from Cliff: “Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also
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!
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:
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
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
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
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):
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
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:
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
A ‘math metal’ song about the golden ratio (aka Phi). More links & stuff in full description below ↓↓↓ See more about the making of the song and maths behind it at: http://www.youtube.com/watch?v=mqK63v2Jzks This was a collaboration with the excellent Dave Brown – his channel is: http://www.youtube.com/user/wwwboyinabandcom (check it out!!!) Also featuring Professor Phil Moriarty
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
The Joker asks the mob for half the money. Why is this a reasonable amount? I’ve explained the scene in more detail here: Negotiating with the mob – Game theory in the Dark Knight part 2 Game Theory 101 on alternating ultimatum game (Rubinstein Bargaining) https://www.youtube.com/watch?v=EunqjqDR9_w If you like my videos, you can support me
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
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 https://twitter.com/wisbin/status/1027607378668208129 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
People around the world have asked me this and similar problems. Learn how to solve using only geometry (and a little bit of algebra). There are many other ways to solve the problem too https://www.mathalino.com/reviewer/plane-geometry/02-area-common-arcs-quarter-circles 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
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
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
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
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
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
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
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