Music on a Clear Möbius Strip – Numberphile

From Numberphile. The mathematical genius of JS Bach – featuring Marcus Du Sautoy. More links & stuff in full description below ↓↓↓ See books by Marcus, including his latest "Thinking Better: The Art of the Shortcut" — https://amzn.to/3j5FygD Marcus’ website with latest info: https://www.simonyi.ox.ac.uk Marcus on Twitter: https://twitter.com/MarcusduSautoy Other Marcus videos on Numberphile: https://bit.ly/Marcus_Numberphile Marcus…

Where Newton meets Mandelbrot (Holomorphic dynamics)

From 3Blue1Brown. How the right question about Newton’s method results in a Mandelbrot set. Video on Newton’s fractal: https://youtu.be/T_S2j5GaLRQ Special thanks: https://3b1b.co/lessons/newtons-fractal#thanks Extra special thanks to Sergey Shemyakov, of Aix-Marseille University, for helpful conversations and for introducing me to this phenomenon. —————— Introduction to Fatou sets and Julia sets, including a discussion of Montel’s theorem…

Trapped Water and Tiny Holes – Numberphile

From Numberphile. Tom Crawford shows why water doesn’t fall through a sieve with small enough holes. More links & stuff in full description below ↓↓↓ Tom Crawford’s website, with links to his work and other outreach: https://tomrocksmaths.com More Tom videos on Numberphile: http://bit.ly/Crawford_Videos Tom on the Numberphile Podcast: https://youtu.be/_HwKGncsGo0 Numberphile is supported by the Mathematical…

Newton’s Fractal (which Newton knew nothing about)

From 3Blue1Brown. Who knew root-finding could be so complicated? Early view of the next part: https://www.patreon.com/posts/57323044 An equally valuable form of support is to simply share the videos. —————— On fractal dimension: https://youtu.be/gB9n2gHsHN4 Mathologer on the cubic formula: https://youtu.be/N-KXStupwsc Some of the videos from this year’s Summer of Math Exposition are fairly relevant to the…

Find your own ABC Conjecture Triple

From Standup Mathematician. Find your own ABC triple: https://abc.tngtech.com Details about Jane Street + University of Oxford’s Black Academic Futures Scholarships: http://www.maths.ox.ac.uk/study-here/postgraduate-study/jane-street-graduate-scholarships Huge thanks to Sebastian Stamminger and Daniel Pape from TNG for all of their help. TNG: https://www.tngtech.com Big Techday: https://www.tngtech.com/tng-ueber-uns/bigtechday.html Here is James Grime talking ABC. https://youtu.be/RkBl7WKzzRw Manim “math animation” community version: https://www.manim.community

Measure the Earth’s Radius! (with this one complicated trick)

From Standup Mathematician. Hannah’s book is out now! https://www.waterstones.com/book/rutherford-and-frys-complete-guide-to-absolutely-everything-abridged/adam-rutherford/hannah-fry/2928377065652 https://www.amazon.co.uk/dp/1787632636/ If you have a spare 2⅔ hours you can watch Matt hand craft a protractor. Yes, I know the audio is glitchy. https://youtu.be/rSox1RRbxXA More about Abu Arrayhan Muhammad ibn Ahmad al-Biruni: https://mathshistory.st-andrews.ac.uk/Biographies/Al-Biruni/ This video was made possible by my Patreon supporters for. Those cocktails were…

Finite Fields & Return of The Parker Square – Numberphile

From Numberphile. Matt Parker introducing Finite Fields and re-visits the infamous Parker Square… Extra footage & become a millionaire by winning The Parker Prize: https://youtu.be/hn8SwBhhDvU More links & stuff in full description below ↓↓↓ The Original Parker Square video: https://youtu.be/aOT_bG-vWyg The paper featured in this video: https://arxiv.org/abs/1908.03236 MATT PARKER STUFF Stand-Ups Maths on YouTube: https://www.youtube.com/user/standupmaths…

Why don’t they teach Newton’s calculus of ‘What comes next?’

From Mathologer. Another long one. Obviously not for the faint of heart 🙂 Anyway, this one is about the beautiful discreet counterpart of calculus, the calculus of sequences or the calculus of differences. Pretty much like in Alice’s Wonderland things are strangely familiar and yet very different in this alternate reality calculus. Featuring the Newton-Gregory…

Stacked Dice Trick – Numberphile

From Numberphile. A third dice trick with Ben Sparks – see the trilogy of tricks at: https://bit.ly/Dice_Trilogy More links & stuff in full description below ↓↓↓ Ben Sparks: https://www.bensparks.co.uk And his YouTube: https://www.youtube.com/c/SparksMaths More Ben Sparks on Numberphile: http://bit.ly/Sparks_Playlist Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by…

The Strange Orbit of Earth’s Second Moon (plus The Planets) – Numberphile

From Numberphile. Featuring Matt Henderson… Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Matt: https://bit.ly/MattHendersonPlaylist Follow his work on Twitter at: https://twitter.com/matthen2 Previous video with Matt (Chaotic Balls): https://youtu.be/6z4qRhpBIyA Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile…

Area of the Q – Numberphile

From Numberphile. Johnny Ball is back talking about Hippocrates, Lunes, and a Fancy Q. More links & stuff in full description below ↓↓↓ Johnny Ball’s website: https://johnnyball.co.uk More Johnny on Numberphile: https://bit.ly/Johnny_Ball An earlier Lunes video we did with Barry Mazur: https://www.youtube.com/watch?v=n_FsAwvxBI8 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are…

The Lightning Algorithm – Numberphile

From Numberphile. Matt Henderson is making lightning in mazes. Check out https://www.kiwico.com/Numberphile and get 50% off your first month of any subscription. More links & stuff in full description below ↓↓↓ More videos with Matt: https://bit.ly/MattHendersonPlaylist Follow his work on Twitter at: https://twitter.com/matthen2 Maze solving on our sister channel, Computerphile: https://www.youtube.com/watch?v=rop0W4QDOUI Numberphile is supported by…

Get Off The Earth (a famous & bamboozling problem) – Numberphile

From Numberphile. Featuring Ben Sparks… Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Ben Sparks: https://www.bensparks.co.uk More Ben Sparks on Numberphile: http://bit.ly/Sparks_Playlist Related Geogebra files… Disappearing bicyclist: https://www.geogebra.org/m/hypuahfc Disappearing face: https://www.geogebra.org/m/azwghu4a Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We…

Why the longest English word is PAPAL and SPA is the pointiest.

From Standup Mathematician. Get Private Internet Access for 2.08 $/month: https://privateinternetaccess.com/standupmaths (That’s cheaper than what I’m paying!) Here are my files with all the distances and angles on a keyboard. http://pi-ratebay.com/files/all_keyboard_distances.txt http://pi-ratebay.com/files/all_keyboard_angles.txt If you want the original coordinates of all keys, I’m pretty sure you can find that on http://pi-ratebay.com/ Thanks to everyone who made…

Mathematics is all about SHORTCUTS – Numberphile

From Numberphile. Featuring Marcus du Sautoy from Oxford University. Check his latest book "Thinking Better: The Art of the Shortcut" Links & stuff in full description below ↓↓↓ Marcus’s new book on Amazon here: https://amzn.to/3xrujmS (US) https://amzn.to/3jmBJD1 (UK) Marcus on the Numberphile Podcast: https://youtu.be/PVSkzNOXG1k And a Numberphile video about Gödel’s Incompleteness Theorem: https://youtu.be/O4ndIDcDSGc The Seven…

The most ridiculously complicated maths card trick.

From Standup Mathematician. Check out the Jane Street podcast: Signals and Threads. My goodness it’s nerdy. I love it. https://signalsandthreads.com/ You can watch the original live-stream of the trick here. I actually did it twice! Yeah, now you’re convinced, you sceptical bunch you. https://youtu.be/hlsN32dBCHQ Here is my previous video about perfect bridge deals. https://www.youtube.com/watch?v=s9-b-QJZdVA 52-Card…

A Problem with Rectangles – Numberphile

From Numberphile. Featuring Tom Crawford and an Oxford Admissions Question… Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Extra footage: https://youtu.be/IGiBTK3EtLs More links & stuff in full description below ↓↓↓ More Tom videos on Numberphile: http://bit.ly/Crawford_Videos Tom on the Numberphile Podcast: https://youtu.be/_HwKGncsGo0 Tom Crawford’s website, with links to his work and other…

Why does this balloon have -1 holes?

From Standup Mathematician. Thank you to BetterHelp for sponsoring this video! To get 10% off your first month of therapy, go to https://betterhelp.com/standupmaths to sign up today. If you are need of urgent mental health support please check for crisis help lines available in your country. USA: https://www.mentalhealth.gov/get-help/immediate-help UK: https://www.nhs.uk/mental-health/advice-for-life-situations-and-events/where-to-get-urgent-help-for-mental-health/ Do check out Jordan Ellenberg’s…

How do you prove a prime is infinitely fragile?

From Standup Mathematician. Consecutive primes which are widely digitally delicate. https://people.math.sc.edu/filaseta/ConsecutiveDigitallyDelicatePrimes2021.pdf Data from the paper: https://people.math.sc.edu/filaseta/ConsecutiveWDDPrimes.html Here is the bonus footage. https://youtu.be/wtzgbJuHSfM And yes, the theme song (along with the remix) is on Bandcamp as ‘pay what you want’. So you can download for free, or pay something to help support the channel. https://standupmaths.bandcamp.com/track/digits-are-forever-inc-prime-remix More…

Chaotic Balls (and other animations) – Numberphile

From Numberphile. Matt Henderson shows us a few animations he created to depict chaos. More links & stuff in full description below ↓↓↓ More videos with Matt: https://bit.ly/MattHendersonPlaylist Follow his work on Twitter at: https://twitter.com/matthen2 Chaos with Ben Sparks: https://youtu.be/kbKtFN71Lfs Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported…

Three Dice Trick – Numberphile

From Numberphile. Ben Sparks with another trick – can you guess how it works before he explains it? More links & stuff in full description below ↓↓↓ This is the second of a trilogy of dice tricks with Ben Sparks… More to come… Martin Gardner called this trick "Guessing The Total". More dice videos from…

On making math videos

From 3Blue1Brown. Announcement for the 2021 Summer of Math Exposition Podcast/New channel: https://www.youtube.com/GrantSanderson Details: https://3b1b.co/SoME1 ↓↓Things referenced through the video↓↓ James Schloss: https://www.youtube.com/user/LeiosOS Free will theorem: https://www.ams.org/notices/200902/rtx090200226p.pdf Kolmogorov complexity and primes: https://people.cs.uchicago.edu/~fortnow/papers/kaikoura.pdf Tadashi Tokieda talk: https://youtu.be/tQQ3oiB32GI Boarbarktree: https://www.youtube.com/channel/UCFeIEAkqvS4fJMTwUtF4OFw Mathologer: https://youtu.be/N-KXStupwsc Manim: https://github.com/3b1b/manim Manim Community edition: https://github.com/ManimCommunity/manim/ Reanimate: https://github.com/reanimate/reanimate Javis: https://github.com/Wikunia/Javis.jl Smoothstep: https://smoothstep.io/ Matt Henderson: https://twitter.com/matthen2/status/1262247041238839296…

The Volume of a Sphere – Numberphile

From Numberphile. 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…

Planing Sequences (Le Rabot) – Numberphile

From Numberphile. Featuring Neil Sloane from the OEIS – and his carpenter’s plane. Mandelbrot papers offer: https://www.patreon.com/posts/52011294 More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile The OEIS: https://oeis.org Discuss this video on Brady’s subreddit: https://redd.it/nrba65 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also…

Parabolas and Archimedes – Numberphile

From Numberphile. This video features Johnny Ball. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (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 Institute (MSRI): http://bit.ly/MSRINumberphile We are also…

Gambling with the Martingale Strategy – Numberphile

From Numberphile. Tom Crawford discussing roulette and gambling with a famed strategy. More Tom videos on Numberphile: http://bit.ly/Crawford_Videos More links & stuff in full description below ↓↓↓ Tom Crawford’s website, with links to his work and other outreach: https://tomrocksmaths.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by…

How many 3D nets does a 4D hypercube have?

From Standup Mathematician. Get to know Jane Street! https://www.janestreet.com/join-jane-street/get-to-know-us/ Which hypercube unfoldings tile space? https://whuts.org/ Yes, you can buy one of the 261 models from this video and support the channel. All hand-numbered by me and with a signed certificate of authenticity. https://mathsgear.co.uk/products/cube-model Here is Giovanna Diaz and Joseph O’Rourke’s paper: https://arxiv.org/abs/1512.02086 A091159 Number of…

A Sequence with a Mistake – Numberphile

From Numberphile. Sequence guru Neil Sloane on a sequence which puzzled him – until he spotted the mistake! More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile The OEIS: https://oeis.org Hanny’s Voorwerp: https://youtu.be/RDr6bSB6Vlg Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science…

A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra

From 3Blue1Brown. How to write the eigenvalues of a 2×2 matrix just by looking at it. Need a refresher on eigenvalues? https://youtu.be/PFDu9oVAE-g Thanks to Tim for the jingle: https://www.youtube.com/acapellascience Help fund future projects: https://www.patreon.com/3blue1brown​ An equally valuable form of support is to simply share the videos. Special thanks to these supporters: https://3b1b.co/quick-eigen-thanks Lockdown math lecture…

The Pigeon Hole Principle: 7 gorgeous proofs

From Mathologer. Let’s say there are more pigeons than pigeon holes. Then, if all the pigeons are in the holes, at least one of the holes must house at least two of the pigeons. Completely obvious. However, this unassuming pigeon hole principle strikes all over mathematics and yields some really surprising, deep and beautiful results.…

Exploring the mysteries of the Prime (gaps!) Line.

From Standup Mathematician. Sign-up for Private Internet Access and we can be VPN buddies! Under $3 a month. https://www.privateinternetaccess.com/standupmaths Thanks to Kerry D. Wong who originally piqued my interest by sending me this: http://www.kerrywong.com/2009/09/06/an-alternative-illustration-of-prime-number-distribution/ Here are the papers about finding arbitrarily large gaps between primes: The first paper: https://arxiv.org/abs/1408.4505​ The paper one day later: https://arxiv.org/abs/1408.5110…

How (and why) to raise e to the power of a matrix | DE6

From 3Blue1Brown. General exponentials, love, Schrödinger, and more. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/mat-exp-thanks —————— The Romeo-Juliet example is based on this essay by Steven Strogatz: http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math The book shown at the start is Vladimir Arnold’s…

Calculating π with Avogadro’s Number

From Standup Mathematician. Check out Steve Mould’s Pythagorean Siphon video: https://www.youtube.com/watch?v=Cg8KQfaT9xY&ab_channel=SteveMould Every Pi Day I calculate the digits of π somehow. This year I counted the number of molecules in a disc as a ‘real accurate’ way to measure its surface area. You can see all the previous videos here: https://www.youtube.com/watch?v=CKl1B8y4qXw&list=PLhtC92GarkjyYbxI3-4qzIWIRbZaw4wuP Yes, you can buy…

The ultimate algorithm

From Mathologer. There must be millions of people who have heard of the Tower of Hanoi puzzle and the simple algorithm that generates the simplest solution. But what happens when you are playing the game not with three pegs, as in the original puzzle, but with 4, 5, 6 etc. pegs? Hardly anybody seems to…

Why π^π^π^π could be an integer (for all we know!).

From Standup Mathematician. Check out the Jane Street programs if you’re considering a mathematics/finance/programming job: https://www.janestreet.com/join-jane-street/our-programs/ Here is Tim Gowers’s reply to the original tweet: https://twitter.com/wtgowers/status/1346212151581700096 Start your Schanuel’s Conjecture journey here: https://mathworld.wolfram.com/SchanuelsConjecture.html 3^3^3^3 on wolfram alpha: https://www.wolframalpha.com/input/?i=3%5E3%5E3%5E3 And for completeness, here is pi^pi^pi^pi: https://www.wolframalpha.com/input/?i=pi%5Epi%5Epi%5Epi If you have opinions about my 2n conjecture, send an…

How lucky is too lucky?: The Minecraft Speedrunning Dream Controversy Explained

From Standup Mathematician. Buy my book Humble Pi now! https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/ UPDATE: Harvard Book Store have totally sold out. My talk on 4 February 2021 at Harvard Book Store: https://www.harvard.com/event/virtual_event_matt_parker/ Here is the original accusation against Dream. Video: https://www.youtube.com/watch?v=-MYw9LcLCb4&ab_channel=Geosquare Paper: https://mcspeedrun.com/dream.pdf And here is Dream’s reply. Video: https://www.youtube.com/watch?v=1iqpSrNVjYQ&ab_channel=DreamXD Paper: https://drive.google.com/file/d/1yfLURFdDhMfrvI2cFMdYM8f_M_IRoAlM/view "Matt flips a coin 100 times."…

The medical test paradox, and redesigning Bayes’ rule

From 3Blue1Brown. About Likelihood Ratios, also sometimes called Bayes Factors*. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/bayes-factor-thanks Home page: https://www.3blue1brown.com The book by my friend Matt Cook about paradoxes mentioned at the end: https://amzn.to/3aBrEzg On the topic,…

How did Ramanujan solve the STRAND puzzle?

From Mathologer. Today’s video is about making sense of an infinite fraction that pops up in an anecdote about the mathematical genius Srinivasa Ramanujan. 00:00 Intro 04:31 Chapter 1: Getting a feel for the puzzle 08:27 Chapter 2: Algebra autopilot 12:37 Chapter 3: Infinite fraction 17:51 Chapter 4: Root 2 21:19 Chapter 5: Euclidean algorithm…

Hamming codes part 2, the elegance of it all

From 3Blue1Brown. Part 1: https://youtu.be/X8jsijhllIA Watch Ben Eater’s video: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks A cleaner perspective on Hamming error correction codes. You can read Hamming’s own perspective on his discovery of these codes…

How to send a self-correcting message

From 3Blue1Brown. A discovery-oriented introduction to error correction codes. Part 2: https://youtu.be/b3NxrZOu_CE Ben Eater:’s take: https://youtu.be/h0jloehRKas Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/hamming-thanks Heavily related is the chessboard puzzle I did with Matt Parker: https://youtu.be/as7Gkm7Y7h4 You can…

The impossible chessboard puzzle

From 3Blue1Brown. An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com —————— 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case…

What is the best way to lace your shoes? Dream proof.

From Mathologer. A blast from the past. A video about my fun quest to pin down the best ways of lacing mathematical shoes from almost 20 years ago. Lots of pretty and accessible math. Includes a proof that came to me in a dream (and that actually worked)! 0:00 Intro 1:31 What’s a mathematical lacing?…