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 soon… 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…

Why aren’t you making math videos? (Also, now there’s a 3b1b podcast)

From 3Blue1Brown. Learn more and submit: https://3b1b.co/SoME1 Podcast/New channel: https://youtu.be/C-i4q-Xlnis ↓↓Things referenced through the video↓↓ Join the discord channel: https://discord.gg/SRTErdZ9 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…

Eureka Sequences – Numberphile

From Numberphile. OEIS founder Neil Sloane with more sequences to ponder – of course! Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile Visit the OEIS: https://oeis.org/ Today’s featured sequences: https://oeis.org/A008864 and https://oeis.org/A001043 Numberphile is supported by the Mathematical…

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…

The Levine Sequence – Numberphile

From Numberphile. Neil Sloane from the OEIS has another number sequence which escalates quickly. More links & stuff in full description below ↓↓↓ More videos with Neil Sloane: http://bit.ly/Sloane_Numberphile Levine’s sequence on the OEIS: https://oeis.org/A011784 Neil is the founder and keeper of the The On-Line Encyclopedia of Integer Sequences: https://oeis.org/ Numberphile Podcast: https://www.numberphile.com/podcast Unmade Podcast:…

Nightingale Diagrams – Numberphile

From Numberphile. Professor Mike Merrifield discusses diagrams popularized by Florence Nightingale. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Professor Mike Merrifield is an astronomer at the University of Nottingham, UK. He’s updating his own Nightingale diagram regularly on Twitter: https://twitter.com/AstroMikeMerri More videos…

Cuneiform Numbers – Numberphile

From Numberphile. Alex Bellos discusses how numbers were written in ancient Cuneiform. More links & stuff in full description below ↓↓↓ More from this interview on Numberphile2: https://youtu.be/n-sxOVSZc-Q Alex Bellos website: http://www.alexbellos.com And his books on Amazon (including the Language Lovers Puzzle Book which features cuneiform): https://amzn.to/3czJjXl More Alex Bellos on Numberphile: http://bit.ly/Bellos_Playlist Search the…

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…

Gabriel’s Horn Paradox – Numberphile

From Numberphile. Featuring Tom Crawford. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/EsX9y0lKsZw Tom Crawford’s website, with links to his work and other outreach: https://tomrocksmaths.com More Tom Crawford videos on Numberphile: http://bit.ly/Crawford_Videos Infinity Paradoxes: https://youtu.be/dDl7g_2x74Q Vuvuzelas on…

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."…

Annoying Puzzles (and Cognitive Reflection Problems) – Numberphile

From Numberphile. This video features Tim Harford. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ See an extra snippet from this interview on Numberphile2: https://youtu.be/1lwocqnBmVc Tim Harford website: https://timharford.com How to Make the World Add Up: https://amzn.to/3oBcDRx Or (different title in the US):…

Why Bayes rule is nicer with odds

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,…

Why was Biden’s win calculated to be ONE IN A QUADRILLION?

From Standup Mathematician. This is Part III out of ‘one with a quadrillion zeros’ parts. Give the gift of Stand-up Maths this Christmas: https://www.patreon.com/standupmaths https://mathsgear.co.uk/ Part I: "Why do Biden’s votes not follow Benford’s Law?" https://www.youtube.com/watch?v=etx0k1nLn78 Part II: "Do these scatter plots reveal fraudulent vote-switching in Michigan?" https://www.youtube.com/watch?v=aokNwKx7gM8 Here is the Supreme Court filing from…

What was the first (known) maths mistake?

From Standup Mathematician. Thanks to Waterstones for choosing Humble Pi as a ‘top 100’ paperback of the year. https://www.waterstones.com/book/humble-pi/matt-parker/9780141989143 Signed copies are available at Maths Gear. It’s cheaper at Waterstones, but not signed. You choose! https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback Thanks to Robert Englund and the Free University of Berlin for producing Archaic Bookkeeping. What a niche but amazing…

Can you solve the banana puzzle?

From Standup Mathematician. Check out the Maths Inspiration shows here: http://mathsinspiration.com/ 24 Nov: Visualizing Math(s) 04 Dec: Christmas Special You should definitely watch Destin’s SmarterEveryDay video: Why Snatch Blocks are AWESOME (How Pulleys Work) https://www.youtube.com/watch?v=M2w3NZzPwOM Thanks to Hugh for actually weighing the bananas. http://www2.eng.cam.ac.uk/~hemh1/ The puzzle is a creation of Rob Eastaway. https://robeastaway.com/ Support me…

Do these scatter plots reveal fraudulent vote-switching in Michigan?

From Standup Mathematician. Here is the Dr Shiva Ayyadurai video I am talking about: https://www.youtube.com/watch?v=Ztu5Y5obWPk This is my previous video on Benford’s Law: https://www.youtube.com/watch?v=etx0k1nLn78 Support me on Patreon and I’ll make more maths videos. Probably not on election data, mind you. (Please, for the love of plot, no more election data.) https://www.patreon.com/standupmaths The page of…

Why do Biden’s votes not follow Benford’s Law?

From Standup Mathematician. My book is cheap at Waterstones and signed at Maths Gear: https://www.waterstones.com/book/humble-pi/matt-parker/9780141989143 https://mathsgear.co.uk/products/humble-pi-signed-paperback Check out Steve Mould’s Numberphile video about Benford’s Law. https://www.youtube.com/watch?v=XXjlR2OK1kM Buy a signed copy of "How Many Socks Make a Pair?" by Rob Eastaway. https://mathsgear.co.uk/products/copy-of-signed-copy-of-why-do-busses-come-in-threes There’s more on Mark Nigrini’s work here: http://www.nigrini.com/benfords-law/ "Benford’s Law and the Detection of…

What is a Vampire Matrix?

From Standup Mathematician. Apply for a paid internship at Jane Street! Or, a job. https://www.janestreet.com/join-jane-street/info-booth/ Vampire Numbers on Numberphile with James Grime. https://youtu.be/3ZMnVd4ivKQ Flammable Math’s original tweet: https://twitter.com/FlammableMaths/status/1306303462607654914 Robin Houston gets involved: https://twitter.com/robinhouston/status/1306539901576503297 Here comes Greg Egan! https://twitter.com/gregeganSF/status/1306565923671736320 Robin’s tweets about characteristic polynomials and the Cayley-Hamilton theorem. I suggested looking them up and working through…

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…

Hamming codes and error correction

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?…

Tips to be a better problem solver [Last lecture] | Lockdown math ep. 10

From 3Blue1Brown. Tips on problem-solving, with examples from geometry, trig, and probability. Past episodes with integrated quizzes: https://itempool.com/c/3b1b Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Huge huge thanks to Ben Eater: https://www.youtube.com/user/eaterbc And Cam Christensen, creator of ItemPool: https://itempool.com/ Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1265480770832855040 Mistakes: 50:35, there should be a…

Intuition for i to the power i | Lockdown math ep. 9

From 3Blue1Brown. i^i, visualized and explained. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Mistakes: At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It’s what we’d think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i)…

The DP-3T algorithm for contact tracing (via Nicky Case)

From 3Blue1Brown. Though many contact tracing apps involve location tracking, they don’t have to. This is a video adaptation of a post by Nicky Case: https://ncase.me/contact-tracing/ New post by Nicky on COVID-19: https://ncase.me/covid-19/ Consider supporting his work: https://www.patreon.com/ncase/ Supporters of this video: https://3b1b.co/ctracing-thanks DP-3T Whitepaper: https://github.com/DP-3T/documents/blob/master/DP3T%20White%20Paper.pdf Full repo: https://github.com/DP-3T Where did the number 60% come…

The power tower puzzle | Lockdown math ep. 8

From 3Blue1Brown. A fun puzzle stemming from repeated exponentiation. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Notes by Ngân Vũ: https://twitter.com/ThuyNganVu/status/1261014161464516608?s=20 Play along on Desmos: https://www.desmos.com/calculator/nul32eaaa9 Related videos. Calculus series: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr In particular look at: https://youtu.be/CfW845LNObM Numberphile on Grahm’s constant: https://youtu.be/XTeJ64KD5cg —————— Video timeline (thanks to user "noonesperfect") 0:36 Question…

What makes the natural log “natural”? | Lockdown math ep. 7

From 3Blue1Brown. All about ln(x). Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1259288683489849344 Errors: At minute 16, the sum should be written with a "…" to indicate going to infinity. At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent…

Logarithm Fundamentals | Lockdown math ep. 6

From 3Blue1Brown. Back to the basics with logarithms. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Triangle of power: https://youtu.be/sULa9Lc4pck Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258222677573001219 —————— The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music…

Euler’s crazy pi formula generator

From Mathologer. Today we derive them all, the most famous infinite pi formulas: The Leibniz-Madhava formula for pi, John Wallis’s infinite product formula, Lord Brouncker’s infinite fraction formula, Euler’s Basel formula and it’s infinitely many cousins. And we do this starting with one of Euler’s crazy strokes of genius, his infinite product formula for the…

Imaginary interest rates | Lockdown math ep. 5

From 3Blue1Brown. Compound interest, e, and how it relates to circles. Full playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Great Mathologer video: https://youtu.be/-dhHrg-KbJ0 Beautiful pictorial summary by @ThuyNganVu: https://twitter.com/ThuyNganVu/status/1258221677990703105 https://twitter.com/ThuyNganVu/status/1258222002889875457 My other videos on imaginary exponents: https://youtu.be/v0YEaeIClKY https://youtu.be/mvmuCPvRoWQ Mistakes: In the off-handed remarks on quaternions, I mentioned rotation in 4d would…