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…

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…

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…

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…

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 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,…

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…

Tips to be a better problem solver [Last live 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…

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…