3Blue1Brown's video: 2021 Summer of Math Exposition results

Take a look at the full playlist (really): https://www.youtube.com/watch?v=fJWnA4j0_ho&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-Z Blog post with more details: https://3b1b.co/some1-results Thanks, as always, to the supporters of this channel for helping to make this whole project possible: http://3b1b.co/thanks ------------------ Typo at 2:00, it should read "Burkard Polster" Videos and posts mentioned in this video. That weird light at the bottom of a mug — ENVELOPES https://youtu.be/fJWnA4j0_ho Hiding Images in Plain Sight: The Physics Of Magic Windows https://mattferraro.dev/posts/caustics-engineering The Beauty of Bézier Curves https://youtu.be/aVwxzDHniEw What Is The Most Complicated Lock Pattern? https://youtu.be/PKjbBQ0PBCQ Pick's theorem: The wrong, amazing proof https://youtu.be/uh-yRNqLpOg Dirac's belt trick, Topology, and Spin ½ particles https://youtu.be/ACZC_XEyg9U Galois-Free Guarantee! | The Insolubility of the Quintic https://youtu.be/BSHv9Elk1MU The Two Envelope Problem - a Mystifying Probability Paradox https://youtu.be/_NGPncypY68 The Math Behind Font Rasterization | How it Works https://youtu.be/LaYPoMPRSlk What is a Spinor? https://in-theory.net/what-is-a-spinor/ Understanding e https://velipeltola.com/understanding-e/ Ancient Multiplication Trick https://youtu.be/CsMrHzp850M 对称多项式基本定理自我探究 https://www.bilibili.com/video/BV19f4y137mJ Lehmer Factor Stencils https://youtu.be/QzohwKT6TNA What is the limit of a sequence of graphs? https://youtu.be/7Gj9BH4IZ-4 Steiner's Porism: proving a cool animation https://youtu.be/fKAyaP8IzlE Wait, Probabilities can be Negative?! https://youtu.be/std9EBbtOC0 This random graph fact will blow your mind https://youtu.be/3QjZ31lj974 Why is pi here? Estimating π by Buffon's n̶e̶e̶d̶l̶e noodle! https://youtu.be/e-RUyCs9B08 Introduction to Waves https://airladon.github.io/ivid-wave/ Complex Functions https://treena.org/lesson/complex-grapher I spent an entire summer finding this spiral https://youtu.be/n-e9C8g5x68 HACKENBUSH: a window to a new world of math https://youtu.be/ZYj4NkeGPdM The Tale of the Lights Puzzle https://youtu.be/9aZsABF-Vj4 The BEST Way to Find a Random Point in a Circle https://youtu.be/4y_nmpv-9lI Secrets of the Fibonacci Tiles https://youtu.be/Ct7oltmdJrM The Tale of Three Triangles https://youtu.be/5nuYD2M2AX8 How Karatsuba's algorithm gave us new ways to multiply https://youtu.be/cCKOl5li6YM Can you change a sum by rearranging its numbers? --- The Riemann Series Theorem https://youtu.be/U0w0f0PDdPA Neural manifolds - The Geometry of Behaviour https://youtu.be/QHj9uVmwA_0 ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here: https://www.3blue1brown.com/faq https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Music by Vincent Rubinetti. https://www.vincentrubinetti.com/ Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u Timestamps: 0:00 - Introduction 2:17 - Winners 7:24 - Honorable mentions ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown