# 2021 Summer of Math Exposition results

From 3Blue1Brown.

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

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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

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

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

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These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
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/

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

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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