Winners and honorable mentions for the SoME2 contest Playlist of all entries:    • Summer of Math Exposition 2 videos   Help fund future projects: https://www.patreon.com/3blue1brown Post with links to all entries: https://www.3blue1brown.com/blog/some2 *Winners* Clear Crystal Conundrums, A Multifaceted Intro to Group Theory https://explanaria.github.io/crystalgroups/ The Lore of Calculus https://www.youtube.com/watch?v=5M2RWtD4EzI How Realistic CGI Works (And How To Do It Way Faster) https://www.youtube.com/watch?v=gsZiJeaMO48 Percolation: a Mathematical Phase Transition https://www.youtube.com/watch?v=a-767WnbaCQ The Coolest Hat Puzzle https://www.youtube.com/watch?v=6hVPNONm7xw *Honorable mentions* How to Take the Factorial of Any Number https://www.youtube.com/watch?v=v_HeaeUUOnc How are memories stored in neural networks? https://www.youtube.com/watch?v=piF6D6CQxUw The shapes of waves of ships and ducks https://www.youtube.com/watch?v=QC3CjBZLHXs Differentiable Programming from Scratch https://thenumb.at/Autodiff/ Researchers Use Group Theory to Speed Up Algorithms — Introduction to Groups https://www.youtube.com/watch?v=KufsL2VgELo Pleasing Panoramas and Matrix Multiplication http://xperimex.com/blog/panorama-homography/ A Tale of Tangent Spheres https://www.youtube.com/watch?v=zR_hpai3XkY Why there are no perfect maps (and why we eat pizza the way we do) https://www.youtube.com/watch?v=HeBP3MG-WHg What Lies Between a Function and Its Derivative? https://www.youtube.com/watch?v=2dwQUUDt5Is 1 Billion is Tiny in an Alternate Universe: Introduction to p-adic Numbers https://www.youtube.com/watch?v=3gyHKCDq1YA The Mathematical Problem with Music, and How to Solve It https://www.youtube.com/watch?v=nK2jYk37Rlg A Curious Track, or What Bikes Are Hiding From Us https://www.youtube.com/watch?v=l7bYY2U5ld8 An Inverse Turing Test https://calmcode.io/blog/inverse-turing-test.html What A General Diagonal Argument Looks Like (Category Theory) https://www.youtube.com/watch?v=dwNxVpbEVcc Why the Circle encloses the Largest Area | Explained using Hill Climbing https://www.youtube.com/watch?v=CFBa2ezTQJQ The Amazing Math behind Colors! https://www.youtube.com/watch?v=gnUYoQ1pwes An Interactive Guide for Bézier Curves https://www.summbit.com/blog/bezier-curve-guide/ Does Every Game Have a Winner https://almostsurelymath.blog/2022/07/28/does-every-game-have-a-winner/ A Finite Game of Infinite Rounds https://www.youtube.com/watch?v=LUCvSsx6-EU Numberphile's Square-Sum Problem was solved! https://www.youtube.com/watch?v=-vxW42R47bc Timestamps: 0:00 - The rising tide 2:08 - Choosing winners 2:54 - Motivation (macro) 8:09 - Motivation (micro) 10:55 - Clarity 12:57 - Novelty 14:26 - Memorability 15:07 - Winners ------------------ 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/ 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 ------------------ 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 Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown