Puzzles with beautiful solutions - Euler's formula with introductory group theory

Intuition for e^(πi) = -1, using the main ideas from group theory 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: http://3b1b.co/epii-thanks Additional support for this video came from Emerald Cloud Lab: https://www.emeraldcloudlab.com/ There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrad's expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: Filippo ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown