Shared March 3, 2017
Intuition for e^(pi i) = -1, and an intro to group theory.
Home page: https://www.3blue1brown.com/
Brought to you by you: http://3b1b.co/epii-thanks
And by the Emerald Cloud Lab:
- Application software engineer: http://3b1b.co/ecl-app-se
- Infrastructure engineer: http://3b1b.co/ecl-infra-se
- Lab focused engineer: http://3b1b.co/ecl-lab-se
- Scientific computing engineer: http://3b1b.co/ecl-sci-comp
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/bl...
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:
Visualizing the Riemann hypothesis and analytic continuation
Visualizing quaternions (4d numbers) with stereographic projection
What's so special about Euler's number e? | Essence of calculus, chapter 5
Power Series/Euler's Great Formula | MIT Highlights of Calculus
e to the pi i for dummies
Pi hiding in prime regularities
Group theory | Math History | NJ Wildberger
But what is the Fourier Transform? A visual introduction.
Why do prime numbers make these spirals?
Taylor series | Essence of calculus, chapter 11
Some light quantum mechanics (with minutephysics)
Music And Measure Theory
But what is a Fourier series? From heat flow to circle drawings | DE4
e to the pi i, a nontraditional take (old version)
Feynman's Lost Lecture (ft. 3Blue1Brown)
Euler's real identity NOT e to the i pi = -1
Differential equations, studying the unsolvable | DE1
Divergence and curl: The language of Maxwell's equations, fluid flow, and more