e^(iπ) in 3.14 minutes, using dynamics | DE5

From the creator

Euler's formula about e to the i pi, explained with velocities to positions. 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: https://www.3blue1brown.com Not familiar with the calculus referenced in this video? Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula, from Mathologer: https://youtu.be/-dhHrg-KbJ0 Another perspective from this channel: https://youtu.be/mvmuCPvRoWQ And yet another from the blog Better Explained: https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ I'm not sure where the perspective shown in this video originates. I do know you can find it in Tristan Needham's excellent book "Visual Complex Analysis", but if anyone has a sense of the first occurrence of this intuition do feel free to share. It's simple and natural enough, though, that it's probably a view which has been independently thought up many times over. Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: @ngvutuan2811 ------------------ These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own

Published 2019-07-07 · Watch on YouTube ↗
Availability and playback restrictions are controlled by the original channel.