video thumbnail 23:10
Winding numbers and domain coloring

2018-03-24

[public] 737K views, 27.6K likes, 212 dislikes audio only

channel thumb3Blue1Brown

An algorithm for numerically solving certain 2d equations.

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/winding-thanks

Writing and animations by Sridhar Ramesh, with editing and narration by Grant Sanderson.

Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For example, in order to determine how often to sample points, you'd want to have some bounds on the rate at which the direction of the output changes. We will perhaps discuss this more in a follow-on video!

Music by Vincent Rubinetti:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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Patreon Funded via Patreon
http://www.patreon.com/3blue1brown
Intro
/youtube/video/b7FxPsqfkOY?t=0
Simple functions
/youtube/video/b7FxPsqfkOY?t=55
Solving equations
/youtube/video/b7FxPsqfkOY?t=165
Graphing 2D functions
/youtube/video/b7FxPsqfkOY?t=202
Colour
/youtube/video/b7FxPsqfkOY?t=277
Functions
/youtube/video/b7FxPsqfkOY?t=343
Color map
/youtube/video/b7FxPsqfkOY?t=420
Theory
/youtube/video/b7FxPsqfkOY?t=449
Winding numbers along borders
/youtube/video/b7FxPsqfkOY?t=1005
Solving equations with winding numbers
/youtube/video/b7FxPsqfkOY?t=1082
Solving equations with complex numbers
/youtube/video/b7FxPsqfkOY?t=1204
The fundamental theorem of algebra
/youtube/video/b7FxPsqfkOY?t=1304
Outro
/youtube/video/b7FxPsqfkOY?t=1371
3Blue1Brown 3Blue1Brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. For more information, other projects, FAQs, and inquiries see the website: https://www.3blue1brown.com
/youtube/channel/UCYO_jab_esuFRV4b17AJtAw
Support on patreon patreon.com
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