Who knew root-finding could be so complicated?
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Interactive for this video:
On fractal dimension:
Mathologer on the cubic formula:
Some articles on Newton's Fractal, and its cousins:
Some of the videos from this year's Summer of Math Exposition are fairly relevant to the topics covered here. Take a look at these ones,
The Beauty of Bézier Curves
The insolubility of the quintic:
The math behind rasterizing fonts:
These animations are largely made using a custom python library, manim. See the FAQ comments here:
You can find code for specific videos and projects here:
Music by Vincent Rubinetti.
Download the music on Bandcamp:
Stream the music on Spotify:
0:00 - Intro
0:48 - Roots of polynomials
5:55 - Newton’s method
11:16 - The fractal
17:56 - The boundary property
23:13 - Closing thoughts
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with UStotal, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
Various social media stuffs:
Oct 12, 2021