One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve, which just so happens to achieve roughness level exactly 2. Slightly rough might be around 1.1-dimension; quite rough could be 1.5; but a very rough curve could get up to 2.0 (or more). A classic example of this is the boundary of the Mandelbrot set. The Sierpinski pyramid also has dimension 2 (try computing it!).
The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose "Hausdorff dimension" is greater than its "topological dimension". Hausdorff dimension is similar to the box-counting one I showed in this video, in some sense counting using balls instead of boxes, and it coincides with box-counting dimension in many cases. But it's more general, at the cost of being a bit harder to describe. ... https://www.youtube.com/watch?v=gB9n2gHsHN4
The Heisenberg uncertainty principle is just one specific example of a much more general, relatable, non-quantum phenomenon.
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For more on quantum mechanical wave functions, I highly recommend this video by udiprod:
https://youtu.be/p7bzE1E5PMY
Minute physics on special relativity:
https://youtu.be/1rLWVZVWfdY
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https://www.youtube.com/watch?v=MBnnXbOM5S4
A visual for derivatives which generalizes more nicely to topics beyond calculus.
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Home page: https://www.3blue1brown.com
Essence of calculus series:
http://3b1b.co/calculus
Really nice applet made based on this video by Reddit user Larconneur:
https://www.geogebra.org/m/rftwacsy
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https://www.youtube.com/watch?v=CfW845LNObM
An algorithm for numerically solving certain 2d equations.
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Special thanks to these supporters: http://3b1b.co/winding-thanks
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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https://www.youtube.com/watch?v=b7FxPsqfkOY
A most beautiful proof of the Basel problem, using light.
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Brilliant's principles list that I referenced:
https://brilliant.org/principles/
Get early access and more through Patreon:
https://www.patreon.com/3blue1brown
...
https://www.youtube.com/watch?v=d-o3eB9sfls
A link to the full video is at the bottom of the screen.
Or, for reference: https://youtu.be/NaL_Cb42WyY
That video explores how this question leads to a quandary on prime numbers, and how a pattern in primes allows for a clean final answer.
Editing from long-form to short by Dawid Kołodziej
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https://www.youtube.com/watch?v=R1e7aHBKLnM
An early draft of part 2 for supporters: https://www.patreon.com/posts/34908022
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John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/
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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 use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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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 on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
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Facebook: https://www.facebook.com/3blue1brown
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https://www.youtube.com/watch?v=8idr1WZ1A7Q
A mug with some unexpectedly interesting math.
Vihart response: https://youtu.be/CruQylWSfoU
Brought to you by you: http://3b1b.co/mug-thanks
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Thanks to all the following channels for participating.
Standup Maths
https://www.youtube.com/user/standupmaths
Wendover Productions
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https://www.youtube.com/watch?v=VvCytJvd4H0
Intuition for e^(pi i) = -1, and an intro to group theory.
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And by the Emerald Cloud Lab:
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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.
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https://www.youtube.com/watch?v=mvmuCPvRoWQ
This is a supplement to the Brachistochrone video, proving Snell's law with a clever little argument by Mark Levi.
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https://www.youtube.com/watch?v=Iq1a_KJTWJ8