This video is based on a proof from H. Vaughan, 1977.
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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 about new videos, subscribe, and click the bell to receive notifications (if you're into that).
Start with part 1: https://youtu.be/X8jsijhllIA
Ben Eater implementing Hamming codes on breadboards: https://youtu.be/h0jloehRKas
Brought to you by you: https://3b1b.co/thanks
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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
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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 links:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
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https://www.youtube.com/watch?v=b3NxrZOu_CE
Full video: https://youtu.be/VYQVlVoWoPY
The full video gives multiple examples of how to lie using visual proofs
Editing from long-form to short by Dawid Kołodziej
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https://www.youtube.com/watch?v=La3MNZLPt7o
This is an excerpt from a video introducing the Fourier series, telling the story from the heat equation on forward
Thanks to Dawid Kołodziej for editing together this short
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https://www.youtube.com/watch?v=nXIHYB0Gp70
Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions.
Brought to you by you: http://3b1b.co/eoc1-thanks
Home page: https://www.3blue1brown.com/
Full series: http://3b1b.co/calculus
Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
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https://www.youtube.com/watch?v=3d6DsjIBzJ4
This comes from a full video dissecting how LLMs work. In the shorts player, you can click the link at the bottom of the screen, or for reference: https://youtu.be/wjZofJX0v4M
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https://www.youtube.com/watch?v=FJtFZwbvkI4
After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak.
One month free audible trial: http://www.audibletrial.com/3blue1brown
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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, 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
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https://www.youtube.com/watch?v=IxNb1WG_Ido
The link to the full video is at the bottom of the screen. For reference, here it is: https://youtu.be/M64HUIJFTZM
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https://www.youtube.com/watch?v=teYL0Er4c3g
Dandelin spheres, conic sections, and a view of genius in math.
Brought to you by you: http://3b1b.co/dandelin-thanks
Home page: https://www.3blue1brown.com
Thoughts on the recent change to be sponsor-free:
https://www.patreon.com/posts/going-sponsor-19586800
Video on Feynman's lost lecture: https://youtu.be/xdIjYBtnvZU
I originally saw the proof of this video when I was reading Paul Lockhart's "Measurement", which I highly recommend to all math learners, young and old.
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https://www.youtube.com/watch?v=pQa_tWZmlGs
An explanation of fractal dimension.
Home page: https://www.3blue1brown.com/
Brought to you by you: http://3b1b.co/fractals-thanks
And by Affirm: https://www.affirm.com/
Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function
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.
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https://www.youtube.com/watch?v=gB9n2gHsHN4