An apparent pattern that breaks, and the reason behind it.
Summer of math exposition: https://3blue1brown.substack.com/p/some3-begins
Learn more at https://some.3b1b.co/
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share the videos.
For the long-time viewers among you, if this sounds familiar, it's because it's a remake of one of the earliest videos on the channel. It's such a wonderful problem, and the audio/pacing in earlier videos was really suboptimal, so I wanted to freshen it up a little here.
Timestamps
0:00 - The pattern
2:20 - Counting chords
4:03 - Counting intersection points
6:20 - Euler's characteristic formula
11:30 - Connection with Pascal's triangle
15:10 - Reflections
15:55 - SoME3
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These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
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
------------------
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:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
...
https://www.youtube.com/watch?v=YtkIWDE36qU
A link to the full video is at the bottom of the screen.
Or, for reference: https://youtu.be/VYQVlVoWoPY
That video gives multiple examples of lying with visual proofs
Editing from the original video into this short by Dawid Kołodziej
...
https://www.youtube.com/watch?v=tjIOqIr80ns
Including some added words on independence.
Main video: https://youtu.be/HZGCoVF3YvM
Brought to you by you: http://3b1b.co/bayes-thanks
------------------
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.
------------------
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:
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
...
https://www.youtube.com/watch?v=U_85TaXbeIo
A curious pattern of integrals that all equal pi...until they don't.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share the videos.
------------------
Original paper from David and Jonathan Borwein
https://carma.edu.au/resources/db90/pdfs/db90-119.00.pdf
Timestamps
0:00 - The pattern
4:45 - Moving average analogy
10:41 - High-level overview of the connection
16:14 - What's coming up next
These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
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
------------------
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:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
...
https://www.youtube.com/watch?v=851U557j6HE
Experiments with toy SIR models
Home page: https://www.3blue1brown.com
Brought to you by you: http://3b1b.co/sir-thanks
Simulations by Harry Stevens at the Washington Post:
https://www.washingtonpost.com/graphics/2020/world/corona-simulator/
Simulations by Kevin Simler at Melting Asphalt:
https://meltingasphalt.com/interactive/outbreak/
Excellent visualization of each country's current growth from Minutephysics and Aatish Bhatia:
https://www.youtube.com/watch?v=54XLXg4fYsc
If you want to hear a mathematician/epidemiologist's summary of COVID-19, I found this MSRI talk very worthwhile:
https://youtu.be/MZ957qhzcjI
Marcel Salathé on Contact Tracing:
https://twitter.com/marcelsalathe/status/1242430736944201730
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
The source code for this video is visible here:
https://github.com/3b1b/manim/blob/shaders/from_3b1b/active/sir.py
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.
Opening music:
Candlepower by Chris Zabriskie is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Source: http://chriszabriskie.com/divider/
Artist: http://chriszabriskie.com/
Other 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.
------------------
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:
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
...
https://www.youtube.com/watch?v=gxAaO2rsdIs
Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.
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
Special thanks to the following supporters: http://3b1b.co/eoc9-thanks
------------------
...
https://www.youtube.com/watch?v=FnJqaIESC2s
A visual explanation of what the chain rule and product rule are, and why they are true.
Full series: http://3b1b.co/calculus
Brought to you by you: http://3b1b.co/eoc4-thanks
And by Brilliant: https://brilliant.org/3b1b
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
------------------
...
https://www.youtube.com/watch?v=YG15m2VwSjA
A link to the full video is at the bottom of the screen.
Or, for reference: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
Editing from long-form to short by Dawid Kołodziej
...
https://www.youtube.com/watch?v=vItzPPpNXEs
Enter as a judge here: https://some.3b1b.co/
Last year's video about the Summer of Math Exposition: https://www.youtube.com/watch?v=cDofhN-RJqg
------------------
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:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
...
https://www.youtube.com/watch?v=7rqKcqx5WKs