From this video: https://youtu.be/YdOXS_9_P4U

The Cosmic Distance Ladder, how we learned distances in the heavens.
Email list: https://3b1b.co/mail
Patreon supporters see early views of new videos: https://www.patreon.com/3blue1brown

Artwork by Kurt Bruns
Thanks to Paul Dancstep for several animations, such as the powers of 10 zoom out and the simulations of shadows on the moon.

Thanks to Tanya Klowden for helpful conversations about the history of the distance ladder.

Argument for why if every shadow of a convex shape is a circle, it must be a sphere: https://mathoverflow.net/questions/39127/is-the-sphere-the-only-surface-with-circular-projections-or-can-we-deduce-a-sp

Timestamps:
0:00 - About Terence Tao and the Distance Ladder
2:02 - Earth
8:07 - Moon
11:15 - Sun
15:45 - Heliocentrism in Antiquity
18:27 - Kepler’s genius
27:16 - Where this leaves us


SEV #5: https://youtu.be/uq83hprtpGE

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

All code for specific videos is visible here:
https://github.com/3b1b/videos/

The music is by Vincent Rubinetti.
https://www.vincentrubinetti.com
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

Mailing list: https://3blue1brown.substack.com
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Patreon: https://patreon.com/3blue1brown
Website: https://www.3blue1brown.com

From this video: https://youtu.be/YdOXS_9_P4U

Based on a construction in this video: https://youtu.be/IQqtsm-bBRU

Full video: https://youtu.be/IQqtsm-bBRU

Series exploring optics: https://www.youtube.com/watch?v=QCX62YJCmGk&list=PLZHQObOWTQDMKqfyUvG2kTlYt-QQ2x-ui

Full video: https://youtu.be/piJkuavhV50

Extracted from this video about holograms: https://youtu.be/EmKQsSDlaa4

Full video: https://youtu.be/IQqtsm-bBRU

The inscribed square/rectangle problem, solved using Möbius strips and Klein bottles.
Playlist with more neat proofs: https://www.youtube.com/playlist?list=PLZHQObOWTQDPSKntUcMArGheySM4gL7wS
Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support
An equally valuable form of support is to simply share the videos.

This argument was originally by Herbert Vaughan, appearing for examples in this issue of the Topology Proceedings.
https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdf

The on-screen argument for why all closed non-orientable surfaces must intersect themselves in 3d is a slight variation on one I heard from Dan Asimov.

2020 Paper by Greene and Lobb:
https://arxiv.org/pdf/2005.09193

Nice Quanta article about this result:
https://www.quantamagazine.org/new-geometric-perspective-cracks-old-problem-about-rectangles-20200625/

Timestamps:
0:00 - Inscribed squares
1:00 - Preface to the second edition
3:04 - The main surface
10:47 - The secret surface
16:45 - Klein bottles
22:38 - Why are squares harder?
25:10 - What is topology?

------------------

These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

All code for specific videos is visible here:
https://github.com/3b1b/videos/

The music is by Vincent Rubinetti.
https://www.vincentrubinetti.com
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

Mailing list: https://3blue1brown.substack.com
Twitter: https://twitter.com/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Website: https://www.3blue1brown.com