3Blue1Brown | But why is a sphere's surface area four times its shadow? @3blue1brown | Uploaded 5 years ago | Updated 2 hours ago
The formula is no mere coincidence.
Help fund future projects: patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/sphere-thanks
Discussion on Reddit: reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its
The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:
youtu.be/KZJw0AYn6_k
Calculus series:
http://3b1b.co/calculus
Thanks to these viewers for their contributions to translations
German: @Dat-Pudding
Hebrew: Omer Tuchfeld
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These animations are largely made using manim, a scrappy open-source python library: 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:
vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
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: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown_animations
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/3blue1brown
0:00 - High-level idea
2:23 - The details
9:12 - Limit to a smooth surface
11:20 - The second proof
15:15 - A more general shadow fact.
The formula is no mere coincidence.
Help fund future projects: patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/sphere-thanks
Discussion on Reddit: reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its
The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:
youtu.be/KZJw0AYn6_k
Calculus series:
http://3b1b.co/calculus
Thanks to these viewers for their contributions to translations
German: @Dat-Pudding
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open-source python library: 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:
vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
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: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown_animations
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/3blue1brown
0:00 - High-level idea
2:23 - The details
9:12 - Limit to a smooth surface
11:20 - The second proof
15:15 - A more general shadow fact.
