But why is a sphere’s surface area four times its shadow?
The formula is no mere coincidence.
Help fund future projects:
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters:
Discussion on Reddit:
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:
Calculus series:
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:
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:
Stream the music on Spotify:
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:
Various social media stuffs:
Website:
Twitter:
Reddit:
Instagram:
Patreon:
Facebook:
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.
1 view
7
3
1 week ago 00:03:07 1
Two Faced (Official Music Video) - Linkin Park
1 week ago 00:00:32 1
…but the people are retarded
2 weeks ago 00:03:02 1
SPX Options Trading : Strategies for Big Gains!
2 weeks ago 01:21:24 1
The Dark Exploitation of La Toya Jackson | Full Documentary (4K 2160p) | the detail.
2 weeks ago 00:04:14 1
The Hunter - Bloodborne (4K UHD 2024)
2 weeks ago 00:13:57 1
Why did Davy Jones Look SO Realistic?
3 weeks ago 00:03:57 1
Don Toliver - BROTHER STONE (FEAT. KODAK BLACK) [Official Music Video]
3 weeks ago 00:06:30 1
Leadstal vs. Leads Sniper: Which Email Extractor REALLY Gets the Job Done? 😎
3 weeks ago 00:04:04 5
Mass Effect Trilogy Trailer
4 weeks ago 00:02:02 12
DayZ Update Teaser
4 weeks ago 00:04:45 1
Hollywood Undead - Hollywood Forever (Official Music Video)
4 weeks ago 00:57:58 1
The dirty secrets of US-Israel relations: with US Ambassador Chas Freeman
4 weeks ago 00:02:14 1
Nightcore - Heathens (Lyrics)
1 month ago 00:04:47 8
Marilyn Manson - Raise The Red Flag (Music Video)
1 month ago 00:03:19 1
BODY COUNT - F*** What You Heard (OFFICIAL VIDEO)
1 month ago 00:15:01 1
Inside the World’s Largest AI Supercluster xAI Colossus
1 month ago 00:03:13 2
Benson Boone - Beautiful Things (Official Music Video)
1 month ago 00:12:50 1
Chip War Erupts! Is China REALLY Winning the Global Tech Battle?
1 month ago 00:18:41 1
Rural Russia attracts Westerners. But why THIS place?
1 month ago 00:04:38 1
Starbomb - Kiss The Elden Ring (Official Music Video)
1 month ago 00:26:52 1
Why Conservative Families Move To Russia Despite War & Sanctions w/ @Siberian_Freedom
1 month ago 00:04:58 1
Know Your Place (Pandorium x Solitude) Lyric Video - Will Ryan Originals
1 month ago 00:03:05 1
Jeorgia Rose - Undertone (Official Music Video)
1 month ago 00:04:31 1
The English Patient - The Heart is and Organ of Fire (re-upload)