At 3:27 it should be (x+1)! = (x+1)x!
At 4:14 the angle on the right is 120°
At 11:11 B1 should be 2R
A video question that I had for a long time and found almost no answer to. So I made one. We find a general formula for the volume of n-dimensional hyperspheres and use that to extend the factorial to half integers.
Hint: snıpɐɹ uı ǝƃuɐɥɔ ʎuıʇ
Further material: https://youtu.be/GNcFjFmqEc8
===Chapters===
0:00 Introduction
3:43 n-Spheres and n-Balls
6:11 Deriving the recursive formulas
9:31 Putting it all together
12:42 Conclusion
===Made with===
Manim (https://www.manim.community/)
===Music===
In order of Appearance:
Home - We're finally landing
https://soundcloud.com/home-2001
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/playlist/3zNK20qC96mVSww60lVi1k
C418 - Beton, AMS
https://c418.org/
https://c418.bandcamp.com/
===Tags===