IMHO: Of all of the videos showing Pi's relationship with the Arithmetic-Geometric Mean (AGM), this is the best one.
Related:
Gauss–Legendre algorithm:
https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorit...
Arithmetic–Geometric Mean (AGM)
https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_m...
Chudnovsky algorithm
https://en.wikipedia.org/wiki/Chudnovsky_algorithm
Landen's transformation
https://en.wikipedia.org/wiki/Landen%27s_transformation
Binary splitting: