[VA] SRC#006- Pi Day 2020 Special: A New Fast Way to Compute Pi

[Bernd Grubert]

Hello Valentin,
Thanks for the interesting way to calculate pi.

My HP 50G says, it could be interpreted as an application of the newton iteration method to the function:

f(x) = c * sqrt((cos(x) + 1) / (cos(x) - 1))

This is the solution of y(x) / y'(x) = -sin(x).
The Newton iteration is then:

x_n+1 = x_n - y(x_n) / y'(x_n) = x_n + sin(x_n)

with x_0 = 3.

Is that correct?

May be there are functions with an even faster convergence.

Kind regards
Bernd

Edit: Corrections and additional explanations.