Calculate Pi Digit By Digit?

Question

Is there a way to calculate pi or any irrational number digit by digit using an iterative algorithm. At each iteration, you get a new digit. Instead of the convergent method.

This would be much more convenient with computers.

Answer 1

http://en.wikipedia.org/wiki/Brent-Salamin_algorithm

Answer 2

I've personally never seen one, although it's possible they exist.

I would assume that such an algorithm couldn't exist because that would require a pattern in the digits of pi, which, although mathemeticians can't prove don't exist, haven't yet been found.

Even besides this, pi would be different in other number systems and instead of each digit representing a value 10 times as precise as the previous one, there would be another factor of "precision increase" with each digit, so if such an algorithm exists, it would be unique to each base.

Overall, I would give it about the same odds as little green men from exactly 314 light years away landing on the Earth at exactly 3:14 on Pi Day next year and doing a Mexican dance.

Answer 3

the reason you're having a project is considering you're lookig for a VB.internet way of doing it. it is math, no longer programming. seek for a math way, then write code to do this math. (BTW, except you're utilising a microscope on a ten foot circle, or you like super Circle distances in microns, 10 digits of pi is plenty greater accuracy than you will ever want.)

Answer 4

Sure -- the first such formula was 1995's Bailey-Borwein-Plouffe algorithm, which has subsequently been improved upon. You can read about it here:

http://en.wikipedia.org/wiki/Bailey-Borwein-Plouffe_formula

Answer 5

No, there are some mathematical proofs that confirm that no formula can be used to find the next number in a pi or the next prime number etc.