Question about Pi in different base

1. Jul 6, 2012

f24u7

Hi, recently I have being thinking about math in different bases, and I was wondering if there is a relationship between ∏ from different bases.

Also is there mathematics related books that discusses math in different bases?

2. Jul 6, 2012

chiro

Hey f24u7.

In terms of a general base you need to calculate the equivalent of a "MOD" function which is used to take an integer and decompose it into a certain base, but for any valid continuous base.

The algorithm to do this is known as the DIV/MOD algorithm.

What you do is you use either a sawtooth function to calculate the modulus, or you can use trigonometric functions. The sawtooth has the same interpretation and application as a normal MOD function that you do in normal number theory applications involving whole positive numbers.

Because you haven't given a base, you will need to use the DIV/MOD definition, use the sawtooth or a similar construction for calculating the "MOD" (or remainder part) and take it from there.

There are quite a few definitions for pi so depending on your problem, and the construction of the DIV/MOD algorithm, you can use the different definitions, your base, and the DIV/MOD formulation to get some particular expression.

The trigonometric functions are useful because of the relationship with pi itself and also with the relationship with MOD in indirect ways.

3. Jul 6, 2012

coolul007

This may be of interest: The Miraculous Bailey-Borwein-Plouffe Pi Algorithm

http://www.andrews.edu/~calkins/physics/Miracle.pdf [Broken]

Last edited by a moderator: May 6, 2017
4. Jul 7, 2012

chiro

Thank you very much for this: I found it immensely useful :)

Last edited by a moderator: May 6, 2017