Question about Pi in different base

[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?

Thanks in advance

 

[chiro]

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?

Thanks in advance

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.

 

[coolul007]

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

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

 

[chiro]

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

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

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