1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about Pi in different base

  1. Jul 6, 2012 #1
    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
  2. jcsd
  3. Jul 6, 2012 #2


    User Avatar
    Science Advisor

    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.
  4. Jul 6, 2012 #3


    User Avatar
    Gold Member

    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
  5. Jul 7, 2012 #4


    User Avatar
    Science Advisor

    Thank you very much for this: I found it immensely useful :)
    Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook