Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Make this definition of pi work

  1. Mar 13, 2010 #1
    I quite like the following definition of pi and I wonder which minimal algebraic rules are needed to make this definition work?

    [tex]\therefore |a|=2\pi k[/tex]

    (For example, are there algebras more general than complex numbers, where this works?)
  2. jcsd
  3. Mar 13, 2010 #2
    Well, in the quaternions [itex]e^{2\pi u} = 1[/itex] where [itex] u [/itex] is any quaternion with [itex] u^2 = -1[/itex]
  4. Mar 13, 2010 #3
    So quaternions probably also work.

    Any more abstract algebra? Hmm, what do I need? I need addition, multiplication, scalar division, limiting process and modulus, right? What has to be fulfilled as to yield pi then?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook