Proof that pi is irrational.

[Sam Finch]

I'm looking for a proof that pi^n is irrational for all natrual numbers n. (ie pi^2 is irrational, pi^3 is irrational etc) Does anyone know where I could find one, or just a proof that pi is irrational, as that's probably a good starting point.

[THEROB]

There is a proof that just pi is irrational at:
http://www.mathstat.usouthal.edu/~lynn/mathematics/pi_irr/pi_irr.html

if you can prove that one irrational number multiplied by another is irrational then pi^n is irrational - I suspect it is.


Rob

[Sam Finch]

THAT LOOKS GREAT!!!

I havn't read it thouroghly enough to follow it yet but it looks like it can be adapted for pi^n


Unfortunatley you can't assume that 1 irrational number times another is also irrational, there's a counterexample (quite a few in fact but you only get 1)


sqr(2) is irrational

sqr(2) * sqr(2) = 2

2 is rational.


but thanks a lot for the link, it should be really helpful.

[THEROB]

Good point