Yogi
Posts:
323
Registered:
12/6/04


Re: Proof the irrationality of pi
Posted:
Sep 9, 2004 9:23 AM


There is a very pretty theorem that says: If c is a positive real number and there exist a function f(x) that is continuous on [0,c], positive on (0,c) and such that f and it iterated antiderivatives can be taken to be integer valued at 0 and c, then c is irrational!
pi is a positive real number. The function f(x)= sin(x) is continuous for all x and so on [0,pi] and is positive on (0, pi). All antiderivatives can be taken to be +/ sin(x) or +/ cos(x) (by always choosing the constant of integration to be 0). Therefore pi is irrational.

