How to prove that Pi exists? [duplicate]

$\begingroup$

Possible Duplicate:
Proof that Pi is constant (the same for all circles), without using limits

How do we prove that the ratio of a circle's circumference to its diameter is a certain real number, the same for any circle (which we call pi)? Is there a pure geometric proof that the ratio is always the same?

$\endgroup$ 3

1 Answer

$\begingroup$

One way to introduce lengths into Euclidean geometry is to use Rene Descartes' co-ordinate geometry. In this setup, using the methods of calculus, you can prove the said result using integration to compute the circumference(with an integral for the length of a curve).

$\endgroup$