how do you go about proving pi is not an algebric number??
thanks for any help
Proof that ? is irrational - Wikipedia, the free encyclopedia
Here are some proofs you might want to look at
You're right.
Pi is Transcendental
pi is transcendental
The last link provides a proof for the fact that pi is transcendental. However it's quite a difficult proof. To proof a number is transcendental is often hard.
There is an article
"Similarities in Irrational Proofs for ..."
in the March 2001 American Mathematical Monthly.
Simple calculus and some, more or less, advanced algebra. There are a few typos as I recall.
The technique is interesting but takes a lot of thought to really understand.
They also have references to other sources.
I'd also be interested in it. The proofs for irrationality of $\displaystyle \pi$ are allready difficult. Showing that $\displaystyle \pi$ is also transcendental is even more difficult.There is a proof using "elementary" calculus. I'll try to find it and post it up later.