Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Does anyone has a link to a site that confirms that $\pi$ is a transcendental number?

Or, can anyone show how to prove that $\pi$ is a transcendental number?

Thank you in anticipation!

share|improve this question
Have you tired searching Google? –  JavaMan Apr 8 '11 at 21:01
math.stackexchange.com/questions/12872/… this question might be of some interest –  InterestedGuest Apr 8 '11 at 21:17
Also mathoverflow.net/questions/21367/… –  lhf Apr 9 '11 at 1:01

2 Answers 2

As suggested by Yuval's comment, the most straightforward way of showing that $\pi$ is transcendental proceeds through the Lindemann–Weierstrass theorem that $e^x$ is transcendental if $x$ is (nonzero and) algebraic; since $e^{i\pi}=-1$ is algebraic, then $i\pi$ must be transcendental, and therefore $\pi$ must be (since $i$ isn't rational, but it is algebraic!). You can find a rough proof of the theorem at its Wikipedia page.

share|improve this answer

Try the short paper The transcendence of $\pi$ by Niven and his book Irrational Numbers.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.