# how $\pi$ is irrational if it is a ratio [duplicate]

How can $\pi$ be an irrational number if it is a ratio of the circumference over the diameter?

Thanks!

## marked as duplicate by Cameron Buie, Andrés E. Caicedo, hardmath, Asaf Karagila♦, NorbertNov 5 '13 at 17:26

• Circumference and diameter are not both integers. – Daniel Fischer Nov 5 '13 at 17:03
• Please write down the question normally...and why being a ratio would be an obstacle for $\;\pi\;$ to be irrational? – DonAntonio Nov 5 '13 at 17:04
• Irrational = Not the ratio of two integers. – Asaf Karagila Nov 5 '13 at 17:18

I can write any real number $\alpha$ as a ratio: $\frac\alpha1.$