how $\pi$ is irrational if it is a ratio

Question

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

Thanks!

Please write down the question normally...and why being a ratio would be an obstacle for $;\pi;$ to be irrational? — DonAntonio, Nov 05 '13 at 17:04

Cameron Buie · Answer 1 · 2013-11-05T17:30:28.833

7

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

What makes a number rational is when can be written as a ratio of integers (with the denominator non-zero).

See this comic for all that needs to be said on the subject.

edited Nov 05 '13 at 17:30

answered Nov 05 '13 at 17:05

Cameron Buie

2

I don't understand the downvote. This answers the question clearly and concisely. – TonyK Nov 05 '13 at 17:27

1 Answers1