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


  • 1
    $\begingroup$ Circumference and diameter are not both integers. $\endgroup$ Nov 5, 2013 at 17:03
  • $\begingroup$ Please write down the question normally...and why being a ratio would be an obstacle for $\;\pi\;$ to be irrational? $\endgroup$
    – DonAntonio
    Nov 5, 2013 at 17:04
  • 1
    $\begingroup$ Irrational = Not the ratio of two integers. $\endgroup$
    – Asaf Karagila
    Nov 5, 2013 at 17:18

1 Answer 1


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.

  • 2
    $\begingroup$ I don't understand the downvote. This answers the question clearly and concisely. $\endgroup$
    – TonyK
    Nov 5, 2013 at 17:27

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