We know that $π = \frac{c}{d}$, where $c$ is circumference of circle and $d$ is diameter of circle. I surprised to see $π = \frac{c}{d}$ where $π$ is an irrational number and $\frac{c}{d}$ is rational number. Here $c$ and $d$ are rational number.

What is a fact that I missed ?

  • 3
    $\begingroup$ $c=\pi d$ so are you sure that $c$ is a rational number? If we let $d=n/\pi$ for a rational $n$, then $c=n$ which is rational... but now $d$ is not rational no more. $\endgroup$
    – Mr Pie
    Aug 3, 2021 at 1:56
  • $\begingroup$ Okey, we can construct a circle with any diameter that we want, so $d$ can be rational. How $c$ is rational in this case? Isn't. $\endgroup$
    – azif00
    Aug 3, 2021 at 1:58
  • $\begingroup$ Did you mean circumference where you typed circumstance? $\endgroup$ Aug 3, 2021 at 2:12
  • 1
    $\begingroup$ $\frac cd$ is written as a fraction but it is not a fraction of integers. If you don't know if $c,d$ are integers then you don't know that $\frac cd$ is rational. A rational is number that can be expressed as a ratio between two integers. As $c$ and $d$ are never both integers at the same time $\pi$ can be written as a ratio of two non-integers but not as a ratio of integers. .... $\frac cd$ is not a rational number because $c$ and $d$ are not both integers. $\endgroup$
    – fleablood
    Aug 3, 2021 at 2:47
  • 1
    $\begingroup$ "Here c and d are rational number." That never happens. Ever. There is no circle in the universe where $c$ and $d$ are both rational. It is impossible. $c$ is always $\pi$ times whatever $d$ is. If $d$ is rational, $c$ is not. If $c$ is rational, $d$ is not. Sometimes $d$ and $c$ are both irrational. SOmetimes one is rational and the other is not. But they are NEVER both rational. Ever. $\endgroup$
    – fleablood
    Aug 3, 2021 at 2:54


Browse other questions tagged .