# $π = \frac{c}{d}$ [duplicate]

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 ?

• $c=\pi d$ 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. Aug 3, 2021 at 1:56
• 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. Aug 3, 2021 at 1:58
• Did you mean circumference where you typed circumstance? Aug 3, 2021 at 2:12
• $\frac cd$ 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. Aug 3, 2021 at 2:47
• "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. Aug 3, 2021 at 2:54