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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 ?

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    $c=\pi d$ 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. – Mr Pie Aug 03 '21 at 01:56
  • 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. – azif00 Aug 03 '21 at 01:58
  • Did you mean circumference where you typed circumstance? – J. W. Tanner Aug 03 '21 at 02:12
  • $\displaystyle \pi = \frac{22}{7}$ close enough for an engineer. –  Aug 03 '21 at 02:15
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    $\frac cd$ 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. – fleablood Aug 03 '21 at 02:47
  • Note: $\frac 2{\sqrt 2} = \sqrt{2}$ is not a rational number. And $\frac e1 = e$ is not a rational number. And $\frac {\pi}4$ is not rational. And $\frac {\pi}1 = \pi$ is not rational. Just because something can be written as a fraction does not mean it is a rational unless it can be written as a fraction between integers (and none of those examples can be). – fleablood Aug 03 '21 at 02:51
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    "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. – fleablood Aug 03 '21 at 02:54

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