Leonard Euler discovered many years ago that
$\frac π 4 = \frac 3 4 \cdot \frac 5 4 \cdot \frac 7 8 \cdot \frac {11} {12} \cdot \frac {13} {12} \cdots$ etc
where the numerators are every prime number and the denominators are the multiple of 4 nearest that prime number. Pretty fascinating if you ask me.
