According to the section Proof using the irrationality of $\pi$ of the Wikipedia article on Euclid's theorem, Euler proved that:
$\frac{\pi}{4}=\frac34\cdot\frac54\cdot\frac78\cdot\frac{11}{12}\cdot\frac{13}{12}\cdots$
where "each denominator is the multiple of four nearest to the numerator". Can someone please explain this formula? I see it, but cannot believe it.