John Wallis

1. Wallis Product

An infinite product for \(\pi\) involving only rational numbers.

$$ \frac{\pi}{2} = \prod_{n=1}^\infty \left( \frac{2n}{2n-1} \cdot \frac{2n}{2n+1} \right) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \dots $$