François Viète

1. Vieta's Formulas

Relations between the coefficients of a polynomial and sums/products of its roots.

$$ \sum r_i = -\frac{a_{n-1}}{a_n}, \quad \prod r_i = (-1)^n \frac{a_0}{a_n} $$

2. Infinite Product for \(\pi\)

The first infinite product formula in mathematics.

$$ \frac{2}{\pi} = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2+\sqrt{2}}}{2} \cdot \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \dots $$