Abraham de Moivre

1. De Moivre's Formula

A fundamental bridge between complex numbers and trigonometry.

$$ (\cos x + i\sin x)^n = \cos(nx) + i\sin(nx) $$

2. Normal Approximation to Binomial

De Moivre was the first to discover the normal curve as an approximation to the binomial distribution.

$$ P\left( \frac{S_n - np}{\sqrt{np(1-p)}} \le x \right) \approx \Phi(x) $$