有哪些有趣的数学公式?

Euler's Identity

eiπ+1=0 e^{i\pi} + 1 = 0

Ramanujan’s Series for π

1π=∑n=0∞(4n)!(1103+26390n)(n!)43964n\frac{1}{\pi} = \sum_{n=0}^{\infty} \frac{(4n)! (1103 + 26390n)}{(n!)^4 396^{4n}}

Gauss-Bernoulli Series

∑n=1∞1n2=π26 \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}

Ramanujan’s Magical Identity

∑n=0∞(−1)n(2n+1)2=π28 \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^2} = \frac{\pi^2}{8}