Euler's formula

Named after Swiss mathematician Leonhard Euler (1707–1783).

Euler's formula

1. (complex analysis) Formula which links complex exponentiation with trigonometric functions:

   ${\displaystyle e^{i\theta }=\cos \theta +i\sin \theta }$

2. (differential geometry) Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures ${\displaystyle \kappa _{1}}$ and ${\displaystyle \kappa _{2}}$ and the angle ${\displaystyle \theta }$ which that direction makes with the first principal direction:

   ${\displaystyle \kappa _{n}(\theta )=\kappa _{1}\cos ^{2}\theta +\kappa _{2}\sin ^{2}\theta }$

• Euler's identity

• Euler's totient function