# Euler's formula

## English

### Etymology

Named after the 18th century Swiss mathematician Leonhard Euler (1707-1783).

### Proper noun

Euler's formula

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Wikipedia

1. (complex analysis) Formula which links complex exponentiation with trigonometric functions:
$e^{i \theta} = \cos \theta + i \sin \theta$
2. (differential geometry) Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures $\kappa_1$ and $\kappa_2$ and the angle $\theta$ which that direction makes with the first principal direction:
$\kappa_n(\theta) = \kappa_1 \cos^2 \theta + \kappa_2 \sin^2 \theta$