Euler's formula

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English[edit]

Etymology[edit]

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

Proper noun[edit]

Euler's formula

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  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

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