Euler's formula

== English == === Etymology === Named after Swiss mathematician Leonhard Euler (1707–1783). === Proper noun === Euler's formula (complex analysis) A formula which links complex exponentiation with trigonometric functions: e i θ = cos ⁡ θ + i sin ⁡ θ {\displaystyle e^{i\theta }=\cos \theta +i\sin \theta } (differential geometry) A formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures κ 1 {\displaystyle \kappa _{1}} and κ 2 {\displaystyle \kappa _{2}} and the angle θ {\displaystyle \theta } which that direction makes with the first principal direction: κ n ( θ ) = κ 1 cos 2 ⁡ θ + κ 2 sin 2 ⁡ θ {\displaystyle \kappa _{n}(\theta )=\kappa _{1}\cos ^{2}\theta +\kappa _{2}\sin ^{2}\theta } ==== Hyponyms ==== Euler's identity ==== Related terms ==== Euler's totient function ==== Translations ====