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Definition 2024

Euler's formula

(complex analysis) Formula which links complex exponentiation with trigonometric functions:
$e^{i\theta }=\cos \theta +i\sin \theta$
(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:
$\kappa _{n}(\theta )=\kappa _{1}\cos ^{2}\theta +\kappa _{2}\sin ^{2}\theta$

Euler's formula

Italian: formula di Eulero f
Japanese: オイラーの公式 ‎(オイラーのこうしき, oirā no kōshiki)
Khmer: រូបមន្តអយល័រ ‎(ruup mʊən 'a'ya'lear)
Korean: 오일러의 공식 ‎(oilleo-ui gongsik)
Lithuanian: Oilerio formulė
Norwegian: Eulers formel
Persian: فرمول اولر
Polish: wzór Eulera m
Portuguese: fórmula de Euler f
Romanian: formula lui Euler f
Russian: фо́рмула Эйлера f ‎(fórmula Ejlera), фо́рмула Эйлера f ‎(fórmula Ejlera)
Serbo-Croatian:

Cyrillic: Еулерова формула f, Ојлерова формула f

Roman: Eulerova formula f, Ojlerova formula f
Slovene: Eulerjeva formula f
Spanish: fórmula de Euler f
Swedish: Eulers formel c
Thai: สูตรของออยเลอร์ ‎(sòot kŏng oyler)
Welsh: fformwla Euler