Euler's formula

English

Etymology

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

Proper noun

Euler's formula

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:

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

Hyponyms

• Euler's identity

Related terms

• Euler's totient function

Translations

Euler's formula

• Afrikaans: Euler se formule
• Arabic: صِيغَة أُويْلِر f (ṣīḡat ʔoyler)
• Bulgarian: формула на Ойлер f (formula na Ojler)
• Catalan: fórmula d'Euler f
• Chinese:

  Mandarin: 歐拉公式／欧拉公式 (Ōulā gōngshì)

• Czech: Eulerův vzorec m
• Danish: Eulers formel c
• Dutch: formule van Euler
• Esperanto: Eŭlera formulo
• Estonian: Euleri valem
• Finnish: Eulerin lause
• French: formule d’Euler f
• German: eulersche Formel f
• Hebrew: נוסחת אוילר
• Hindi: यूलर का सूत्र (yūlar kā sūtra)
• Icelandic: jafna Eulers
• Indonesian: rumus Euler
• 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 aylaa)
• Korean: 오일러의 공식 (oilleoui 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