# Euler's identity

## Mathematical equation linking e, i and pi / From Wikipedia, the free encyclopedia

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For other uses, see List of things named after Leonhard Euler § Identities.

In mathematics, **Euler's identity**^{[note 1]} (also known as **Euler's equation**) is the equality

$e^{i\pi }+1=0$

where

- $e$ is Euler's number, the base of natural logarithms,
- $i$ is the imaginary unit, which by definition satisfies $i^{2}=-1$, and
- $\pi$ is pi, the ratio of the circumference of a circle to its diameter.

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula $e^{ix}=\cos x+i\sin x$ when evaluated for $x=\pi$. Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof^{[3]}^{[4]} that π is transcendental, which implies the impossibility of squaring the circle.