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In mathematics, Euler's identity (also known as Euler's equation ) is the equality

e

i

π

+

1

=

0

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

where

e is Euler's number, the base of natural logarithms,

i is the imaginary unit, which satisfies i2 = −1, and

π 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 considered to be an example of mathematical beauty, perhaps a supreme example as it shows a profound connection between the most fundamental numbers in mathematics.

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