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
where
- is Euler's number, the base of natural logarithms,
- is the imaginary unit, which by definition satisfies , and
- 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 when evaluated for . 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.