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Euler's Number ©Numberphile
1740 Jan 1

Euler's Formula

Berlin, Germany

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". When x = π, Euler's formula may be rewritten as eiπ + 1 = 0 or eiπ = -1, which is known as Euler's identity.