An Etymological Dictionary of Astronomy and Astrophysics

A formula which expresses an → exponential function with an → imaginary number  → exponent in terms of → trigonometric functions:
e^iθ = cos θ + i sinθ,
e^-iθ = cos θ - i sinθ,
cosθ = (e^iθ + e^-iθ)/2,
sinθ = (e^iθ - e^-iθ)/2i.

In the particular case of θ = π, Euler’s formula becomes: e^iπ + 1 = 0, which is considered by many mathematicians to be the most elegant mathematical equation. → mathematical elegance.

See also: → Euler; → formula.