Euler's identity. This equation, named for Swiss mathematician Leonhard Euler (1707-1783), defines the relationship between several fundamental mathematical constants. The mathematical constant 'e' (an irrational number) is the base of the natural logarithm, used for calculating exponential functions. Here, it is raised to the power of pi multiplied by 'i'. Pi, a transcendental number and a trigonometric and geometric constant, is the ratio of the circumference of a circle to its diameter. 'i' is the square root of minus 1, and the basis of the complex number system. This equation linking these numbers is considered an example of great mathematical beauty.