Euler's Number

Euler's number, written e and approximately equal to 2.71828, is a mathematical constant that is the base of the natural logarithm, defined as the limit of the quantity one plus one over n, raised to the power n, as n grows without bound. It can also be defined as the sum of the infinite series of the reciprocals of the factorials of the non negative integers, and it is the unique base for which the derivative of the exponential function equals the function itself, a property that makes it fundamental throughout calculus. The constant is named after the Swiss mathematician Leonhard Euler, who popularized it and proved several of its key properties in the eighteenth century, though the constant itself had already appeared implicitly in Jacob Bernoulli's work on compound interest. Like pi, e is both irrational and transcendental, meaning it is not the root of any polynomial with rational coefficients, a fact proved by Charles Hermite in 1873.