E (mathematical constant)

The number e is a mathematical constant that is the base of the natural logarithm and exponential function. It is approximately equal to e plays important and recurring roles across mathematics. It is comparable in significance to 0, 1, π, and i—all five of which appear in Euler's identity e i π + 1 = 0 {\displaystyle e^{i\pi }+1=0} . Like π, the constant e is irrational (it cannot be represented as a ratio of integers) and transcendental (it is not a root of any non-zero polynomial with rational coefficients). The constant is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with other numbers named after Euler. Alternatively, e can be called Napier's constant after John Napier. The Swiss mathematician Jacob Bernoulli introduced the constant while studying compound interest.