1,183 Pages

Not to be confused with Euler's constant. See E for other e's.

e is a number commonly used as base in logarithmic and exponential functions.

The letter e in mathematics usually stands for the so-called "natural base" for logarithms and exponential functions.

, the natural logarithm
, the exponential function with base e

## Value

Euler's number is an irrational number (and a transcendental number), but it can be approximated as 2.71828 18284 59045 23536...

## Applications

Euler's number has many practical uses, particularly in higher level mathematics such as calculus, differential equations, discrete mathematics, trigonometry, complex analysis, statistics, among others.

## Properties

The reason Euler's number is such an important constant is that is has unique properties that simplify many equations and patterns.

Some of the defining relationships include:

• (most useful in calculus)
• is that function such that (useful in differential equations)

One of the original defining attributes of e is the fact any bank account having a 100% APR interest rate which is compounded continuously, will grow at the exponential rate et, where t is time in years, discovered by Jacob Bernoulli. To get times the initial principal, leave it in there for years. Intuitively, compounding an initial account will yield e times the initial principal after one year.

Community content is available under CC-BY-SA unless otherwise noted.