E (mathematical constant)

The correct title is e (mathematical constant).

is a mathematical constant which is an irrational number and a transcendental number.

Definition
is a number that is used almost everywhere in mathematics (like how &pi; is used in physics and mathematics). is discovered to be equal to $$\lim_{n\rightarrow\infty}{(1+{1\over n})}^n$$, making it important in compound interest.

is conjectured to be a normal number.

Continued fraction expansion
$$2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{6+\ddots}}}}}}}}$$

or, [2; 1, 2, 1, 1, 4, 1, 1, 6, ..., 1, 1, 2n, ...]

Approximations
3, $8⁄3$, $11⁄4$, $19⁄7$, $87⁄32$, $106⁄39$, $193⁄71$, $1264⁄465$ ...

Euler's identity
Due to Euler's formula, Euler's identity is known to be $$e^{i\pi}+1=0$$. The picture below can show know how it was calculated. The formula is in radians.

Natural logarithm
The natural logarithm [$$\ln(n)=\log_e(n)$$] has as the base.

The natural logarithm is also used with other numbers.