1683 Euler’s number

${\displaystyle \underset{\mathit{n\to \infty }}{lim}{\left(1+\frac{1}{n}\right)}^n=\sum _{n=0}^{\infty }\frac{1}{\mathit{n}!}=e}$

Key to the mathematical symbols:

lim

The limit

n→∞

as n approaches infinity

(1 + 1/n)ⁿ

of 1 + the reciprocal of n to the power of n

=

equals

∑

the sum

n = 0

as n goes from zero

∞

to infinity

1/n!

of the reciprocal of n factorial, that is, the inverse of n(n - 1)(n - 2) . . . 1

=

equals

e

the irrational transcendental constant and base of the natural logarithms known as Euler’s number

See also in The book of science:

• 495 BCE—Proof of the Pythagorean theorem—Pythagoras
• 1736—Graph theory—Leonhard Euler
• 1758—Euler characteristic—Leonhard Euler
• 1768—Pi—Johann Heinrich Lambert, Ferdinand von Lindemann

Readings in wikipedia:

• “Jacob Bernoulli”
• “Leonhard Euler”
• “e (mathematical constant)”
• “List of representations of e”
• “Mathematical constant”
• “Compound interest”
• “Natural logarithm”
• “Exponential function”
• “Euler’s identity”
• “Diminishing returns”

Other readings:

• “The number e,” MacTutor Math History Archive