The "curious" repetition of 1828....................repetition..........reiteration.......chaos theory.........

e (Euler's Number)

The number e is a famous irrational number, and is one of the most important numbers in mathematics.
The first few digits are:

2.7182818284590452353602874713527 (and more ...)

It is often called Euler's number after Leonhard Euler.
And Euler is spoken like "Oiler".

e is the base of the Natural Logarithms (invented by John Napier).
e is found in many interesting areas, so it is worth learning about.

Calculating

There are many ways of calculating the value of e, but none of them ever give an exact answer, because e is irrational (not the ratio of two integers).
But it is known to over 1 trillion digits of accuracy!
For example, the value of (1 + 1/n)ⁿ approaches e as n gets bigger and bigger:

n	(1 + 1/n)n
1	2.00000
2	2.25000
5	2.48832
10	2.59374
100	2.70481
1,000	2.71692
10,000	2.71815
100,000	2.71827

Another Calculation

The value of e is also equal to 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! + 1/7! + ... (etc)

(Note: "!" means factorial)

The first few terms add up to: 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 = 2.718055556