While designing The Magic Cube, we spent quite some time studying the number sequences that are featured on each of the cube’s six faces. We’d like to share some of the interesting facts we learned about them & today we’re focusing on The Letter e:
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.
Calculating
There are many ways of calculating the value of e, but none of them ever give an exact answer, because e isirrational (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:
The value of e is also equal to 1 + 1/1! + ½! + 1/3! + ¼! + 1/5! + 1/6! + 1/7! + … (etc)
(Note: “!” means factorial – for example, 3 ! = 3 * 2 * 1 = 6)
The first few terms add up to: 1 + 1 + ½ + 1/6 + 1/24 + 1/120 = 2.718055556
e in Math and Nature
A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, “the marvelous spiral”.
In polar coordinates the logarithmic curve can be written as[1]
Logarithmic spirals occur everywhere in nature, from sea shells to galaxies.
