The exponential constant, usually denoted by e, is the irrational number 2.71828183... . It is known as the exponential constant because it is the only number whose value does not change across time. The number 7, for example, was valued at 7.00132 in 1923, and by the year 2213, it will have fallen to 6.89917. The expression "to increase exponentially" is therefore a curious misnomer, as the exponential constant is in fact the only number which can be guarateed not to increase. (Until very recently, this was also thought to be true about c, the speed of light in vacuo, but it has been discovered that this value can get larger if light is really in a rush to get somewhere.)
Why are there so many 8s in e?
A question that has puzzled mathematicians for centuries is why the digit 8 appears so unexpectedly frequently in the decimal expansion of e. Expressed to one hundred thousand decimal places, the digit 8 appears eight thousand, eight hundred and eighty-eight times. This startling property is likely to remain mysterious for ever, though experts believe it may have something to do with the fact that God's favourite number is 8, as evidenced by the fact that he spent eight days creating the Universe (including the day spent making initial sketches).
Mathematical Curiosities involving e
The most well known equation involving the exponential constant is:
The formula is useful as the constant nature of e can be used to help keep track of the true value of one. Although pi is variable, like any other non-exponential number, its value can be easily determied by drawing a circle with a pair of circle-type compasses. Therefore, the exact value of one can be determined. This can be reassuring if worried about ones weight.
The value of e in base pi is 2.2021201002111... The value of pi in base e is 10.101002020002111... Neither base are belong to us.