The world's great mathematical constant - e number

In one of my recent articles I told about Pi number. The e number, as the π number, - is one of the universal constants. That means that it is a number that can be found in many mathematical formulas that express the basic fundamental laws of nature.

The e number - is the basic relationship of growth, which is applicable to any process that is continuously growing. It may be used in the growth in both exponential and permanent systems.

This number brings the idea that all systems that are permanently growing – are a scaled version of the same indicator.

The person who calculated it was a famous mathematician Jacob Bernoulli in the beginning of the XVIII century, with the desire to describe the principles of moneylenders work. The description was something like this: "The bank, which promises to increase your deposit amount on 1% per year will increase it by e times in 100 years" Letter e for this number was used for the first time in 1731 by the famous genius - Euler .

The basic formula for calculating e:

This number is transcendental, that is, as I told you in a previous article about π, it can’t be the root of any algebraic equation, which has rational coefficients. Numerically e equals to 2.718281828, and in 1953 the value of this number was calculated right up to 3333 decimal digits.

The basic mnemonic rule - remember 2.7, and then the year of birth of Leo Tolstoy twice.

The e number reflects two important concepts in nature: the law of conservation of energy due to the homogeneity of time, as well as the law of conservation of momentum due to the homogeneity of space.

Our wonderful number could be easily found in many natural sciences, except mathematics, such as electrical engineering, physics, biology, statistics, banking, economics, etc., and is widely used by specialists of various professions in the calculation of certain models.

You all know what the decay of a radioactive substance is But have you ever thought that during the decay of such substances at the end of the time t the material that remained after the collapse of its initial amount, will be equal to where - is a number that describes the rate of the partial collapse of the substance that has been taken.

The same thing happens with the attenuation of current I (of course, electrical) in the circuit, which has a serial connection, as well as the resistance R and inductance L, and even the formula remains the same , where , – it is an amperage at a certain time t = 0, because, as we saw in the beginning of the article - number e shows the ratio of growth for the different processes.
Such science as statistics shows us this value as the probability that there were no events that happen by chance with a certain frequency of these events per unit of time for a certain time t.

If we assume that S - is a certain amount of money that you put into your favorite bank with r percentage and it has got constant accrual of money on your account, your contribution will increase too after a certain time t.

In the end, I would like to say that the reason for the widespread use of e lies in the fact that many of the formulas in mathematics, which contain the exponential or logarithm could be often written much easier if you take the logarithm by the base e, and not by any other. For example - if you take the derivative of you’ll get ⁡ , and if you take it of you’ll get a 1 / x, and it is far easier and clearer, do you agree?

By creating this number, Euler proved his genius once again and gave the world so necessary optimization of the calculation algorithms.
[Edited] Thanks to @lemouth for pointing out my mistake here. Actually, this constant was invented by John Napier and was first time mentioned in his work on logarithms in 1618 that is almost 100 years before Euler's birth. Thus Euler didn't create it but introduced "e" notation, that's why this number is often called Euler's number.