Introduction
Euler’s number, or the well-known constant, is one of the most relevant and important irrational numbers in mathematics and algebra. A natural number cannot represent a base number in an exponential function. This number is widely used in the world of mathematics. It is an irrational number, and scientists cannot know its exact value because it has an infinite number of decimal places, so it is considered an irrational number. In mathematics, it is possible to define the number e as the basis of a natural exponential function, sometimes called the base of non-Persians, since non-Persian mathematicians were the first to use it. Since this number is actively used for many mathematical calculations and formulas, studying its appearance and use is necessary for understanding mathematics.
The Emergence of Number e
The history of this number’s origin and first use is quite long. The famous and important mathematician Leonard Euler, one of the most prolific mathematicians of all time, used the symbol e in the theory of logarithms in 1727 (Calinger 38). The coincidence of the first letter of the surname with the name of the number itself is purely accidental. The first approximation to numbers was obtained by Jacob Bernoulli when solving the problem of long-term interest for initial fixed quantities, which led him to understand and study the fundamental algebraic limit, and its value was fixed at 2.7182818 (Larson 4). This is the first official mention of the most accurate definition of the number e.
Use of Number e
This number plays a very important role in the field of calculation. Moreover, it is part of many fundamental results such as limits, derivatives, integrals, and series. In addition, it has a set of properties that allow it to be used to define expressions that have important applications in many areas of human knowledge. The use of the number e leads to the analysis of such processes as population growth, the decay of radium, or the multiplication of bacteria (Barroso et al. 4). The number e is also used in solving several important mathematical problems. Having a huge application in mathematics, the question remains: how is it used in real life, that is, what is the practical application of the Euler number? The answer to it is as simple as the question of its mathematical application. It manifests itself mainly in the growth of some value, whether it be the growth of a cell or a bank account (Strogatz 136).
For example, someone puts one dollar in a bank that pays 4% per annum. If the interest is simple, then every year, the amount of the deposit increases by 4% of the initial capital. Every dollar in twenty-five years will “grow” and turn into two dollars. If the bank pays compound interest, the dollar will grow faster because after each interest accrual, the capital increases a little, and the next time interest is charged on a larger amount. The more often they recalculate and add profit to the fixed capital, the faster the contribution grows. With compound interest compounded annually, one dollar over 25 years will turn into $2.66.
Conclusion
Various types of growth are characteristic of many processes in animate and inanimate nature. The study of the examples of mathematical uses of the number e considered in the paper is important for the analysis of its potential. The number e is used in a variety of areas from mathematical calculations to banking. This means that this formula is a vital element in the modern world. In addition, although engineers often use decimal logarithms in calculations in building design, in mathematical analysis, there are almost exclusively natural logarithms with a base equal to the number e. The type of growth discussed in the above example has one very important feature: at any given time, the growth rate is proportional to the amount of what is growing. In other words, the ratio of the increment of a changing quantity to its current value is always the same. Quantities of this type change like a snowball rushing from the top of a mountain: the larger the lump becomes, the faster the snow sticks to it. This type of growth is characteristic of many processes in animate and inanimate nature.
Works Cited
Barroso, Connie, et al. “A meta-analysis of the relation between math anxiety and math achievement.” Psychological Bulletin. vol. 147, no. 2, 2021, pp. 134-168. Web.
Calinger, Ronald S. Leonhard Euler: Mathematical genius in the enlightenment. Princeton University Press, 2019.
Larson, Nathaniel. The Bernoulli numbers: a brief primer. 2019. Whitman College. Theses
Strogatz, Steven. Infinite Powers: How Calculus Reveals the Secrets of the Universe. Mariner Books, 2019.