INVESTIGATION ON THE NUMBER “e” AND THE NUMBER “π”

 

"The mathematical constant (e) is one of the most important irrational numbers. It appears in various branches of Mathematics, being the base of natural logarithms and being part of the equations of compound interest" (William Fernando Estrada, 2019), however, who made this number known was the Swiss mathematician Jacob Bernoulli while he was studying the compound interest. Because it appears in exponential functions its presence stands out in the study of accelerated growths and decreases, for example in bacteria populations, disease spread and the radioactive decay.

The number e, sometimes known as Euler's number or Napier's constant, "was recognized and used for the first time by the Scottish mathematician John Napier" (Dorrie, Heinrich (1965), who introduced the concept of the logarithm to mathematical calculus.

"The number e, like the number pi and the golden number (φ), is an irrational number, not expressible by a ratio of two integers" (Eves Howard Whitley; 1969) or, it cannot be represented by an exact decimal numeral or a repeating decimal. Furthermore, like pi, it is a transcendent number, that is, it cannot be the root of any algebraic equation with rational coefficients. The value of e truncated to its first decimal places is as follows:

 "e = 2, 718281828459045235360" (Roger Cotes, 1714).

Jonh Napier (1550 - 1617)

Pi is one of the most interesting numbers in the world of mathematics, because it has an infinite number of decimal places. “It is a mathematical constant used frequently in the area of mathematics,​ physics and engineering” (Romero, Sarah; 2019); In addition to that, March 14 is the international day of this issue. 

It is defined as “the constant that relates the perimeter of a circumference to the width of its diameter: π = L / D” (Jones, William; 1706). It enters in the classification of irrational numbers, meaning, with infinite decimal places. "The Greek letter pi will be used as a symbol of this number and its value is, in its first ten digits, equal to π = 3.1415926535" (Euler, Leohnard; 1748). It has its origin since 3rd century BC, when the Greek physicist Archimedes determined its value with an error of 0.024%, later in the 2nd century Ptolemy improved the approach and established the value in 3.14166, however, it wasn’t until the 18th century that Willliam Jones and Euler mentioned it in their work.  

The number pi is highly relevant in mathematics, especially in geometry and trigonometry, in physical it´s in equations that describe the principles of the Universe; it is important to note that it is used for the manufacture of many products of our daily life, in the same way it is used in other branches such as astronomy, statistics or topography in various studies, just to mention some of its various applications. 

 

Leonhard Euler (1707 - 1783)