Introduction
Exponential is one of the major mathematical constants most used in today’s mathematical manipulation and study. Studies carried out indicate some of its unique characteristics and features which have enhanced its applications in arithmetical analysis. This paper gives an illustration of the major characteristics of constant in relation to numerous studies which have been carried out and those that are being carried out in the current developmental framework.
An exponential ‘e’, is normally a mathematical constants and is normally applied in various arithmetic and logical calculations. The exponential constant is basically the base of a natural logarithm. Natural logarithm is the logarithm having base e, where e=2.718281828. e is a unique number with the property that the area of the region bounded by the hyperbola y=1/x and the vertical lines x=1 and x=e is 1. In science and engineering it is denoted as In x while in mathematics it is denoted as log x. The natural logarithm is preferable in calculus because its derivative bears a simple equation;while logarithms in other bases consists of complicated derivatives; .Natural logarithms can also be written as the sum or difference of more simple logarithms. Natural logarithms bear the following features;
Scholars have over time prove that that e is irrational by showing simply that e bears a continued infinite fraction. Additionally, some scholars like Liouville proved that the exponential is not able to satisfy any quadratic equation or expression. However, other scholars like Hermitte proved that the exponential was transcendental despite the fact that it had a high degree of irrationality measure.
According to Sondow’s study, e is indeed irrational. He was able to evaluate its aspect by clearly indicating an illustration of nested sequence of closed intervals. Using the given data, I relation could be drawn to illustrate characteristic behavior of the function under various conditions. Notably, the exponential can be used with many functions to bring about a desired meaning to any correlation or pattern of numbers, figures r mathematical functions. Basically, it is because of this reason that numerous studies have been carried out using the exponential. Additionally, it is a mathematical constant which can be easily manipulated when combined using all other forms of mathematical operations. For characteristic determinations of figures and certain relation of numbers, the exponential has been incorporated through multiplication especially. Then regulate other relative factors accordingly in the pattern in which it is employed.
Activity of PPO.
It is evident that many relations could be drawn from the constant with slight variations of other parameters and factors accordingly.
Works cited:
Sondow, J. A Geometric Proof that Is Irrational and a New Measure of Its Irrationality. Amer. Math. Monthly 113, 637-641, 2006.
Stoneham, R. A General Arithmetic Construction of Transcendental Non-Liouville Normal Numbers from Rational Functions. Acta Arith. 16, 239-253, 1970.
Stoneham, R. A General Arithmetic Construction of Transcendental Non-Liouville Normal Numbers from Rational Functions. Acta Arith. 16, 239-253, 1970.
