# Special Constants in Mathematics

In mathematics, there are several constants, some of which have approximate values, and some have derived by performing mathematical operations. A number whose value is determined by an unambiguous interpretation is called a mathematical constant. These constants usually referred to students in the classroom by a symbol or by the names of mathematicians to facilitate using it across multiple numerical problems.

Constants appear in many areas of mathematics. For example, Euler’s number, pi, etc., occurring in such different contexts such as number theory, geometry, and calculus. In number theory, the main topic is complex numbers where mathematical constants appear. The more popular constants have been studied during the ages and estimated at various decimal places. There are many constants that will be introduced with the students at different levels of their education. At earlier studies like primary and secondary school syllabus they will only deal with pi, e, I with limited information on their derivation.

The most commonly used mathematical constant is pi, which appears mainly in geometry. The reason behind this is the definition of pi has derived from the Euclidean geometry. Also found in many areas and branches of mathematics such as the Gaussian integral in calculus concept of complex analysis,  in number theory as the roots of unity, and Cauchy distributions in probability. However, its existence is not only limited to mathematics. It appears in many formulas of other subjects, some of the physical constants defined naturally with the combination of pi.

Euler’s number is also referred to as exponential growth constant, and it appears in many areas of mathematics such as limits. It has applications to derangements, probability theory but not in the same way as to how it is related to exponential functions. Students can also see this constant on the scientific calculators. In the case of statistics and probability distributions, Euler’s number is involved in many formulas. The value of this constant is treated as an irrational number since it has the decimal expansion which is known as terminating non-recurring.

Unit imaginary number or imaginary unit is denoted as i and is a mathematical concept that extends the real number system beyond to the rational and irrational numbers, which in turn gives at least one root for each polynomial. When referring to the complex numbers solved examples, this constant appears multiple times with different powers. Each power of this constant possesses different values. The reason for using the term “imaginary” is, there is no real number which has a value for a negative square.

In geometry, one more constant exists which may or may not be noticed by the students. Root two or radical two is known as Pythagoras constant. It is the positive algebraic number that means, when multiplied this constant by itself, gives the number two. More precisely, it is called the principal square root of two, to distinguish it from the negative number with the same characteristic. Generally, this constant is used mostly with right triangles and diagonals of squares while calculating the measure of the desired side. Also, this is the first irrational number with more than sixty decimal places.