List of Mathematical Constant

Mathematics is an important branch that deals with numbers used in daily life. Scientists and scholars in olden times performed some daily life tasks like calculation of the area of circles and measurement of ancient civilizations which led to some standard values that are known as constants today.

These constants include Euler’s Constant, Pi, and Golden Ratio. In this article, we will study the list of mathematical constants and what these constants signify. We will also discuss how constants are used in algebra and calculus. Some important concepts like Transcendental Numbers will also be covered in the article.

What are Mathematical Constants?

The term ‘constant’ refers to any quantity that is fixed and does not vary with any changing parameter. In mathematics, constants are of different types like proportionaity constants which are used to establish relations between physical quantities and are also used to simplify mathematical calculations.

These values were calculated again and again and it was noticed that these values don’t vary with other quantities. For example, you might think that the value of pi might vary as the perimeter of a circle changes but you will be surprised to know that the value of pi is always equal to 3.14…. which is equal to the ratio of the perimeter of a circle divided by two times its radius. That is why constants are fundamental quantities in mathematics.

Significance of Constants in Mathematics

The fixed nature of constants makes them extremely important in mathematics. Let us see the significance of constants

• Constants like proportionality constants are used to establish relationships between different physical quantities.

• Constants can be used as a reference [oint concerning which calculations can be verified in various experiments.

• Constants are often used in dimensional analysis of various formulas therefore units of constants are also important.

• Constants are used to define some important mathematical equations like the ones used in calculus.

• Introducing constants helps to understand the nature of the equation or the system that is defined by the equation.

Some Important Constants in Mathematics

Let us go through the important mathematical constants one by one.

Euler’s Constant “e”

Euler’s constant was discovered by a mathematician named Jacob Bernoulli. The constant is known as the exponential growth constant and is an important constant in mathematics. Many scientists tried to compute the value of this constant but e is an irrational number and a transcendental number therefore, it has many digits following the decimal place. The value of the constant has been given to 10 decimal places.

• Symbol: e
• Value of constant: 2.7182818284

Uses of Euler’s Constant “e”

The constant is used in various applications like

• It is used as the base of a natural logarithmic function.
• It is used in formulas of calculas often used for calculating limits at certain points.
• Other equations that make use of this constant are equations involving the calculation of compound interest.
• radioactive engineering uses this constant to the calculate life of a radioactive compound using a decay factor that uses this constant.
• This constant is also used for defining various probability distribution curves like normal distribution functions.

Pi (π)

Pi was discovered by a Greek mathematician Archimedes. The constant is known as Archimedes’ constant π and is an important constant in mathematics. Many scientists tried to compute the value of this constant but pi is an irrational number and a transcendental number therefore, it has many digits following the decimal place. The value of the constant has been given to 10 decimal places.

• Symbol: π
• Value of Constant: 3.1415926536

Uses of Pi (π)

The constant is used in various applications like

• It is used as the ratio of the circumference and diameter of a circle.
• It is used in formulas of mathematics while dealing with roots of complex equations like roots of unity.
• Other equations that make use of this constant are equations involving the calculation of Gaussian integral.
• The formulas of physics use this constant to calculate wave function and study modern physics.
• This constant is also used for defining various probability distribution curves like Cauchy distributions

Golden Ratio (φ)

Phi (φ) was discovered by Michael Mästlin in a letter to his former student Kepler. The constant is known as the Golden Ratio and is an important constant in mathematics. Many mathematician tried to compute the value of this constant and the value of the constant has been given.

• Symbol: φ
• Value of the constant: 1.6180339887498948482

Uses of Golden Ratio (φ)

The constant is used in various applications like

• It is used as the ratio of the length of the diagonal of a regular pentagon to the length of a regular pentagon’s side.
• It is used in various sequences of mathematics that deal with recursion like the Fibonacci sequence
• Other equations that make use of this constant’s specialty are equations involving the ratio of two quantities where the ratio of the sum to the larger quantity is the same as the ratio of the larger quantity to the smaller one
• The formulas of physics, geometry, and art use this constant to calculate certain values.
• This constant is also used for studying mathematical concepts like Lagrange’s approximation theorem

Euler’s Constant (γ)

(γ) was discovered by Swiss mathematician Leonard Euler. The constant is known as the Euler–Mascheroni constant and is an important constant in mathematics. Many scientists tried to compute the value of this constant and the value of the constant has been given

• Symbol: γ
• Value of the constant: 0.57721 56649 01532

Uses Euler’s Constant (γ)

The constant is used in various applications like

• It is used for the calculation of the Laplace transform of the natural logarithm.
• It is used in various studies of mathematics like studies involving gamma function.
• Other equations that make use of this constant is the Shannon entropy equation in mathematics.
• The formulas of physics dealing with time equations like harmonic series.
• This constant is also used for studying mathematical concepts like number theory, and probability.

Constants in Algebra

Algebra is a branch of mathematics that deals with symbols rather than numbers alone. Constants form an important part of algebra. Like the formal definition, constants in algebra are numbers that do not change value. When we look at algebraic expressions, equations, and functions, it is made up of different constants.

Different algebraic terms like 4xy, and 2x² have constants 4 and 2 since their value is fixed.

Example: In equation 12x² + 9x – 2 = 7l + 5

In the given equation, the number that never changes will be called a constant i.e. ‘5’ and ‘-2’.

The letters x and l are the variables.

Constants in Calculus

Calculus is a branch of mathematics that deals with integrals and limits of equations rather than basic mathematical operations. Constants form an important part of calculus. The derivative of a constant results in 0 whereas integrating a constant value multiplies the constant by the argument in the integration.

Example: Consider the constant function f(x) = 4, now let us see the integration of the constant and derivative.

∫f(x)dx = ∫4dx = 4x + c where c is new constant

On differentiating,

f'(x) = 0

Miscellaneous Constants in Mathematics

Let us see the list of some other Constants in Mathematics

Symbol	Name	Value
i	Unit imaginary number	i2 = -1
K	Khinchin’s constant	2.6854520010
√2	Pythagoras’ constant, square root of 2	1.41421 35623 73095
β	Bernstein’s constant	0.28016 94990
Ω	Omega constant	0.56714 32904
K	Landau–Ramanujan constant	0.76422 36535

Transcendental Numbers

Transcendental numbers are real numbers or maybe complex numbers that are not the roots of a polynomial having integral coefficient terms. Note that every real transcendental has to be irrational to satisfy the condition for Transcendental Number.

Some examples of important Transcendental Numbers include Euler’s constant “e” and Pi’s “π”, Liouville constant, and the Champernowne constant. These numbers are useful in the field of mathematics.

FAQs List of Mathematical Constant

What is the Most Important Mathematical Constant?

Archimedes’ Constant π is considered to be the most important mathematical constant due to its vast applications.

How are Mathematical Constants Used in Formulas?

Constants represent fixed values in formulas like the area of a circle is given by πr² where π is the constant.

What is Difference Between a Constant and a Variable?

Constants are the values that have a fixed value independent of other parameters while variables can take any value and have no constant value.

Are there Infinite Mathematical Constants?

As of now, there are a fixed number of constants and their count is large but new constants are being found with time.

How do Mathematical Constants Relate to Real-World Problems?

Yes, mathematical constants are used in real life like pi is the ratio of the perimeter of the circle to its diameter, the Golden Ratio is used in the calculation of the Fibonacci sequence, and many more constants are used for studying proportionality relations.