Exploring the Beauty of Mathematics: Famous Theorems and Their Significance

Mathematics is magical. It is the language of nature, a source of inspiration and fear, and boosts our intelligence. Steeped in logic, its concepts and theories are the foundation of science and technology. The subject is an attempt by humans to codify, represent, and analyze reality.

There are n-number of theorems in mathematics. Every theorem is the brainchild of one or many brilliant minds who gave the masses some powerful abstract tools for analysis. Every math problem, math assignment, geometry, and calculus assignment utilizes one or the other mathematical concepts. Hundreds of such concepts exist and have been used to solve numerous conceptual and real-life mathematical problems.

Here in this article, we look at some of the most famous mathematical theories ever.

A Look At Some Groundbreaking Mathematical Theorems

• The Fundamental Theorem of Calculus

Calculus finds applications in every branch and aspect of science. Solid & fluid mechanics, material sciences, quantum mechanics, relativity, thermodynamics, electrostatics & current electricity, astronomy, nuclear physics, information theory, signal processing, wave motion, applied sciences, social sciences – the list goes on and on. Applicational problems in calculus are many & diverse. If you are stuck with your calculus assignments, connect with MyAssignmentHelp.com, USA’s largest math assignment help service.

The fundamental theorem of calculus links differentiation (understanding the output change concerning the input) with integration (summation of some entity).

• The first part of the theorem states that the indefinite integration of a function is obtained by its integration over an interval.
• The second part states that integrating a function over a specific interval equates to changing its antiderivative.

• The Pythagoras Theorem

One of the oldest and most famous theorems in mathematics, it was developed around 550 B.C. by Pythagoras. However, the idea behind the theorem was known to mathematicians of the Babylonian, Hindu, and Chinese civilizations much before that.

You should be familiar with Pythagoras’s theorem. It states that in any right-angled triangle, the area of the square of the hypotenuse is equal to the sum of the squares of the other two sides, the base and the height.

• Fermat’s Theorem

This is yet another infamous theorem in number theory. Developed by Pierre Fermat in the 17^th century, it highlights the impossibility of obtaining a solution to aⁿ + bⁿ= cⁿ when n exceeds 2.

Fermat’s theorem finds applications in cryptography, data science, information theory, etc.

• The Mean-Value Theorem

Also known as the Lagrange theorem, the mean value theorem is one of the most important theorems in mathematics and calculus.

• Rolle’s theorem is a special case of the mean value theorem that states the existence of a value that makes a differentiable function zero, provided the function’s outputs are equal at the ends of a particular interval.
• The mean value theorem states that if a function f is continuous over a closed interval [a, b]and differentiable over the same open-ended interval (a, b), then there exists a point within that interval whose tangent is parallel to the secant line connecting (a, f(a)), and (b, f(b)).

Here’s an illustration.

The mean value theorem has some interesting real-life applications. It finds usage in automatic number plate recognition systems that use optical character recognition to read car plates at different fixed points along a particular stretch of road. The system then uses the theorem to determine the car’s average speed. Using the mean value theorem, the car’s average speed within a stretch is calculated, and if it exceeds the speed limit, a penalty is imposed.

• The Binomial Theorem

The last theorem in our list is the Binomial theorem that defines the pattern inherent in polynomial multiplication. The pattern defined by the theorem is as follows à

The theorem describes and predicts the pattern of algebraic expansion of the powers of a binomial expression. Binomial theorem finds applications in trigonometry, complex numbers theories such as deMoivre’s formula, infinite series & sums, probability, etc.

Well, that’s about it for this write—up. Hope it was an interesting read for everyone. If you need expert help with your geometry or math assignment, connect with Myassignmenthelp.com, one of the USA’s top assignment help services.

All the best!