# 10 Equations That Changed The World

525 Engineers=Equations. An engineer’s life is full of equations. Although we engineers complaint about being victimized by half a million of equations in our degrees but the truth is that these equations itself help us to understand the world with unbiased eyes with the use of several numbers & formulas. There have been many equations that changed the world.

There are several brighter minds in history who have changed the way to measure & understand the universe by formulating several equations & theories with the use of mathematics. Just like inventions, equations have also transformed our world.

## 1. NEWTON’S LAW OF UNIVERSAL GRAVITATION

One of the most significant equations that changed the world is Newton’s law of universal gravitation. It states that any 2 bodies in the universe attract each other with the force which is directly proportional to the product of their masses & inversely proportional to the square of the distance between them. And it is a remarkable piece of scientific history. It explains perfectly why the planets move in the way they do. However, it is also remarkable for its universal nature as it not only shows how gravity works on earth, but it also shows how gravity works in our solar system or anywhere in the universe. Newton is one of the greatest geniuses the world has ever seen. Here are some interesting facts about Isaac Newton.

## 2. MAXWELL’S EQUATION

These equations are a set of 4 equations that describe electromagnetic force. These are the foundations of the explanation that how electromagnetism works. Modern physics depends on the quantum mechanical explanation of electromagnetism.

## 3. LOGARITHMS

These are the inverses or opposites of exponential functions. It has useful applications in data storage. For example, all data bits are stored in the form of 0 & 1. To determine how many bits you need to represent 64 possibilities you would calculate “log of 64 with base 2”. The answer shows that you would need 6 bits to represent 64 possibilities, since, 2^6=64. Before the development of digital computers & scientific calculators, the method used was to multiply together large numbers. It speeded up calculations in physics, astronomy & engineering thus becoming one of the equations that changed the world.

## 5. SCHRODINGER’S EQUATION

Schrodinger’s equation is also one of the equations that changed the world. It is a partial differential equation which describes how a quantum state of the quantum system changes with time. Moreover, it explains the behavior of atoms & subatomic particles. It is very necessary for most of the modern technologies like nuclear power, microchips, electron microscopes, semiconductor-based computers & lasers which all work on this phenomenon.

## 6. INFORMATION THEORY

It is a branch of applied mathematics, electrical engineering & computer science which involves quantification, storage & communication of information. Also, it is a measure of disorder. It measures the symbolically representable information content of the message. The mathematical study of information & the results are central to how we communicate over networks. It is used in data compression & channel coding. It is also instrumental in the development of internet & mobile phones.

## 7. FOURIER TRANSFORMATION

It allows us to break messy functions into a combination of a number of simple waves. Have you ever pointed a camera at a monitor/TV? You will notice some wavy lines which you cannot see with eyes. Moreover, Fourier theory states “Any signal, (visual images) can be expressed as a sum of sinusoids.”

Although, it is also essential in understanding more complex waves such as human speech. It is used in modern signal processing & analysis & data compression.

## 8. NAVIER-STOKES EQUATION

As an illustration, it represents the flow of incompressible fluids such as water flowing through a pipe or airflow over an airplane wing. This equation can be used to model weather, ocean currents & flow of hot air. In effect, we have approximate solutions to this equation which help computers to simulate fluid motion.

## 9. EINSTEIN’S THEORY OF RELATIVITY

In the first place, he showed mass & energy are interchangeable & are related to each other through the square of the speed of light by the equation E=m(c^2). Identically, there are 2 types of relativity:- special relativity & general relativity.

Correspondingly, special relativity shows that the speed of light is the universal speed limit. Chiefly, it is 3.8 m/sec whereas the speed of time changes for the person moving with different speeds.

As a result, general relativity shows that mass not only creates a gravitational field around it but also bends the space-time around it. Consequently, more massive is the object, greater is the bend. Time slows down around objects such as black holes.

Apart from this, Einstein is also famous for “Einstein’s riddle” which is one of the hardest puzzles in the world.

## 10. SQUARE ROOT OF -1

Ultimately there are various solutions in mathematics where we come across numbers like the square root of -1. So as to overcome the difficulties arisen mathematicians came up with the concept of imaginary numbers & started to represent the square root of -1 with the alphabet “i” & any number consisting “i” was termed as an imaginary number. Thereupon the properties of complex numbers such as their symmetry make them essential in electronics & signal processing.