# 17 Equations that changed the World # 17 Equations that changed the World (Source of Tabled by mathematics tutor and blogger Larry Phillips)

Mathematics is far reaching, far ranging and widespread. The above are the 17 equations that changed the course of History and enshaped the way we apply Mathematics in our day-to-day and routine lives irrespective of the the line if work whether it be Marketing, Finance, Accounting, Web Developers, Therapy, Trainers or any other profession involving Math or not in its core.

In 2013, the famed Mathematician and Science Author Ian Stewart published a book named “17 Equations that changed the World” where highlighted upon this undermined topic.

As on can sight the First Column represents the ‘Name of Equation’; the second column represents the ‘Derived Equation’followed by the ‘Name Of Person and in Year it was invented’.

## Pythagoras Theorem

invented back in 530BC by Sir Pythagoras helps one to compute length of Hypotenuse Side using the other two adjacent sides in a right angled triangle which has great applications in Architecture and Construction, Laying out Square Angles,Navigation,Surveying and helped the world create better maps.This Theorem applies curved,non-Euclidean Geometry distinguishing from the normal Euclidean Geometry.This 3 letter formula has eased woodworking,physical construction projects,to make sure building are square not to mention has made life easy for travellers using 2-dimensional navigation.Catograhers use it in applying from telescope’s line of sight to calculating steepness of slopes of hills and mountains.

## Logarithms

invented by John Napler in 1610 was one of the biggest breakthroughs in that era as it provided back bone to a lot of other theories related to Maths and Physics.It put numbers on a human friendly scale. Helped us perform tedious calculations before there were calculators as they use to turn multiplication into addition greatly speeding up calculations in Physics,Astronomy and Engineering.It is the base of Richeter Scale and Decibel used to measure Earthquakes which uses the logarithmic scale.Not to mention its uses in Macro-Economic applications of GDP calculations alongside in Science to calculate say growth of Bacteria in petri dish over time and identifying pH of a substance based on hydrogen ion concentration.

## Calculus

by Sir Isaac Newton in 1668 is used to arrive to solution when studying Mathematical Models.Calculus has its application and usage to Architect Engineer,Electrical Engineering and Space Flight Engineering(Among application in Engineering);Medical Science uses it  in Epidemology and by Biologists;Statistics and Research Analysis use calculus to evaluate survey data and consider the value of different variables;In Physics Integration is very much needed to calculate velocity and trajectory of an object.Lastly it  helped us to turn away from Mysticism and Alchemy to Rational Science and provided a great deal of contribution to development of Modern World

## Law of Gravity

by Newton,1687 was one of the discoveries which explained question which even go older than time such as why does things are attracted towards the ground.It even explains the difference between Mass And Gravitation.It even provides a base to understand the other Laws of Motion invented by Sir Isaac Newton.Why is Earth Round?,Frontiers of Gravity,Terminal Velocity and applying the Gravitational Formula.Along with that it helped us understand movement of the Stars and Planets.

## The Square Root of Minus One

by Euler,1750 forms the Complex or Imaginary Numbers which don’t have a real meaning but are useful as they make a lot of math consisitent and easy to handle

Most of our modern technology depends on principles of Complex Number used in Signal Processing,Eigenvalues and Fast Fourier Transform.The fundamental principles of Electromagnetism highly require knowledge of i=square root of -1.This rule by Euler has simplified a lot of Mathematical and Statistical Operations and even as we speak there are scientific breakthroughs being made in different parts of the World as it has a lot of scope for further research.

## Euler’s formula for Polyhedra

by Euler,1751 i.e the no.of vertices(V) plus no.of faces(F) less no.of edges(E) works in a convex 3-Dimensional Polyhedron.Aided us to send rockets to space as well as to comprehend DNA Replication.This formula helped in formation of Topology,a branch of Mathematics which in turn is useful in Modern Physics.This Polyhedron Formula by Euler helped the world understand Pick’s Theorem,Monochromatic Lines and The Sylvester-Gallai Theorem Revisited even better and to an extend which truly has a wider application in Modern World.

## Normal Distribution

in 1810 by C.F.Gauss has great usage in Model applications of Physics,Biology and Social Sciences and even gives out a detailed account of behaviour of large groups of Independent Processes.Needless to mention how it transformed how we understand Medical trials and how we gamble and play poker.It is even used in Transportation Engineering and Civil Engineering and data processing of Height,Weight and Strenth in General Population.Also to analyse the errors of measurements made in astronomical observations.

## Wave Equation

by J. d’Almbert,1746 as its name suggests explains the movement of Waves which was first unpredictable and a mystery.A lot of phenomena including light,gravity,matter and sound which are described using Wave Equation.Also a more advance use is made by Klein-Gordon Equation in Relativistic Quantum Mechanics. However a larger application is in Geophysics describing non-linear wave models-Acoustic Waves in both air and water,Electro-magnetic waves in different media and Seismic Waves of wave processes in India.It even tells us what Earth is made up of and helps us find oil easier

## Fourier Transform

by J.Fourier,1822 is the heart and soul of modern signal processing,analysis and data compression as it amplifies the messy wave function of a recording into merely a combination of a number of simple waves.The Spectrum of Signals and Digital Signal Processing alongside other Data Manipulation alongside this it is even used in Optics,Geology and Astronomy.Even in market signal forecasts material estimations.Using this we are  now able to compress thousands of photos in a single tiny dongle.

## Navier-Stokes Equation

by Claude Louis Navier and George Gabriel Stokes,1845 describes the motion of viscious fluid substances,it is in the formulation of velocities and vectors alongwith velocity distribution and pressure distribution. The Newtonian fluid, a fluid where the rate of strain is linear to its stress, has various flow characteristics which can be described by this equation. Basicially, it can be shown that such a fluid follows the Newton law of Viscosity. Benzene, oil flowing through a pipeline, pouring water from a jug are all applications of the Navier-Stokes Equation.

## Maxwell’s Equations

by J.C.Maxwell,1865. The 4 equations given to us by James Clerk Maxwell have their basis in magnetic along with electrical potentials for explicitly solving equations in analytical and various quantum mechanics principles. His work has created a base for various electromagnetic inventions and applications, as it forms the basis of all modern wireless communications as we know it today. He was the first to discover that the Electromagnetic waves travel at light speed with the help of these unified 4 equations. In simple words, the equations say that electrical fields shall generate multiple magnetic fields.

## Second Law of Thermodynamics

in 1874 by L.Boltzmann.

This law literally drove the Industrial Revolution and gave us more proficient generators for future use in the modern world. Boltzmann stated that when the system is a closed one, entropy steadily increases i.e there is a transfer of heat from hot to the cold. The uniqueness of this equation is that it does not work two ways. So for example, if we put ice in hot water, melting begins. However, the water does not start freeze like the ice.

## The famed Equation of Relativity

by Einstein in 1905.

One of the brilliant minds the world has ever seen gave us his infamous special and general relativity theories. It helped us understand The Blackhole, The Big Bang ,Nuclear Power also GPS on our phones. The General Relativity theory helps expand our knowledge about the space time continuum and the special relativity theory gives insights into about the speed of light and how people perceive things differently.

## Schrodinger’s Equation

by E.Schrodinger in 1927 explains how atomic particles behave at a quantum level was explained by this equation. Modern Computer Chips and Lasers are founded based on the principles of Schrodinger’s Equation. The wavefunction helps to find the energy level and position of a particular particle. The Eigen values of given by Fourier help solve this equation and help apply it in real life.

## Information Theory

by C.Shannon,1949 helped the world in Data Compression using the concept of entropy and even error-correcting and error-detection codes.Even Linguistics borrows and uses great deal of research by C.Shannon.Cryptology,the Science of Secure communication along with Logarithm Information Theory uses Information Theory in Analysis of Communication Systems.Not to mention that the Entire Internet has basis in Shanon Theory.

## Robert May’s Chaos Theory

in 1975 helped to build a predictive model in Robotics in eliminating trial-and-error type.Encryption Algorithms and Hash Functions even DNA computing not to mention stream ciphers and watermarking uses this.In Biological Field it helps in predicting the weather better and equation also predicts the growth rate of Butterfly Population.

## Black-Scholes Equation

in 1990 by F.Black and M.Scholes explains the Massive Growth and Profits of the Financial Sector in the 2000’s and the Financial Crisis of 2008-2009.It can be used to determine the price a European Call Option using a geometric Brownian motion.It is even used in other financial instruments for Financial Interpretation and Derivation.

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