# Equations that Rule our World

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Equations are made up of intricate or simple connections of numerals and variables. They are a simplified representation of a relationship which can be defined by a mathematical statement. The persistence behind the work of previous mathematicians, physicists, and philosophers in narrowing down complex relations to a sequence of symbols that we can use for convenience is often undermined. To bring light to this effort, here are some of the most prominent equations that rule our world.

Pythagorean Theorem (a^2 + b^2 = c^2): One of most recurrent formula that build the foundation of further concepts in the mathematical world is the famed Pythagorean Theorem. Introduced by Greek philosopher and mathematician, Pythagoras (570-495 BC), it accurately exhibits the relationship that exists within a right-angled triangle and can be further applied to a multitude of geometric shapes. To summarize, it states that the squared length of the hypotenuse equals the sum of the squared values of the other two sides.

Pythagorean Theorem (a^2 + b^2 = c^2): One of most recurrent formula that build the foundation of further concepts in the mathematical world is the famed Pythagorean Theorem. Introduced by Greek philosopher and mathematician, Pythagoras (570-495 BC), it accurately exhibits the relationship that exists within a right-angled triangle and can be further applied to a multitude of geometric shapes. To summarize, it states that the squared length of the hypotenuse equals the sum of the squared values of the other two sides.

Pythagorean Theorem (a^2 + b^2 = c^2): One of the most recurrent formulas that build the foundation of further concepts in the mathematical world is the famed Pythagorean Theorem. Introduced by Greek philosopher and mathematician, Pythagoras (570-495 BC), it accurately exhibits the relationship that exists within a right-angled triangle and can be further applied to a multitude of geometric shapes. To summarize, it states that the squared length of the hypotenuse equals the sum of the squared values of the other two sides.

Einstein’s Theory of Relativity (E=mc^2): Another distinguished equation is one that was introduced by the celebrated physicist, Albert Einstein, involving his noteworthy Theory of Relativity. Within the theory, it has been mentioned how space-time is disrupted due to the presence of massive objects (e.g. Earth and similar planetary bodies). Einstein, within his discoveries, presented two postulates on which this theory was developed. One, that the laws of physics can be stated to be the same for observers experiencing constant motion, and two, that the speed of light is an unchanging quantity. The equation, similarly involving the speed of light, E=mc^2, is based on the principle that all energy has a mass equivalence, and conversely, all mass has an energy equivalence which can be determined through the renowned formula.

Einstein’s Theory of Relativity (E=mc^2): Another distinguished equation is one that was introduced by the celebrated physicist, Albert Einstein, involving his noteworthy Theory of Relativity. Within the theory, it has been mentioned how space-time is disrupted due to the presence of massive objects (e.g. Earth and similar planetary bodies). Einstein, within his discoveries, presented two postulates on which this theory was developed. One, that the laws of physics can be stated to be the same for observers experiencing constant motion, and two, that the speed of light is an unchanging quantity. The equation, similarly involving the speed of light, E=mc^2, is based on the principle that all energy has a mass equivalence, and conversely, all mass has an energy equivalence which can be determined through the renowned formula.

Einstein’s Theory of Relativity (E=mc^2): Another distinguished equation is the one that was introduced by the celebrated physicist, Albert Einstein, involving his noteworthy Theory of Relativity. Within the theory, it has been mentioned how space-time is disrupted due to the presence of massive objects (e.g. Earth and similar planetary bodies). Einstein, within his discoveries, presented two postulates on which this theory was developed. One, that the laws of physics can be stated to be the same for observers experiencing constant motion, and two, that the speed of light is an unchanging quantity. The equation, similarly involving the speed of light, E=mc^2, is based on the principle that all energy has a mass equivalence, and conversely, all mass has an energy equivalence which can be determined through the renowned formula.

Normal Distribution: Debatably one of the most pivotal concepts within statistics, normal distribution demonstrates how an experiment’s results will always produce a similar bell curve on plotting, given that the data follow a normal distribution. The graphical representation is also known by the name “Gaussian curve”, after the German mathematician, Carl Friedrich Gauss who was its founder. Throughout the curve, it can be found that the majority of results lie at the average point, or the mean, while a minority of the points can deviate to extremes from the average; however, the curve is found to be symmetric about its mean. The bell curve carries significant application and usage in other fields, such as physics and social sciences.
The standardized value of a normally distributed random variable Z is calculated using the following formula.
x = the value that is being standardized
m = the mean of the distribution
s = standard deviation of the distribution

Normal Distribution: Debatably one of the most pivotal concepts within statistics, normal distribution demonstrates how an experiment’s results will always produce a similar bell curve on plotting, given that the data follow a normal distribution. The graphical representation is also known by the name “Gaussian curve”, after the German mathematician, Carl Friedrich Gauss who was its founder. Throughout the curve, it can be found that the majority of results lie at the average point, or the mean, while a minority of the points can deviate to extremes from the average; however, the curve is found to be symmetric about its mean. The bell curve carries significant application and usage in other fields, such as physics and social sciences.
The standardized value of a normally distributed random variable Z is calculated using the following formula.
x = the value that is being standardized
m = the mean of the distribution
s = standard deviation of the distribution

Normal Distribution: Debatably one of the most pivotal concepts within statistics, normal distribution demonstrates how an experiment’s results will always produce a similar bell curve on plotting, given that the data follow a normal distribution. The graphical representation is also known by the name “Gaussian curve”, after the German mathematician, Carl Friedrich Gauss who was its founder. Throughout the curve, it can be found that the majority of results lie at the average point, or the mean, while a minority of the points can deviate to extremes from the average; however, the curve is found to be symmetric about its mean. The bell curve carries significant application and usage in other fields, such as physics and social sciences.
The standardized value of a normally distributed random variable Z is calculated using the following formula.
x = the value that is being standardized
m = the mean of the distribution
s = standard deviation of the distribution

Isaac Newton’s Law of Universal Gravitation: It is undoubtedly one of the most momentous equations, which illustrates the reasoning behind the revolving of planets and the exertion of gravity. With this equation, Newton notably succeeded in paving the way for further physicists in understanding the happenings within our universe. He conveyed within his celebrated Principia Mathematica that planets revolve due to the force of gravity, and that gravity itself is, in fact, universal. Until Einstein’s Theory of Relativity was introduced centuries later, Newton’s provided equation enabled one to determine the exerted force between two bodies.

Isaac Newton’s Law of Universal Gravitation: It is undoubtedly one of the most momentous equations, which illustrates the reasoning behind the revolving of planets and the exertion of gravity. With this equation, Newton notably succeeded in paving the way for further physicists in understanding the happenings within our universe. He conveyed within his celebrated Principia Mathematica that planets revolve due to the force of gravity, and that gravity itself is, in fact, universal. Until Einstein’s Theory of Relativity was introduced centuries later, Newton’s provided equation enabled one to determine the exerted force between two bodies.

Isaac Newton’s Law of Universal Gravitation: It is undoubtedly one of the most momentous equations, which illustrates the reasoning behind the revolving of planets and the exertion of gravity. With this equation, Newton notably succeeded in paving the way for further physicists in understanding the happenings within our universe. He conveyed within his celebrated Principia Mathematica that planets revolve due to the force of gravity, and that gravity itself is, in fact, universal. Until Einstein’s Theory of Relativity was introduced centuries later, Newton’s provided equation enabled one to determine the exerted force between two bodies.

Calculus (Differential and Integral Equations): Calculus, earlier known as Infinitesimal Calculus, is a branch of mathematics discovered by Sir Isaac Newton and Gottfried Wilhelm Leibniz, and was initially introduced in the mid-1600s. Calculus deals with differential equations and integral equations, both of which perform the inverse functions of one another. Differentiation deals with measuring the rate at which a quantity is changing, whereas integration allows one to determine length, area, volume and other quantities through means of the integral of a curve. One of the most beneficial uses of calculus is in the formation of models, to better understand the impact of altering a system and observing how the system would consequently react.

Calculus (Differential and Integral Equations): Calculus, earlier known as Infinitesimal Calculus, is a branch of mathematics discovered by Sir Isaac Newton and Gottfried Wilhelm Leibniz, and was initially introduced in the mid-1600s. Calculus deals with differential equations and integral equations, both of which perform the inverse functions of one another. Differentiation deals with measuring the rate at which a quantity is changing, whereas integration allows one to determine length, area, volume and other quantities through means of the integral of a curve. One of the most beneficial uses of calculus is in the formation of models, to better understand the impact of altering a system and observing how the system would consequently react.

Calculus (Differential and Integral Equations): Calculus, earlier known as Infinitesimal Calculus, is a branch of mathematics discovered by Sir Isaac Newton and Gottfried Wilhelm Leibniz, and was initially introduced in the mid-1600s. Calculus deals with differential equations and integral equations, both of which perform the inverse functions of one another. Differentiation deals with measuring the rate at which a quantity is changing, whereas integration allows one to determine length, area, volume and other quantities through means of the integral of a curve. One of the most beneficial uses of calculus is in the formation of models, to better understand the impact of altering a system and observing how the system would consequently react.

Logarithms: Logarithms, discovered by John Napier in 1614, have assisted us greatly in narrowing down intricate and time-consuming calculations. This discovery carried on to redefining trigonometry by simplifying the process of achieving an end result. Initially, logarithms were introduced to further aid in the field of astronomy, due to the highly complex nature of equations and calculations used in that field.

Logarithms: Logarithms, discovered by John Napier in 1614, have assisted us greatly in narrowing down intricate and time-consuming calculations. This discovery carried on to redefining trigonometry by simplifying the process of achieving an end result. Initially, logarithms were introduced to further aid in the field of astronomy, due to the highly complex nature of equations and calculations used in that field.

Logarithms: Logarithms, discovered by John Napier in 1614, have assisted us greatly in narrowing down intricate and time-consuming calculations. This discovery carried on to redefining trigonometry by simplifying the process of achieving an end result. Initially, logarithms were introduced to further aid in the field of astronomy, due to the highly complex nature of equations and calculations used in that field.

Maxwell’s Equations: Four principal and immensely intricate equations managed to form the basis of electromagnetism that we know today by elucidating the distinct qualities of both magnetic and electric fields. The set of equations consist of the following: Gauss’ Law, Gauss’ Magnetism Law, Faraday’s Law, and Ampere’s Law. Maxwell’s equations are notably named after the mathematician who discovered them, James Clerk Maxwell. These four equations are known for using an extremely complex degree of mathematics to convey the complexities of magnetism.

Maxwell’s Equations: Four principal and immensely intricate equations managed to form the basis of electromagnetism that we know today by elucidating the distinct qualities of both magnetic and electric fields. The set of equations consist of the following: Gauss’ Law, Gauss’ Magnetism Law, Faraday’s Law, and Ampere’s Law. Maxwell’s equations are notably named after the mathematician who discovered them, James Clerk Maxwell. These four equations are known for using an extremely complex degree of mathematics to convey the complexities of magnetism.

Maxwell’s Equations: Four principal and immensely intricate equations managed to form the basis of electromagnetism that we know today by elucidating the distinct qualities of both magnetic and electric fields. The set of equations consist of the following: Gauss’ Law, Gauss’ Magnetism Law, Faraday’s Law, and Ampere’s Law. Maxwell’s equations are notably named after the mathematician who discovered them, James Clerk Maxwell. These four equations are known for using an extremely complex degree of mathematics to convey the complexities of magnetism.

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Maryam Ali, currently studying at Lahore Grammar School 55 Main, is an avid writer aspiring to convey her passion for mathematics and the sciences through the written word. Her prime interests include using public speaking and writing to communicate the voice of the underprivileged and impart her enthusiasms to others.
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