A Brief History of Equations
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This article provides a brief history of several equations and theories throughout history. It will provide an idea of what each equation is for and will describe the important events in each of their histories. This is not an in-depth article. It is only meant to provide a brief explanation of each equation or theory.
Newton's Law of Gravitation
This equation was first seen in Philosophiæ Naturalis Principia Mathematica, which came out in July 1687. Newton created this equation in Lincolnshire County, modern-day England. Its purpose is to show the idea that all particles of matter in the universe attract each other through gravity. This equation shows how strong that attraction is. The story goes that Isaac Newton saw an apple fall and wondered why fruit always fell straight to the earth. According to his own laws of motion, anything starting to move from a standing position is undergoing acceleration. When there is acceleration, there is a force. The apple started in the tree and ended up on the earth, meaning that there must be a force of attraction between the apple and the earth. If there is an attraction at that elevation, there should be an attraction at higher elevations, which raised the question: Why doesn't the moon come crashing into the earth? Imagine a cannonball being shot. It has enough force to continue moving straight. The earth pulls the cannonball toward it, but it has enough force to continue moving around the earth. If there were no gravity, the cannonball would continue flying straight away from the earth. If there is a balance between the force exerted on it to set it into motion and gravity, an orbit is caused.[1]
Newton's Second Law
This equation was created in 1716. Newton is given most of the credit for the equation F=ma. Although Galileo Galilei did all the testing at the Leaning Tower of Pisa, Galileo also established that gravity produces acceleration. Newton used Galileo's findings to prove F=ma.[2] The purpose of this equation is to show that the force exerted on an object is the mass of the object times the acceleration.[3]
E=mc2
This equation was created by Albert Einstein in 1905. It was published in a three-page article in a scientific journal in Bern. It was titled "Does the Inertia of a Body Depend Upon Its Energy-Content?" The purpose of this equation is to show that the energy in an object is its mass times the speed of light squared. Einstein liked to ponder riddles, and one such riddle was: If a person were flying in space at the speed of light with a mirror in his or her hand, what would they see? From there, he assumed that the speed of light was a constant. He returned to the mathematical electromagnetic equations that were worked out years previously and plugged in the speed of light for c (a constant). Out came the equation E=mc2. If the speed of light is a constant, then energy is interchangeable with matter and mass. The purest form of energy is electromagnetic radiation moving at a set speed. If matter or mass goes at that speed (mass multiplied by the speed of light), it becomes energy, and if energy moves at a slower speed, it becomes matter. Twenty years after the equation was formulated, the technology to test it was created, and it was proven true.[4]
π=c/d
The purpose of this equation is to show the ratio of a circle's circumference divided by its diameter. In 1900 BC, the Babylonians estimated pi to be about 3.125. In the same century, the Egyptians estimated pi to be 256/81, which is about 3.16. In 250 BC, Archimedes of Syracuse used 96-sided Archimedes polygons to estimate pi to be between 3.1408 and 3.14285. Later, in 460 AD, Zu Chongzhi used the same method as Archimedes, but instead of 96-sided polygons, he used 12,288-sided polygons to estimate π to 355/113. In 1400 AD, Madhava of Sangamagrama used the Madhava-Leibniz series to accurately estimate pi to 11 decimal places. 307 years later, in 1707 AD, William Jones was the first to use the Greek letter π to represent pi. The longest accurate calculation of π before the advent of the computer was done by D. F. Ferguson, who calculated pi to 620 digits.[5]
Euler Characteristic
The Euler Characteristic states that V-E+F=2. Its purpose is to show that the vertices of a 3D figure minus its edges plus its faces always equals 2, as long as the shape isn't inverted. Leonhard Euler created this equation in 1751. He made this observation while observing different shapes and three-dimensional figures.[6]
Minimal Surface
Leonhard Euler and Joseph-Louis Lagrange created this equation in Switzerland and Italy during 1768. Its purpose is to find the surface of least area stretched across a given closed contour. For example, a bubble on a bubble wand.[7]
General Relativity
This theory was created by Albert Einstein in 1915 in Berlin. Its purpose is to show that massive objects cause a distortion in space-time, which is felt as gravity. This distortion can cause gravitational lensing, gravitational redshift, and gravitational waves. In 1905, Einstein determined that the laws of physics are the same for all non-accelerating observers and that the speed of light in a vacuum was independent of the motion of all observers. He called this the theory of Special relativity. Einstein spent 10 years trying to include acceleration in his theory and published it in 1915 as the theory of general relativity.[8]
References
- ↑ Jha, Alok. "Newton's Universal Law of Gravitation". The Guardian. Retrieved 8 February 2018.
- ↑ Maimon, Ron. "How Did Newton Discover His Second Law?". Physics Stack Exchange. Retrieved 12 February 2018.
- ↑ Jha, Ramanand. "Do You Know Who Invented F=ma?". Research Gate. Retrieved 15 February 2018.
- ↑ Orman, Mort. "How Einstein Arrived at E=mc^2". Stress Cure. Retrieved 1 March 2018.
- ↑ Purewal, Sarah. "A brief history of pi". PC World. Retrieved 8 March 2018.
- ↑ "The Euler Characteristic". MT. Retrieved 23 March 2018.
- ↑ Sabitov. "Minimal Surface". Encyclopedia of Math. Retrieved 25 March 2018.
- ↑ Redd, Nola. "Einstein's Theory of General Relativity". Space. Retrieved 25 March 2018.
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