[Child of God]: 416.Essays.Origin and Application of the Ellipse

The ellipse can be described as a squashed, stretched or otherwise distorted circle, though unlike a circle, can take on different shapes. The mathematical definition of an ellipse is:

the set of all points such that the sum of the distances from two fixed points is constant. The distance from any point of the ellipse to one focus plus the distance from that same point to the other focus is always the same number for a particular ellipse

Its origin and construction has fascinated many a person, while its application continues to be utilized. 
Ellipses have engaged the minds of many famous mathematicians in history. It was first discovered by Menaechums, a Greek mathematician and tutor to Alexander the Great in B.C.E 4th Century, along with the parabola and hyperbola as sections of a cone. The ‘Father of Geometry’, Euclid of Alexandria wrote about it in his treatise on mathematics, called The Elements, in B.C.E 3rd Century , but it was Apollonius of Perga who gave the Ellipse, with the parabola and hyperbola, its current name.  In India, the Ellipse was also being discovered, and is found the Bhagvati Sutra, which is dated before B.C.E 4th Century, where it is named the Parimandal. Pappus of Alexandria, AD 4th Century, the last great Greek geometer and commentator of Apollonius studied the focus
and directrix , but it was Johaness Kepler who utilized the shape in the 17th Century. Kepler was the first to recognize that the planets orbited the sun in ellipses, not circles, with the sun at the center. The Cartesian coordinate system, developed by Rene Descartes in the 17th Century, allowed for a formula to be developed for the ellipse where before the only construction method know was none-formulaic. Edmond Halley proved that the 1682 comet, which now bears his name, had the orbit of an ellipse, and Srinivasa Aiyangar Ramanujan in 1914 studied elliptic functions.
Thanks to the Cartesian coordinate system, there are now two ways in which an ellipse can be constructed, either geometrically or formulaically. To construct an ellipse geometrically, one merely:

has to punching two thumb tacks into some paper, looping a string around the tacks, stretching the string with a pencil, and moving the pencil around the tacks while keeping the string taut. The figure traced out is an ellipse and the thumb tacks are at the two foci of the ellipse.

Uses of the ellipse are extremely prominent in everyday life. Gears found in many machines are in the shape of ellipses, large transport vehicles, such as gasoline trucks, are in elliptical shapes due to its stable shape. The Earth itself is an ellipsoid (that is, a three-dimensional shape as a result of rotating an ellipse), and of the planets in the Solar System orbit in elliptical shapes.                                          This mathematical curve is invaluable to astronomy as it allows scientists to properly map out satellite orbits and the physics needs for shuttles. Any cylinder sliced at an angle becomes an
ellipse. Cams, used in the manufacturing of sewing machines and punch presses are elliptical, act as necessary parts in vehicles. “Because of knowledge of the ellipse, man was able to design the engine, relying on the cam and camshaft to generate the up-and-down motion from the elliptical cams moving in a rotary manner.”  Punch presses are used to make small metal objects, from rifle barrels to triggers to nuts and bolts to wire. Understanding of the elliptical shape is used in the study and understanding of optics, from telescopes to microscopes to the human eye, as well as in the study of sound waves and the human ear. An understanding of the ellipse in important for medical knowledge, as “model[ling] the cross section of the forearm bone. By doing this, doctors (with help from mathematicians) are able to determine if a broken arm requires surgeon to correct the rotation the rotation that may have occurred on breaking.”
Rich in history and use, it is fair to say the ellipse is an essential aspect of life, and that an understanding of the ellipse is mandatory for a complete and comprehensive understanding of creation within which we find ourselves.