History of Conic Sections

Algebra 2 HS Mathematics Unit: 11 Lesson: 01 History of Conic Sections

Image Credit: http://commons.wikimedia.org/wiki/User:Magister_Mathematicae. (2012). Scalable Image of Conic Sections [Web Photo]. Retrieved from http://en.wikipedia.org/wiki/File:Conic_Sections.svg

When the ancient Greeks began the study of curves known as conic sections, it was for the fun of studying figures but appeared to have no practical application. Many years later it was found that the knowledge gained from their studies had tremendous scientific and real world applications. The conic sections, which include the circle, the ellipse, the parabola, and the hyperbola, are not only found throughout the natural world but are evident in everything from architecture to astronomy.

Menaechmus, one of Plato's pupils, is generally credited with developing the first definition of a conic section. Euclid is credited with writing at least four books on conic sections. However, all work from Menaechmus and Euclid has been lost. Archimedes also studied conic sections. Although most of his work has also been lost, one book on solids of revolution of conics did survive.

The ancient Greek geometer Appolonious of Perga, revised the definition of conic sections in the 3rd century B. C. to more closely mirror the definition used today. He determined that by slicing a right circular cone at varying angles, all four conic sections could be obtained. Appolonious applied his discoveries about conic sections to planetary motion which helped in the development of Greek astronomy.

Hundreds of years later, the work of Appolonious was translated into Arabic. Although most of the original works of Appolonious were lost, the Arabic translation has survived. In approximately 1070 A.D. Omar Khayyam, using the theories set by Appolonius, applied conic sections to solve algebraic equations. No further important scientific applications were found for the conic sections until the 17th century, when Johannes Kepler, Blaise Pascal, and Rene Descartes extended the theory of conic sections to include the principles of continuity, projective geometry, and analytic geometry. Toward the end of the 17th century, Isaac Newton discovered that the orbits of two massive objects interact according to a universal gravitation law to form conic sections, if their

Algebra 2 HS Mathematics Unit: 11 Lesson: 01 common center of mass is considered to be at rest. If they are bound together, their orbits will follow ellipses. If they are moving apart, their orbits will follow parabolas or hyperbolas.

Conic sections abound in the physical world. Today, the properties of conic sections are applied in a variety of situations. Gears that drive machines are circular. The predicted orbits of solar bodies are elliptical. Radio dishes and car headlights are parabolic. Ripple tanks and echo locators use the properties of hyperbolas. Conics are everywhere.