How Menaechmus Use Conic Sections

Kimmey1 Conic sections are one of the most commonly studied topics in the field of geometry. Not only are they commonly studied, but they are very important. You may not realize it but we use conic sections in the things we do everyday. Also, without conic sections problems that seem very simple to us would seem very difficult and complicated to solve. Without people like Menaechmus or many other geometers who worked with conic sections, or discovered them, we would be living in a world without a lot of basic things that we use. Around the years 360-350 BC, it is said that Menaechmus discovered conic sections. The way that Menaechmus did this was a challenge that somebody gave all mathmaticians. Basically the story goes that in

The people of the city were confused and asked Plato what he thought. Plato interpreted it as doubling the volume of a given cube, unfortunatly Plato was unable to solve it, but he gave the question to three of his students. One of his students at the time was Menaechmus. Menaechmus eventually solved the question with something new he had developed. He had developed conic sections, or more specifically parabolas, hyperbolas, and ellipses. His original names for a parabola was a section of a right angle cone. He called a hyperbola a section of an obtuse cone. Menaechmus called ellipses a section of an acute cone. Someone else who brought many new ideas to conic sections was also Apollonius of Perga. Most of his work in the field was written down in his

A parabola is defined as a two dimensional mirror-symmetrical curve. The shape of a parabola is similar to that of a U. A parabola is described as created from the intersection of a right circular conical surface with a plane that is parallel to another plane which is tangential to the conical surface. All parabolas that are formed are geometrically similar, which means that they have the same shape and are to scale. We can also see parabolas in everyday life. The most common examples of parabolas is the path of an object in the air. Another common parabola is a suspension bridge, the cables form the parabola. Another parabola in real life is a fountain or jet of water. There are also some important formulas for parabolas. The first formula is for a regular parabola in vertex form, let (h,k) represent the vertex. The formula is y=a(x-h)^2+k. The second formula is used for a parabola, in vertex form, and the orientation of the parabola will be sideways, again let (h,k) represent the vertex. The formula is x=a(y-k)^2+h. The formulas can also be written in a different form, the second form they can be written in is standard form. The formula for a parabola in standard form is