What are conic sections?

short answers for big questions

Conic sections are often referred to just as conic and they result from a certain curve that is obtained through the intersection of a plane with a double cone. According to the angle of intersection that the plane produces together with the cone, we can obtain a Parabola, a circumference, an ellipse or a hyperbola. There are some special cases, which do not have any interest concerning the study of conics, in which that intersection results in a point or in a straight line.

conic sections

How did they emerge?

It is thought that its emergence is connected with an attempt to solve one of the three most famous ancient problems, the Cube Duplication. The legend has it that in 427 B.C the city of Athens was harshly hit by the plague and a quarter of its inhabitants were lost. So as to appease gods, the inhabitants took advice with Apollo’s Oracle, who asked for the duplication of a certain altar to honour god Apollo. The shape of the altar was a cube. The Athenians hurried in order to duplicate the measures of the edges and so they built a new altar. However, the plague didn’t vanish from the city. After having taking a new advice with the Oracle, he told that the volume of the altar had been multiplied by 8 and not as it had been asked to. From then on people assisted to the beginning of several attempts so as to obtain a cube having twice the volume of another cube by only using a non measuring rod and a compass. The study of conics must have emerged during one of the several attempts to solve this classical problem.

Is there any practical application for the conics?

There are lots of practical applications but let’s see some few examples: in 1609 Johannes Kepler found that the orbits of the planets around the sun consisted in an ellipse; in1638 Galileo Galileo published a book in which he described that the trajectory of a projectile (like the bullet of a cannon for instance) could be calculated by means of a parabola; the dish aerial use the properties of parabolas in order to be able to pick up the signal that is sent by the satellites; some types of telescopes use two mirrors – a bigger one which is parabolic and a smaller one that is hyperbolic. These are just some of the examples for the use of the conics which have practical applications in several fields concerning the domain of physics, chemistry, economics and engineering.

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