Conic Sections

Abstract

Conic sections, as their name suggests, are curves obtained by cutting a cone by a plane. They have been studied since ancient times, originally because of their affinity with the circle, and with revived interest since the 17th century when it was found that they model the paths of projectiles, comets, and planets. Another motive for studying them is their ability to “construct” numbers not constructible by ruler and compass, such as $\sqrt[3]{{2.}}$ Perhaps the best way to explain why the same curves arise in these apparently unrelated situations is to say that conic sections are the simplest curves, apart from straight lines. Therefore, of all the curves that can turn up in the world of mathematics, the conic sections will turn up most often.