Curves in the Plane

Geometry before calculus involves only the simplest of curves: straight lines, broken lines, arcs of circles, ellipses, hyperbolas and parabolas. These are the curves that form the basis of Greek geometry. Although other curves (such as the cissoid of Diocles and the spiral of Archimedes) were known in antiquity, the general theory of plane curves began to be developed only after the invention of Cartesian coordinates by Descartes ¹ in the early 1600s.