Famous Plane Curves

Plane curves have been a subject of much interest beginning with the Greeks. Both physical and geometric problems frequently lead to curves other than ellipses, parabolas and hyperbolas. The literature on plane curves is extensive. Diocles studied the cissoid in connection with the classic problem of doubling the cube. Newton ¹ gave a classification of cubic curves (see [Newton] or [BrKn]). Mathematicians from Fermat to Cayley often had curves named after them. In this chapter, we illustrate a number of historically-interesting plane curves.