Bitangent

From Wikipedia, the free encyclopedia

The Trott curve (black) have 28 real bitangents (red). This images show 7 of these; other bitangets are symmetric with respect of the origin.

In mathematics, a bitangent to a curve C is a line L that touches it in two distinct points P and Q. That is, L is an tangent line at P and at Q.

Bézout's theorem implies that a plane curve with a bitangent must have degree at least 4. The case of the 28 bitangents to a general plane quartic curve was a celebrated piece of geometry of the nineteenth century, a relationship being shown to the 27 lines on the cubic surface. Such bitangents are in general defined over the complex numbers, and are not real (see Salmon's Higher Plane Curves). For an example where they are, see Trott curve.