Barycentric Coordinates

Although much of the work we do in mathematics uses the familiar Cartesian coordinate system, there are other systems that can be very useful for a variety of tasks.

For example, many curves are easier to generate and analyze in polar coordinates than in rectangular ones.This edition's Geometer's Corner is about another coordinate system that is beginning to see more use. It is used to perform calculations in computer graphics, and it is useful in the study of the triangle.

The inspiration for this column comes from a series of conversations I have had over the years with Steve Sigur, a mathematics teacher at the Paideia School in Atlanta. Steve is currently working with Princeton geometer John Conway on a soon-to-bereleased book called The Triangle Book, which can best be described as an up-to-date collection of all that is known about triangles. In the book, they make extensive use of barycentric coordinates, the subject of this column.