Abstract

A planimeter is a mechanical analog device that evaluates definite integrals. A typical planimeter features a dial and a stylus attached to an arm. As the stylus traverses the boundary of a region, the dial reads off the enclosed area. Planimeters have been mostly forgotten since the advent of computers, but at one time they were fairly commonplace.

I will explain the history and mathematics of planimeters, and I will demonstrate one that I made from two pieces of cast-off junk. It has only one moving part, but it can evaluate any definite integral that it can reach.

Bio

Richard Hammack is a professor of mathematics at Virginia Commonwealth University. He holds a B.F.A in painting from Rhode Island School of Design, a M.S. in computer science from VCU and a Ph.D in mathematics from UNC Chapel Hill. Prior to VCU, he taught at UNC, Wake Forest University and Randolph-Macon College.