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.