how does one measure area? as an example, how can one determine the area of a region on a map for the purpose of real estate appraisal? wouldn't it be great if there were an instrument that would measure the area of a region by simply tracing its boundary? it turns out that there is such an instrument: it is called a planimeter. in this talk we will discuss a particular type of planimeter called the compensating polar planimeter. there will be a little bit of history and some analysis involving line integrals and green's theorem. finally, there will be a chance to see and touch actual examples of these fascinating instruments from the speaker's collection.