Polyline simplification is an important process in computational geometry. The objective is to reduce the number of points of a complicated path while maintaining its basic shape. This need arises naturally in cartography, where very complicated paths frequently occur as coastlines, river basins, and other natural forms. The sample data in this Demonstration, for example, is a sequence of latitude-longitude pairs recorded by a GPS during a bike ride in western North Carolina. The algorithm implemented in this Demonstration is called the Douglas-Peucker algorithm.