JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Clark University is collaborating with JSTOR to digitize, preserve and extend access to Economic Geography.Although tessellations of Thiessen polygons are attractive conceptually as simple spatial models, their value in this regard is limited by the restrictive nature of both the model assumptions and the patterns which they generate. This paper suggests two simple ways by which Thiessen polygon models can be modified to produce what are designated "weighted polygon" models. The approach involves the recognition that the edges in a tessellation of Thiessen polygons are a special case of Descartes' ovals. Two specific, weighted polygon models are produced using other realizations of Descartes' ovals. Both new models are given both assignment and growth interpretations, and their relationships with other existing geographic models are explored. Using equivalencies identified in this way, applications of the models are examined.Thiessen polygons are now familiar to many geographers as well as to a diversity of other scientists, including animal and plant biologists, anthropologists, archaeologists, astronomers, geologists, and statisticians; although to many of these groups they are more likely to be known by one of their other names of which the most current are Dirichlet Domains and Voronoi Polygons.The definition of Thiessen polygons is straightforward. Consider a labelled set of points, ai, a2, ..., an, located in a plane. With each point, ai, we associate a set of all locations, x, in the plane whose distance from ai is equal to their minimum distance from the points faj}. The set of all such locations x which thus satisfy (xai) < (xai)