A theory, advanced by W. Christaller (1933, trans. 1966) and, later, A. Lösch (1954), concerned with the way that settlements evolve and are spaced out. Christaller envisaged an isotropic plain with an even distribution of purchasing power. Travel costs were the same in any direction and all parts of the plain were served by a central place, so that the spheres of influence of the central places completely filled the plain. Central goods and services were to be purchased from the nearest central place and no excess profit was to be made by any central place. Christaller contended that each central place should have a hexagonal market area since this polygon represents the most effective packing of the plain and is most nearly circular.
To ensure that goods and services are freely available, central places emerge at the centre of a hexagon containing six lower-order places. One higher-order place will serve a total of two lower-order neighbours. This may mean that two distinct lower-order places are served or that the central place will serve one-third of each of the six lower-order places surrounding it. This will bring to two the total of lower-order places served, and, with the addition of the central place itself, three places are served. This method of serving the market is known as the k = 3 system.
A different system of hexagons would evolve if transport costs are to be minimized. The hexagon is rotated so that the settlements are located evenly at the mid-point of the hexagon's sides. Now the central place serves a half share in the surrounding six settlements: a total of three places plus the central area. Therefore k = 3 + 1 = 4; the k = 4 system. The most efficient pattern for the administration of settlements sees all six lower-order centres inside the hexagonal area of the central place, k = 7.
All these places fit into a hierarchy. Higher-order places stand out from the hexagonal pattern of lower-order centres, but are themselves packed in hexagons around an even higher-order central place. Christaller envisaged this hierarchy as going all the way up to major regional centres. It should be said that hexagonal patterns are very rarely found in real life.
Lösch, who had worked independently of Christaller, extended these ideas. He plotted the ten smallest market areas, each with a different k value. Each network surrounded a common central place. Tracings of each network were laid over each other and the tracings were positioned so as to produce the largest number of places occurring for each k value. The result was a central place with city-rich and city-poor areas spread out in wedges around the major central place. Such a pattern is found around Indianapolis.
Common sense tells us that the basic postulates of these models do not exist but they still give insight into the nature of town development and distribution.
Central place theory
