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Urban Growth and Spatial Structure: Mathematical Models and Empirical Evidence

Bruce E. Newling
Geographical Review
Vol. 56, No. 2 (Apr., 1966), pp. 213-225
DOI: 10.2307/212879
Stable URL: http://www.jstor.org/stable/212879
Page Count: 13
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Urban Growth and Spatial Structure: Mathematical Models and Empirical Evidence
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Abstract

Two basic assumptions are made: (1) that urban population density declines exponentially with distance from the center of the city; and (2) that the density gradient itself declines through time. From these, two propositions are deduced: (1) the rule of intraurban allometric growth, which states that the rate of growth is a positive exponential function of distance from the center of the city; and (2) the density-growth rate rule, which states that intraurban residential population densities at the beginning of a given period, and the associated rates of population change prevailing during that period, are related by an inverse power function. Two equations for estimating the total population within a city or urban region are presented, the first employing the density parameters in conjunction with the radius and the second employing the density parameters in conjunction with the perimeter density. Data presented within this mathematical framework demonstrate (1) that the urban region (SMA) has a perimeter density of about 2000 persons per square mile and (2) that there is a critical intraurban density (found, in the two cases cited, to be about 30,000 per square mile) which, if exceeded, will eventually be associated with population decrease in the areas concerned. Such areas are the central business district or localities where pathological social conditions are either incipient or already evident.

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