Distribution of distances in pregeographical space: Hans Kuiper. (Studies in Spatial Analysis). Gower Publishing Company, Old Post Road, Brookfield, VT 05036, U.S.A., 1986. 296 pp. + viii. ISBN 0-566-05214-8. $56.00.

Christian Werner

doi:10.1016/0191-2607(89)90010-1

Abstract

Distribution of distances in pregeographical space: Hans Kuiper. (Studies in Spatial Analysis). Gower Publishing Company, Old Post Road, Brookfield, VT 05036, U.S.A., 1986. 296 pp. + viii. ISBN 0-566-05214-8. $56.00.

Highlights

He limits his choice of bounded areas A in R: to circles, squares, and rectangles; to study distance distributions between pairs of points in A he considers either all points in A or a discrete subset B of A consisting of the vertices of a square grid; and to measure distance between any two points he uses three different distance measures: the Manhattan distance, the Euclidean distance, and the maximum of the differences of the x/y coordinates
He studies only the following three types of distance distributions: “contact distributions,” which represent the frequency of pairs of points with distance d, from the set of points under consideration, ordered by d; “distance density functions,” which represent, for each distance d, the proportion of pairs of points both of which are located in A, relative to the set of point pairs with one of the points located in A, and the other anywhere; and “road-area density functions,” which represent for each distance d, the proportion of pairs of points with distance d or less located with one point located in A, relative to the set of point pairs with distance d or less with one point located in A and the other anywhere
Selecting a point x at random from a given set S, the three distributions reflect either the actual frequencies of points in S located at distance d from x. or the proportion of points in S relative to all points with distance d from x, or the proportion of “area” in S located within distance d of x relative to the entire area within distance d from x. It is a matter of simple combinatorics to see that the author has defined a total of S4 mathematical distributions, and the largest part of the book consists of painstaking calculations of many of them

Summary

Introduction

Book Reviews economic principles were applied. In their theoretical analysis, they make two major assertions. In Distribution of Distances in Pregeographical Space, Hans Kuiper calculates mathematical distance distributions in bounded areas of the two-dimensional Euclidean space and compares some of them with empirical distance distributions in selected European countries.

Results

Conclusion