Distortion in Maps

Abstract

All maps which cartographers use to represent the earth and most maps which psychologists use to represent experimental data are distorted; i.e., distances in the maps do not exactly equal distances in the original space. Here mean-squared error is used to measure distortion and the problem is to find a map which minimizes it. After developing some theory about maps in general, the paper examines a special case of mapping a circular cap on the sphere. Lambert’s azimuthal projection, a standard map which preserves areas, is found to be close to the minimizing map.

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