Description

The Minkowski distance metric is a general metric that includes as special cases the Euclidean metric, the city block metric and the supremum metric.

This animation depicts "equal distance" from the origin. In a Euclidean metric equidistant is a circle around the point, such as the origin. For other distance metrics, the equidistant set looks different. The city block metric is diamond shaped, where as the supremum metric is a box. The Euclidean metric can be characterized "as the crow flies." The city block metric has its name because it corresponds to a city planners rectangular grid. In that space, the distance from one point to another is functionally characterized by the number of city blocks that one has to walk.

The Minkowski metric represents a family of different distances, with the city block, the Euclidean and the supremum metrics as special cases.

Richard Gonzalez, University of Michigan

gonzo at umich dot edu

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