Taxicab Metric


The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by


for all points P_1(x_1,y_1) and P_2(x_2,y_2). This number is equal to the length of all paths connecting P_1 and P_2 along horizontal and vertical segments, without ever going back, like those described by a car moving in a lattice-like street pattern.

See also

Equivalent Metrics, Graph Distance, Metric, Spanning Tree, Taxicab Number

This entry contributed by Margherita Barile

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Dickau, R. M. "Shortest-Path Diagrams.", E. F. Taxicab Geometry: An Adventure in Non-Euclidean Geometry. New York: Dover, 1986.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 172 and 227, 1990.Willard, S. General Topology. Reading, MA: Addison-Wesley, p. 16, 1970.

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Taxicab Metric

Cite this as:

Barile, Margherita. "Taxicab Metric." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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