Circles in discrete and continuous taxicab geometry

A taxicab geometry, considered by Hermann Minkowski in 19th-century Germany, is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between the origin and any point (x, y) is the sum of x and y.

Manhattan distance

In taxicab geometry, the red, yellow, blue, and green paths all have the same length.

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