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In taxicab geometry, the lengths of the red, blue, green, and yellow paths all equal 12, the taxicab distance between the opposite corners, and all four paths are shortest paths. Instead, in Euclidean geometry, the red, blue, and yellow paths still have length 12 but the green path is the unique shortest path, with length equal to the Euclidean ...
A sphere formed using the Chebyshev distance as a metric is a cube with each face perpendicular to one of the coordinate axes, but a sphere formed using Manhattan distance is an octahedron: these are dual polyhedra, but among cubes, only the square (and 1-dimensional line segment) are self-dual polytopes.
Minkowski distance (L p distance), a generalization that unifies Euclidean distance, taxicab distance, and Chebyshev distance. For points on surfaces in three dimensions, the Euclidean distance should be distinguished from the geodesic distance, the length of a shortest curve that belongs to the surface.
Arc length – Distance along a curve; Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric ...
English: Image showing an intuitive explanation of why circles in taxicab geometry look like rotated squares. Created with a specially written program (posted on talk page), based on design of bitmap image created by Schaefer .
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski .
Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [ 1 ] [ 2 ] [ 3 ] More abstractly, it is the study of semimetric spaces and the isometric transformations between them.
In taxicab geometry, p = 1. Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. While each side would have length 2 r {\displaystyle {\sqrt {2}}r} using a Euclidean metric , where r is the circle's radius, its length in taxicab geometry is 2 r .
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