One-dimensional space

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In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number.[1]

One-dimensional geometry[edit]

Polytopes[edit]

The only regular polytope in one dimension is the line segment, with the Schläfli symbol { }.

Hypersphere[edit]

The hypersphere in 1 dimension is a pair of points[2], sometimes called a 0-sphere as its surface is zero-dimensional. Its length is

L = 2r

where r is the radius.

Coordinate systems in one-dimensional space[edit]

Main article: Coordinate system

The most popular coordinate systems are the number line and the angle.

References[edit]

  1. ^ Гущин, Д. Д. "Пространство как математическое понятие" (in Russian). fmclass.ru. Retrieved 2015-06-06. 
  2. ^ Gibilisco, Stan (1983). Understanding Einstein's Theories of Relativity: Man's New Perspective on the Cosmos. TAB Books. p. 89.