# One-dimensional space

In physics and mathematics, a sequence of *n* numbers can specify 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]}

In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field *k* is a one-dimensional vector space over itself. Similarly, the projective line over *k* is a one-dimensional space. In particular, if *k* = ℂ, the complex numbers, then the complex projective line P^{1}(ℂ) is one-dimensional with respect to ℂ, even though it is also known as the Riemann sphere.

More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.

## Polytopes

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

## Hypersphere

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

where is the radius.

## Coordinate systems in one-dimensional space

One dimensional coordinate systems include the number line and the angle.

- Number line
- Angle

## References

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