- Hypersphere
- Coordinate systems in one-dimensional space
- References
In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When {{nowrap|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 {{nowrap|1=k = ℂ}}, the complex numbers, then the complex projective line P1(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.
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
{{main|Coordinate system}}One dimensional coordinate systems include the number line and the angle.
References
2. ^{{cite book|title=Understanding Einstein's Theories of Relativity: Man's New Perspective on the Cosmos|url=https://books.google.ru/books?id=fzZMuP2sF9sC&pg=PA98&dq=one-dimensional+space+Hypersphere&hl=en&sa=X&ei=5nl0VeiiFeGeywPKqIL4Cg&ved=0CBwQ6AEwAA#v=onepage&q=one-dimensional%20space%20Hypersphere&f=false|publisher=TAB Books|year=1983|last=Gibilisco|first=Stan |page=89}}
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