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Geometers
by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers
by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov
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Aone-dimensional space (1D space) is amathematical space in which location can be specified with a singlecoordinate. An example is thenumber line, eachpoint of which is described by a singlereal number.^[1] Anystraight line or smoothcurve is a one-dimensional space, regardless of the dimension of theambient space in which the line or curve is embedded. Examples include thecircle on a plane, or aparametric space curve.Inphysical space, a 1Dsubspace is called a "lineardimension" (rectilinear orcurvilinear), withunits oflength (e.g.,metre).

Inalgebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more specific terms. Anyfield${\displaystyle K}$ is a one-dimensionalvector space over itself. Theprojective line over${\displaystyle K,}$ denoted${\displaystyle {\mathbf{P}}^1(K),}$ is a one-dimensional space. In particular, if the field is thecomplex numbers${\displaystyle \mathbb{C},}$ then thecomplex projective line${\displaystyle {\mathbf{P}}^1(\mathbb{C})}$ is one-dimensional with respect to${\displaystyle \mathbb{C}}$ (but is sometimes called theRiemann sphere, as it is a model of thesphere,two-dimensional with respect to real-number coordinates).

For everyeigenvector of alinear transformationT on a vector spaceV, there is a one-dimensional spaceA ⊂V generated by the eigenvector such thatT(A) =A, that is,A is aninvariant set under the action ofT.^[2]

InLie theory, a one-dimensional subspace of aLie algebra is mapped to aone-parameter group under theLie group–Lie algebra correspondence.^[3]

More generally, aring is alength-onemodule over itself. Similarly, theprojective line over a ring is a one-dimensional space over the ring. In case the ring is analgebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.

One dimensional coordinate systems include thenumber line.

• 
  Number line

• Univariate
• Zero-dimensional space

• Dimension
• 1 (number)

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