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Traditional geometry allowed dimensions 1 (a [[line (geometry)|line]] or curve), 2 (a [[Plane (mathematics)|plane]] or surface), and 3 (our ambient world conceived of as [[three-dimensional space]]). Furthermore, mathematicians and physicists have used [[higher dimension]]s for nearly two centuries.[{{cite book|author=Mark Blacklock|title=The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siècle|url=https://books.google.com/books?id=nrNSDwAAQBAJ|year=2018|publisher=Oxford University Press|isbn=978-0-19-875548-7|access-date=18 September 2019|archive-date=27 December 2019|archive-url=https://web.archive.org/web/20191227145318/https://books.google.com/books?id=nrNSDwAAQBAJ|url-status=live}}] One example of a mathematical use for higher dimensions is the [[configuration space (physics)|configuration space]] of a physical system, which has a dimension equal to the system's [[degrees of freedom]]. For instance, the configuration of a screw can be described by five coordinates.[{{cite book|author=Charles Jasper Joly|title=Papers|url=https://books.google.com/books?id=cOTuAAAAMAAJ&pg=PA62|year=1895|publisher=The Academy|pages=62–|access-date=18 September 2019|archive-date=27 December 2019|archive-url=https://web.archive.org/web/20191227195202/https://books.google.com/books?id=cOTuAAAAMAAJ&pg=PA62|url-status=live}}] |
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Traditional geometry allowed dimensions 1 (a [[line (geometry)|line]] or curve), 2 (a [[Plane (mathematics)|plane]] or surface), and 3 (our ambient world conceived of as [[three-dimensional space]]). Furthermore, mathematicians and physicists have used [[higher dimension]]s for nearly two centuries.[{{cite book|author=Mark Blacklock|title=The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siècle|url=https://books.google.com/books?id=nrNSDwAAQBAJ|year=2018|publisher=Oxford University Press|isbn=978-0-19-875548-7|access-date=18 September 2019|archive-date=27 December 2019|archive-url=https://web.archive.org/web/20191227145318/https://books.google.com/books?id=nrNSDwAAQBAJ|url-status=live}}] One example of a mathematical use for higher dimensions is the [[configuration space (physics)|configuration space]] of a physical system, which has a dimension equal to the system's [[degrees of freedom]]. For instance, the configuration of a screw can be described by five coordinates.[{{cite book|author=Charles Jasper Joly|title=Papers|url=https://books.google.com/books?id=cOTuAAAAMAAJ&pg=PA62|year=1895|publisher=The Academy|pages=62–|access-date=18 September 2019|archive-date=27 December 2019|archive-url=https://web.archive.org/web/20191227195202/https://books.google.com/books?id=cOTuAAAAMAAJ&pg=PA62|url-status=live}}] |
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In [[general topology]], the concept of dimension has been extended from [[natural number]]s, to infinite dimension ([[Hilbert space]]s, for example) and positive [[real number]]s (in [[fractal geometry]]).[{{cite book|author=Roger Temam|title=Infinite-Dimensional Dynamical Systems in Mechanics and Physics|url=https://books.google.com/books?id=OB_vBwAAQBAJ&pg=PA367|year=2013|publisher=Springer Science & Business Media|isbn=978-1-4612-0645-3|page=367|access-date=18 September 2019|archive-date=24 December 2019|archive-url=https://web.archive.org/web/20191224015857/https://books.google.com/books?id=OB_vBwAAQBAJ&pg=PA367|url-status=live}}] In [[algebraic geometry]], the [[dimension of an algebraic variety]] has received a number of apparently different definitions, which are all equivalent in the most common cases.[{{cite book|author1=Bill Jacob|author2=Tsit-Yuen Lam|title=Recent Advances in Real Algebraic Geometry and Quadratic Forms: Proceedings of the RAGSQUAD Year, Berkeley, 1990–1991|url=https://books.google.com/books?id=mHwcCAAAQBAJ&pg=PA111|year=1994|publisher=American Mathematical Soc.|isbn=978-0-8218-5154-8|page=111|access-date=18 September 2019|archive-date=28 December 2019|archive-url=https://web.archive.org/web/20191228124040/https://books.google.com/books?id=mHwcCAAAQBAJ&pg=PA111|url-status=live}}] |
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In [[general topology]], the concept of dimension has been extended from [[natural number]]s, to infinite dimension ([[Hilbert space]]s, for example) and positive [[real number]]s (in [[fractal geometry]]).[{{cite book|author=Roger Temam|title=Infinite-Dimensional Dynamical Systems in Mechanics and Physics|url=https://books.google.com/books?id=OB_vBwAAQBAJ&pg=PA367|year=2013|publisher=Springer Science & Business Media|isbn=978-1-4612-0645-3|page=367|access-date=18 September 2019|archive-date=24 December 2019|archive-url=https://web.archive.org/web/20191224015857/https://books.google.com/books?id=OB_vBwAAQBAJ&pg=PA367|url-status=live}}] In [[algebraic geometry]], the [[dimension of an algebraic variety]] has received a number of apparently different definitions, which are all equivalent in the most common cases.[{{cite book|author1=Bill Jacob|author2=Tsit-Yuen Lam|author-link2=Tsit Yuen Lam|title=Recent Advances in Real Algebraic Geometry and Quadratic Forms: Proceedings of the RAGSQUAD Year, Berkeley, 1990–1991|url=https://books.google.com/books?id=mHwcCAAAQBAJ&pg=PA111|year=1994|publisher=American Mathematical Soc.|isbn=978-0-8218-5154-8|page=111|access-date=18 September 2019|archive-date=28 December 2019|archive-url=https://web.archive.org/web/20191228124040/https://books.google.com/books?id=mHwcCAAAQBAJ&pg=PA111|url-status=live}}] |
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