Category:Geometry - Revision history

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Dcadmin: Created page with "'''Geometry''' (from the {{lang-grc|γεωμετρία}}; ''geo-'' "earth", ''-metron'' "measurement") is a branch of mathematics concerne..."

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Created page with "'''Geometry''' (from the {{lang-grc|γεωμετρία}}; ''geo-'' "earth", ''-metron'' "measurement") is a branch of mathematics concerne..."

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'''Geometry''' (from the {{lang-grc|γεωμετρία}}; ''[[wikt:γῆ|geo-]]'' "earth", ''[[wikt:μέτρον|-metron]]'' "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Geometry arose independently in a number of early cultures as a practical way for dealing with [[length]]s, [[area]]s, and [[volume]]s. Geometry began to see elements of formal [[mathematical science]] emerging in the West as early as the 6th century BC.<ref name="Boyer 1991 loc=Ionia and the Pythagoreans p. 43">{{Harv|Boyer|1991|loc="Ionia and the Pythagoreans" p. 43}}</ref> By the 3rd century BC, geometry was put into an [[axiomatic system|axiomatic form]] by [[Euclid]], whose treatment, [[Euclid's Elements|Euclid's ''Elements'']], set a standard for many centuries to follow.<ref>Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews (1998). ''[https://books.google.com/books?id=oLXgFdfKp78C&pg=PA1&dq&hl=en#v=onepage&q=&f=false Fractal geometry in digital imaging]''. [[Academic Press]]. p. 1. {{ISBN|0-12-703970-8}}</ref> Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC.<ref name="Staal 1999"/> Islamic scientists preserved Greek ideas and expanded on them during the [[Middle Ages]].<ref name="ReferenceA">{{MacTutor Biography|id=Thabit|title=Al-Sabi Thabit ibn Qurra al-Harrani}}</ref> By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as [[René Descartes]] and [[Pierre de Fermat]]. Since then, and into modern times, geometry has expanded into [[non-Euclidean geometry]] and [[topological manifold|manifolds]], describing spaces that lie beyond the normal range of human experience.<ref>{{cite magazine |last= Lamb |first= Evelyn |date= 2015-11-08|title=By Solving the Mysteries of Shape-Shifting Spaces, Mathematician Wins $3-Million Prize |url=http://www.scientificamerican.com/article/by-solving-the-mysteries-of-shape-shifting-spaces-mathematician-wins-3-million-prize/ |magazine=Scientific American |location= |publisher= |access-date=2016-08-29 }}</ref>

While geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric.<ref name="Tabak 2014 xiv">{{cite book |last= Tabak|first= John|date= 2014|title= Geometry: the language of space and form|url= |location= |publisher= Infobase Publishing|page=xiv |isbn=978-0816049530}}</ref>

Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics.

@@ Line 1: / Line 1: @@
 '''Geometry''' is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
-Geometry arose independently in a number of early cultures as a practical way for dealing with [[length]]s, [[area]]s, and [[volume]]s. Geometry began to see elements of formal [[mathematical science]] emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an [[axiomatic system|axiomatic form]] by [[Euclid]], whose treatment, [[Euclid's Elements|Euclid's ''Elements'']], set a standard for many centuries to follow.<ref>Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews (1998). ''[https://books.google.com/books?id=oLXgFdfKp78C&pg=PA1&dq&hl=en#v=onepage&q=&f=false Fractal geometry in digital imaging]''.
+Geometry arose independently in a number of early cultures as a practical way for dealing with [[length]]s, [[area]]s, and [[volume]]s. Geometry began to see elements of formal [[mathematical science]] emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an [[axiomatic system|axiomatic form]] by [[Euclid]], whose treatment, [[Euclid's Elements|Euclid's ''Elements'']], set a standard for many centuries to follow.
-Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC.<ref name="Staal 1999"/> Islamic scientists preserved Greek ideas and expanded on them during the [[Middle Ages]]. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as [[René Descartes]] and [[Pierre de Fermat]]. Since then, and into modern times, geometry has expanded into [[non-Euclidean geometry]] and [[topological manifold|manifolds]], describing spaces that lie beyond the normal range of human experience.
+Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as [[René Descartes]] and [[Pierre de Fermat]]. Since then, and into modern times, geometry has expanded into [[non-Euclidean geometry]] and [[topological manifold|manifolds]], describing spaces that lie beyond the normal range of human experience.
-While geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric.
+While geometry has evolved significantly over the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric.
 Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics.

@@ Line 3: / Line 3: @@
 Geometry arose independently in a number of early cultures as a practical way for dealing with [[length]]s, [[area]]s, and [[volume]]s. Geometry began to see elements of formal [[mathematical science]] emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an [[axiomatic system|axiomatic form]] by [[Euclid]], whose treatment, [[Euclid's Elements|Euclid's ''Elements'']], set a standard for many centuries to follow.<ref>Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews (1998). ''[https://books.google.com/books?id=oLXgFdfKp78C&pg=PA1&dq&hl=en#v=onepage&q=&f=false Fractal geometry in digital imaging]''.
-[[Academic Press]]. p. 1. {{ISBN|0-12-703970-8}}</ref> Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC.<ref name="Staal 1999"/> Islamic scientists preserved Greek ideas and expanded on them during the [[Middle Ages]].<ref name="ReferenceA">{{MacTutor Biography|id=Thabit|title=Al-Sabi Thabit ibn Qurra al-Harrani}}</ref> By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as [[René Descartes]] and [[Pierre de Fermat]]. Since then, and into modern times, geometry has expanded into [[non-Euclidean geometry]] and [[topological manifold|manifolds]], describing spaces that lie beyond the normal range of human experience.<ref>{{cite magazine |last= Lamb |first= Evelyn |date= 2015-11-08|title=By Solving the Mysteries of Shape-Shifting Spaces, Mathematician Wins $3-Million Prize |url=http://www.scientificamerican.com/article/by-solving-the-mysteries-of-shape-shifting-spaces-mathematician-wins-3-million-prize/ |magazine=Scientific American |location= |publisher= |access-date=2016-08-29 }}</ref>
+Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC.<ref name="Staal 1999"/> Islamic scientists preserved Greek ideas and expanded on them during the [[Middle Ages]]. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as [[René Descartes]] and [[Pierre de Fermat]]. Since then, and into modern times, geometry has expanded into [[non-Euclidean geometry]] and [[topological manifold|manifolds]], describing spaces that lie beyond the normal range of human experience.
-While geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric.<ref Geometry: the language of space and form|url= |location= |publisher= Infobase Publishing|page=xiv |isbn=978-0816049530}}</ref>
+While geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric.
 Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics.