61. Euclidean Geometry - Retrieved from http//en.wikipedia.org/wiki/euclidean_geometry . Categories Articles with unsourced statements since August 2007 All articles with http://www.pwsz.wsanok.pl/wiki/Euclidean_geometry

Euclidean geometry Jump to: navigation search A representation of Euclid from The School of Athens by Raphael Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria . Euclid's text Elements is the earliest known systematic discussion of geometry . It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms , and then proving many other propositions theorems ) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fit together into a comprehensive deductive and logical system The Elements begin with plane geometry , still taught in secondary school as the first axiomatic system and the first examples of formal proof . The Elements goes on to the solid geometry of three dimensions , and Euclidean geometry was subsequently extended to any finite number of dimensions . Much of the Elements states results of what is now called number theory , proved using geometrical methods.

62. * Euclidean Geometry - (GIS): Definition Euclidean Geometry Top The process of calculating distances and areas based upon the Euclidean concept of space. Space is thus ordered according to a http://en.mimi.hu/gis/euclidean_geometry.html

wr("What is what? Everything you always wanted to know.") Home Menu(0); pozicio('GIS','Euclidean Geometry') MimiF1("GIS",0); Euclidean Geometry InitAdv(0) Euclidean Geometry [Top] The process of calculating distances and areas based upon the Euclidean concept of space. Space is thus ordered according to a 2-dimensional plane, and movement can take place in any direction within that plane. InitAdv(1) Euclidean geometry has become closely connected with computational geometry computer graphics , discrete geometry , and some areas of combinatorics. InitAdv(2) The study of space origin ates with geometry , first the Euclidean geometry and trigonometry of familiar three-dimensional space, but later also generalized to non-Euclidean geometries which play a central role in general relativity. InitAdv(3) For the sake of illustration we will stick to the simpler and more familiar Euclidean geometry setting where all data are represented in Cartesian coordinate s. InitAdv(4) Flat space has minimal (zero) curvature and obeys the precepts of Euclidean geometry . In flat space

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64. Ask NRICH: Hyperbolic Trig Functions http//en.wikipedia.org/wiki/Noneuclidean_geometry History or http//www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-euclidean_geometry.html) http://nrich.maths.org/discus/messages/67613/68695.html?1140971526

65. Category Talk:Euclidean Geometry - Wikipedia, The Free Encyclopedia that the term Euclidean geometry by defolt means plane geometry Tosha 0646, 13 Mar 2005 (UTC). Retrieved from /wiki/Category_talkeuclidean_geometry http://www.adorons.com/wiki/Category_talk:Euclidean_geometry

Category talk:Euclidean geometry From Wikipedia, the free encyclopedia Jump to: navigation search edit Plane geometry I would remove subcategory plane geometry and leave Multi-dimensional geometry , since by defolt Euclidean geometry means plane geometry... Tosha 10:47, 19 Jul 2004 (UTC) That is simply false. Euclid did solid geometry, e.g. see . In any case, Euclidean geometry means primarily not what Euclid did, but "flat-space" geometries of any dimension. (Not to mention that the term for geometry of more than 3 dimensions should not be that, which i have never before heard in a geometric context, but, IIRC "higher-dimensional".) In any case, i'd like to see that Category:Plane geometry restored, and a Category:Solid geometry to make the Cats of some use to people with a sound education who are not math majors. Or for that matter were math majors but did their graduate work in other fields! Jerzy (t) 05:18, 2005 Mar 13 (UTC) No it is not, see the main article, we should not care about what Euclid did, what is iportant that the term Euclidean geometry by defolt means plane geometry Tosha 06:46, 13 Mar 2005 (UTC)

66. Wiki Non-Euclidean Geometry Wapedia Wiki Wiki NonEuclidean geometry. Contents 1. Concepts of non-Euclidean geometry 2. History 3. Models of non-Euclidean geometry http://wapedia.mobi/en/Non-Euclidean_geometry

Wiki: Non-Euclidean geometry Contents: 1. Concepts of non-Euclidean geometry 2. History 3. Models of non-Euclidean geometry 3. 1. Elliptic geometry ... Wapedia: For Wikipedia on mobile phones

67. CategoryEuclidean Geometry - Retrieved from http//en.wikipedia.org/wiki/Categoryeuclidean_geometry . Categories Classical geometry. Views. Category; Discussion; Edit this page http://www.gay.com.pl/wiki/Category:Euclidean_geometry

68. Non-Euclidean Geometry Retrieved from http//en.wikipedia.org/wiki/Noneuclidean_geometry . Categories Geometry Non-Euclidean geometry Hyperbolic geometry. http://www.mind42.com/wiki/Non-Euclidean_geometry

Non-Euclidean geometry From Wikipedia, the free encyclopedia Jump to: navigation search Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry , which are contrasted with Euclidean geometry . The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that, within a two-dimensional plane, for any given line l and a point A , which is not on l , there is exactly one line through A that does not intersect l . In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l , while in elliptic geometry, any pair of lines intersect. (See the entries on hyperbolic geometry and elliptic geometry for more information.) Another way to describe the differences between these geometries is as follows: Consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line. In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels. In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry the lines "curve toward" each other and eventually intersect.

69. Euclidean Geometry - WikiClone.org , The Free Encyclopedia in the original Greek, with English translations and commentaries (HTML with figures). Retrieved from http//en.wikipedia.org/wiki/euclidean_geometry http://www.wikiclone.org/en/wiki/Euclidean_geometry.html

BÅ‚Ä d ! Plik nie został utworzony! Home Main Categories Community Portal Search: Latest Added: Gigantopithecus [en] 1月6日 (旧暦) [ja] 1965 [hr] Euclidean geometry [en] ... IEEE Computer Society [en] Language: ar id bg ca ... zh Euclidean geometry From Wikipedia, the free encyclopedia Jump to: navigation search A representation of Euclid from The School of Athens by Raphael Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria . Euclid's text Elements is the earliest known systematic discussion of geometry . It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms , and then proving many other propositions theorems ) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fit together into a comprehensive deductive and logical system The Elements begin with plane geometry , still taught in secondary school as the first axiomatic system and the first examples of formal proof . The Elements goes on to the solid geometry of three dimensions , and Euclidean geometry was subsequently extended to any finite number of dimensions . Much of the Elements states results of what is now called number theory , proved using geometrical methods.

70. Geometry - Searchy Search account with links to biographies of some of the people involved.wwwgroups. dcs.st-andrews.ac.uk/~history/HistTopics/Non-euclidean_geometry.html http://www.searchy.co.uk/?q=geometry

71. Non-Euclidean Geometry - The UCSC Wikipedia Trust Project Retrieved from http//wikitrust.cse.ucsc.edu80/index.php/Non-euclidean_geometry . Categories Geometry Non-Euclidean geometry Hyperbolic geometry http://wiki-trust.cse.ucsc.edu/index.php/Non-Euclidean_geometry

Non-Euclidean geometry From The UCSC Wikipedia Trust Project Jump to: navigation search Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes hyperbolic elliptic and absolute geometry which are contrasted with Euclidean geometry . The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that for any given line l and a point A which is not on l there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, and in elliptic geometry, any pair of lines intersect. (See the entries on hyperbolic geometry and elliptic geometry for more information.) Another way to describe the differences between these geometries is as follows: Consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line. In Euclidean geometry the lines remain at a constant distance and are known as parallels.

72. Non-euclidean Geometry NFnd. This article is licensed under the GNU Free Documentation License. This article was taken from and can be viewed by clicking Here. http://air-conditioning.lookitup.co.nz/nz/Non-euclidean_geometry

Non-euclidean geometry Fnd This article is licensed under the GNU Free Documentation License This article was taken from and can be viewed by clicking Here Archie Andrews - OTR

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74. Site Web Stats - Free Web Statistics This page is based on the copyrighted Wikipedia article ( euclidean_geometry ); it is used under the GNU Free Documentation License . http://encyclopedia.topliterature.com/?title=Euclidean_geometry

75. Non-Euclidean Geometry http//pediaview.com/openpedia/Noneuclidean_geometry. All Wikipedia text is available under the terms of the GNU Free Documentation License. http://pediaview.com/openpedia/Non-Euclidean_geometry

Non-Euclidean geometry Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry , which are contrasted with Euclidean geometry . The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that, within a two-dimensional plane, for any given line l and a point A , which is not on l , there is exactly one line through A that does not intersect l . In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l , while in elliptic geometry, any pair of lines intersect. (See the entries on hyperbolic geometry and elliptic geometry for more information.) Another way to describe the differences between these geometries is as follows: Consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line. In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels. In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry the lines "curve toward" each other and eventually intersect.

76. ø Euclidean Geometry Data ø See full license termsIt uses material from the Wikipedia article euclidean_geometry . compliance August 13th 2007. Powered by www.aadet.com http://www.aadet.com/article/Euclidean_geometry

www.aadet.com Site Search: Home Popular Articles Maecenas Harry Potter ... Years Euclidean geometry history Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria . Euclid's text Elements was the earliest known systematic discussion of geometry . It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axiom s, and then proving many other proposition s ( theorem s) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fitted together into a comprehensive deductive and logical system. The Elements begin with plane geometry , still often taught in secondary school as the first axiomatic system and the first examples of formal proof . The Elements goes on to the solid geometry of three dimension s, and Euclidean geometry was subsequently extended to any finite number of dimension s. Much of the

77. Non-Euclidean Geometry - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.orggetWikiPage.aspx?s=Noneuclidean_geometry . Categories Geometry Non-Euclidean geometry Hyperbolic geometry http://www.seattletixx.com/admin/getWikiPage.aspx?s=Non-euclidean_geometry

78. Non-Euclidean Geometry - Encyclopedia , The Free Encyclopedia Noneuclidean geometry on PlanetMath; Lobachevski - Non-Euclidean Geometry. Retrieved from http//en.wikipedia.org/wiki/Non-euclidean_geometry http://www.wielkaencyklopedia.com/en/wiki/Non-Euclidean_geometry.html

Main Page Contents Current events Search: Enter your search terms Submit search form Links: Zał³Å¼ swoje darmowe forum dyskusyjne Free MP3 Download Filmiki erotyczne Najlepsze kredyty kredyt konsolidacyjny ... Centralwings - Tanie Bilety dobry i tani hosting i domeny pl Najlepsze forum SAT HACCP ISO 22000 wiadomosci Last time: Non-Euclidean geometry [en] Europa [pt] Kategorio:Antropologio [eo] Granola bar [en] ... FN FNC [ja] Wybierz język: ar id bg ca ... Edycja Non-Euclidean geometry From Wikipedia, the free encyclopedia Jump to: navigation search Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry , which are contrasted with Euclidean geometry . The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that, within a two-dimensional plane, for any given line l and a point A , which is not on l , there is exactly one line through A that does not intersect l . In hyperbolic geometry, by contrast, there are

79. Hyperbolic Geometry - Term Explanation On IndexSuche.Com (See article on noneuclidean_geometry for more history. Hyperbolic geometry has many properties foreign to euclidean_geometry, all of which are http://www.indexsuche.com/Hyperbolic_geometry.html

Hyperbolic geometry , also called saddle geometry or Lobachevskian geometry , is the non-Euclidean_geometry obtained by replacing the with the ''hyperbolic postulate'', which states: "Given a line ''L'' and any point ''A'' not on ''L'', at least two distinct lines exist which pass through ''A'' and are parallel to ''L''." In this case ''parallel'' means that the lines do not intersect ''L'', even when extended, rather than that they are a constant distance from ''L''. Hyperbolic geometry was initially explored by Saccheri in the , who nevertheless believed that it was inconsistent , and later by Bolyai Gauss , and Lobachevsky , after whom it is sometimes named. (See article on non-Euclidean_geometry for more history.) There are three model s commonly used for hyperbolic geometry. The Klein model uses the interior of a circle for the hyperbolic plane , and chord s of the circle as lines. This model has the advantage of simplicity, but the disadvantage that angle s in the hyperbolic plane are distorted. The Poincaré disc model also employs the interior of a circle, but lines are represented by arcs of circles that are

80. Non-Euclidean Geometry - Wikipedia, The Free Encyclopedia Schopenhauer s criticism of the proofs of the Parallel Postulate. Retrieved from http//knowledgehunter.info/w/Noneuclidean_geometry http://knowledgehunter.info/wiki/Non-Euclidean_geometry

Portals A-Z Categories Random ... discussion Non-Euclidean geometry Behavior of lines with a common perpendicular in each of the three types of geometry On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very nearly 180°. In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry , which are contrasted with Euclidean geometry . The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that, within a two-dimensional plane, for any given line l and a point A , which is not on l , there is exactly one line through A that does not intersect l . In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l , while in elliptic geometry, any pair of lines intersect. (See the entries on hyperbolic geometry and elliptic geometry for more information.)

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