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1. Euclidean Geometry - Wikipedia, The Free Encyclopedia
http://en.wikipedia.org/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.

2. CiteULike: Tag Euclidean_geometry [3 Articles]
Recent papers classified by the tag euclidean_geometry. posted to nmiller for_gabe euclidean_geometry by AlisonBabeu on 2007-06-12 150135 as
http://www.citeulike.org/tag/euclidean_geometry
##### Tag euclidean_geometry [3 articles]
Recent papers classified by the tag euclidean_geometry.
• Computational complexity of diagram satisfaction in Euclidean geometry J. Complex. , Vol. 22, No. 2. (April 2006), pp. 250-274. by Nathaniel Miller posted to n-miller by AlisonBabeu on 2007-06-12 15:01:35 as Case Analysis in Euclidean Geometry: An Overview Theory and Application of Diagrams: First International Conference, Diagrams 2000, Edinburgh, Scotland, UK, September 2000. Proceedings (2000), pp. 1-13. by Nathaniel Miller posted to n-miller by AlisonBabeu on 2007-06-12 14:37:59 as CDEG: Computerized Diagrammatic Euclidean Geometry Diagrammatic Representation and Inference : Second International Conference, Diagrams 2002 Callaway Gardens, GA, USA, April 18-20, 2002. Proceedings (2002), pp. 321-322. by Nathaniel Miller posted to n-miller by AlisonBabeu on 2007-06-12 14:50:20 as
RIS
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Tags related to: euclidean_geometry Filter: n-miller CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

3. E-Tutor - Dictionary - 'non-euclidean_geometry'
eTutor, Home, Enroll, Tour, Contact Us, Dictionary Home, Index, About. Definition of non-euclidean geometry . Noun. geometry based on axioms different
http://www.e-tutor.com/et3/dictionary/define/non-euclidean_geometry
##### Noun
• geometry based on axioms different from Euclid's Search: Dictionary Google Get this dictionary without ads as part of the e-Tutor Virtual Learning Program
• 4. Non-Euclidean Geometry - Indopedia, The Indological Knowledgebase
MacTutor Archive article on nonEuclidean geometry (http//www-groups.dcs.st-and. ac.uk/~history/HistTopics/Non-euclidean_geometry.html)
http://www.indopedia.org/Non-Euclidean_geometry.html
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##### Non-Euclidean geometry
à¤à¥à¤à¤¾à¤¨à¤à¥à¤¶: - The Indological Knowledgebase The term non-Euclidean geometry (also spelled: non-Euclidian geometry ) describes both 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. In Euclidean geometry, if we start with a point A and a line l , then we can only draw one line through A that is parallel to l . In hyperbolic geometry, by contrast, there are infinitely many lines through A parallel to l , and in elliptic geometry, parallel lines do not exist. (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 lines in a plane that are both perpendicular to a third line. In Euclidean and hyperbolic geometry, the two lines are then parallel. In Euclidean geometry, however, the lines remain at a constant distance , while in hyperbolic geometry they "curve away" from each other, increasing their distance as one moves farther from the point of intersection with the common perpendicular. In elliptic geometry, the lines "curve toward" each other, and eventually intersect; therefore no parallel lines exist in elliptic geometry.

 5. Ytmnd - You're The Man Now Dog! Keyword information for euclidean_geometry. Total sites with this keyword 1 ? euclidpwned.ytmnd.com. DaBee Uber New Euclidean Haxhttp://ytmnd.com/keyword/euclidean_geometry?PHPSESSID=6c8a7d337f857d0f802b409648

6. Non-Euclidean Geometry - Wikipedia, á¯á  á ááá¢ á¥
http//chr.wikigadugi.org/wiki/Noneuclidean_geometry . Geometry Non-Euclidean geometry Hyperbolic geometry
##### ááá´áá Wikipedia, á¯á  á ááá¢ á¥á¦áá²á¢
á¥á-Euclidean áááá ááááá hyperbolic Euclidean áááá ááááá . á¯á  á¤áµáá¨á á§áá´á¿á¢ á á°áµ Euclidean á á´ á¥á-Euclidean áááá ááááá á¨áá¢ á¯á  á¤áá³á á¤á¬á¢á Euclid 5th á áááá l A l A l . á­á«á¾áá¢ hyperbolic áááá ááááá, á¾á¥á¢ á§áá´á¾á¢, áá¾á¢ A l hyperbolic áááá ááááá á¤áµáá á¦á¢á á áááá. á­á«á¾áá¢ Euclidean áááá ááááá á¯á  á áááá áá¦á°áá² á¾á¾á¢ ááªá¯á¸ ááá´áá á áááµ á¾á¾ááá², á á´ ááªáá¬ áá¦áá©á. á­á«á¾áá¢ hyperbolic áááá ááááá á¤áá "á áá²á² á¤á£áá¾" ááá´áá á áááµ á¾á¾ááá², á§á¾áá¤á© á­á«á¾áá¢ áá¾ á¢á´á¢ á áµáªá á áááá á¤ááá¢ ááá´áá á¯á  ááªááá± áá¦á¾áá«áá á¬áá ááá³á© á ááá¦á; á¾áá© á¯á  á áááá á¢á³ááµá­ á¤á¯áá² á¡á áá¦áá©á. á­á«á¾áá¢ á¬á©áá«á áááá ááááá á¯á  á áááá "á áá²á² á«áá³áªá" á áááµ á¾á¾ááá² á á´ á­áµá±á¶á¸ áá¦á¾áá«áá.

7. Euclidean Geometry
Geometry of the type described originally by Euclid in his book Elements and based on five axioms, one of which is the controversial parallel postulate.
http://www.daviddarling.info/encyclopedia/E/Euclidean_geometry.html
 GEOMETRY TOPOLOGY SPACE AND TIME A ... CONTACT entire Web this site Euclidean geometry Geometry of the type described originally by Euclid in his book Elements and based on five axioms , one of which is the controversial parallel postulate . Various forms of non-Euclidean geometry began to emerge in the 19th century, with enormous implications for science and philosophy. Related categories GEOMETRY SPACE AND TIME TOPOLOGY Also on this site: BACK TO TOP var site="s13space1234"

8. Non-euclidean Geometry - Wikipedia
http://nostalgia.wikipedia.org/wiki/Non-euclidean_geometry
##### Non-euclidean geometry
Printable version

Geometries resulting from the negation of the fifth postulate of Euclid(see euclidean geometry The famous fifth postulate can be formulated thus: Given a straight line and a point A not on that line, there exists exactly one straight line through A which never intersects the original line.

9. Non-euclidean Geometry - English Dictionary
english to english dictionary containing references.
http://www.online-dictionary.biz/english/vocabulary/reference/non-euclidean_geom
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##### Non-euclidean Geometry - English Dictionary
1. geometry based on axioms different from Euclid''s
##### Related words
elliptic geometry geometry hyperbolic geometry mathematics ... Z
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10. Euclidean Geometry - Wikipedia
Euclidean geometry. Euclidean geometry, also called flat or parabolic geometry, is named after the Greek mathematician Euclid. Euclid s text Elements is
http://facetroughgemstones.com/wikipedia/eu/Euclidean_geometry.html
##### Euclidean geometry
Euclidean geometry , also called " flat " or " parabolic " geometry, is named after the Greek mathematician Euclid . Euclid's text Elements is an early systematic treatment of this kind of geometry , based on axioms (or postulates ). This is the kind of geometry familiar to most people, since it is the kind usually taught in high school Euclidean geometry is distinguished from other geometries by the parallel postulate , which is usually phrased as follows: Through a point not on a given straight line, one and only one line can be drawn that never meets the given line. In particular, this postulate separates Euclidean geometry from hyperbolic geometry , where many parallel lines could be drawn through the point, and from elliptic and projective geometry , where no parallel lines exist. (Euclidean geometry does, however, share the parallel postulate with some geometries, such as certain finite geometries[?] Since Euclid's time, other mathematicians have laid out more thorough axiomatic systems for Euclidean geometry, such as

11. Topic:Euclidean Geometry - Wikiversity
http://en.wikiversity.org/wiki/Topic:Euclidean_geometry
##### From Wikiversity
Jump to: navigation search Euclid, the developer of Euclidean Geometry Welcome to the Euclidean Geometry Learning Project , part of the School of Mathematics . The purposes of this learning project are to facilitate the study and further understanding of Euclidean Geometry, and to assist students currently studying it in class. See below for more information about the learning project. From Wikipedia:
Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first 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 fitted together into a comprehensive deductive and logical system. More

12. Non-Euclidean Geometry References
R Bonola, NonEuclidean Geometry A Critical and Historical Study of its Development (New York, 1955). T R Chandrasekhar, Non-Euclidean geometry from early
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/References/Non-Euclidean_
##### References for: Non-Euclidean geometry
Version for printing
• R Bonola, Non-Euclidean Geometry : A Critical and Historical Study of its Development (New York, 1955).
• T R Chandrasekhar, Non-Euclidean geometry from early times to Beltrami, Indian J. Hist. Sci.
• N Daniels,Thomas Reid's discovery of a non-Euclidean geometry, Philos. Sci.
• F J Duarte, On the non-Euclidean geometries : Historical and bibliographical notes (Spanish), Revista Acad. Colombiana Ci. Exact. Fis. Nat.
• H Freudenthal, Nichteuklidische Geometrie im Altertum?, Archive for History of Exact Sciences
• J J Gray, Euclidean and non-Euclidean geometry, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 877-886.
• J J Gray, Ideas of Space : Euclidean, non-Euclidean and Relativistic (Oxford, 1989).
• J J Gray, Non-Euclidean geometry-a re-interpretation, Historia Mathematica
• J J Gray, The discovery of non-Euclidean geometry, in Studies in the history of mathematics (Washington, DC, 1987), 37-60.
• 13. Do Mathematical Proofs Exist, Of Things That We Are Not Sure Exist? Text - Physi
Consider the four (or five) axioms of Euclidean geometry (from http//en.wikipedia.org/wiki/euclidean_geometry) Any two points can be joined by a straight
http://www.physicsforums.com/archive/index.php/t-21343.html
 Physics Help and Math Help - Physics Forums PF Lounge General Discussion Philosophy ... PDA View Full Version : Do mathematical proofs exist, of things that we are not sure exist? Rader Do mathematical proofs exist, of things that we are not sure exist, especially those, that do not have observational confirmed data? chroot Mathematical proofs certainly exist. Mathematics doesn't rely on observational data, though. Math works this way: 1) Define your axioms. 2) Find all true statements (proofs) that can be generated from those axioms. - Warren selfAdjoint Do mathematical proofs exist, of things that we are not sure exist, especially those, that do not have observational confirmed data? Sure. There are for example proofs about transfinite cardinals, which no experiment in a finite part of spacetime can ever verify. The axioms Warren mentioned can be any statements that are consistent among themselves. Lewis Carrol (pen name of Charles Dodgson, a mathematician) used to amuse himself by constructing self consistent statements concerning dragons and teapots. He set them up as sorites (extended syllogisms), but they could equally well have been set up as axioms, and theorems proven from them. Rader Mathematical proofs certainly exist. Mathematics doesn't rely on observational data, though. Math works this way:

 14. IPOP2 Euclidian Geometry en.wikipedia.org/wiki/Noneuclidean_geometry - 47k - www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-euclidean_geometry.html - 29k -http://ipop2.com/search?l=g&m=g&q=Euclidian Geometry

15. Science Central : Science - Math - Geometry - Non-Euclidean
//www.geocities.com/timsheltonjones/http//wwwgroups.dcs.st-andrews.ac. uk/~history/HistTopics/Non-euclidean_geometry.htmlhttp//www.math.columbia.edu/
http://www.sciencecentral.com/category/415815
 Friday, 14 March, 2008 Home Submit Science Site Add to Favorite Contact search for Directories Aeronautics and Aerospace Agriculture Anomalies and Alternative Science Astronomy ... Technology Category: Science Math Geometry Non-Euclidean SUBMIT A SITE Non-Euclidean Order by Popularity Alphabet Sites Records 1-12 of 12 NonEuclid - Hyperbolic Geometry Article + Software Applet (Popularity: NonEuclid is a software simulation offering straightedge and compass constructions in hyperbolic geometry. Spherical Trigonometry, Arc Distance Formula (Popularity: Finding the shortest distance between two points on the earth given latitude and longitude. Download ... Non-Euclidean Geometry with LOGO (Popularity: Review of a new version of LOGO developed at Cardiff. Non-Euclidean Geometry - Mathematics and the Liberal Arts (Popularity: A resource for student research projects and for teachers interested in using the history of ... Book List on Non-Euclidean Geometry (Popularity: From theTreasureTroves collection. The Ontology and Cosmology of Non-Euclidean Geometry (Popularity: A philosophical essay.

16. Models/Non-Euclidean_Geometry ..
models/Noneuclidean_geometry ..
http://www.eg-models.de/models/Non-Euclidean_Geometry/_noapplet.html
 models/Non-Euclidean_Geometry

 17. Webaroo - The Wikipedia In hyperbolic geometry the sum of the three angles are always less than 180° and can approach zero, http//en.wikipedia.org/wiki/euclidean_geometryhttp://notebook.webaroo.com/webpack/wikipedia/wikipedia?topic=Mathematics&subtop

 18. SQL*Plus Report Noneuclidean_geometry, 1, Non-euclidean_geometry, 1. Emblem_of_india.png, 6, Emblem_of_India.png, 6. CUR_TITLE, CUR_NAMESPACE, CUR_TITLE, CUR_NAMESPACEhttp://users.sosdg.org/~larne/pagenames.html

19. Non-Euclidean Geometry
From http//wwwgroups.dcs.st-and.ac.uk/~history/HistTopics/Non-euclidean_geometry. html. In about 300 BC Euclid wrote The Elements, a book which was to
http://meta-religion.com/Mathematics/Articles/non-euclidean_geometry.htm
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##### Non-Euclidean Geometry
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##### Non-Euclidean geometry
Article by: J J O'Connor and E F Robertson
From: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html In about 300 BC Euclid wrote The Elements, a book which was to become one of the most famous books ever written. Euclid stated five postulates on which he based all his theorems:
• To draw a straight line from any point to any other. To produce a finite straight line continuously in a straight line. To describe a circle with any centre and distance. That all right angles are equal to each other. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
It is clear that the fifth postulate is different from the other four. It did not satisfy Euclid and he tried to avoid its use as long as possible - in fact the first 28 propositions of The Elements are proved without using it. Another comment worth making at this point is that Euclid, and many that were to follow him, assumed that straight lines were infinite.

20. Euclidean Geometry - Wiktionary