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1. Euclidean Geometry - Wikipedia, The Free Encyclopedia
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, whose Elements is the earliest known systematic
http://en.wikipedia.org/wiki/Euclidean_geometry
##### Euclidean geometry

 2. Euclidean Geometry Summary And Analysis Summary | BookRags.com Euclidean geometry summary with 40 pages of lesson plans, quotes, chapter summaries, analysis, encyclopedia entries, essays, research information, and more.http://www.bookrags.com/Euclidean_geometry

 3. Non-Euclidean Geometry - Uncyclopedia, The Content-free Encyclopedia NonEuclidean geometry is essentially a not important branch of geometry that does not involve Euclidean geometry. In the latter case, it was Lord Knonn Euclid (in his 1707http://uncyclopedia.wikia.com/wiki/Non-Euclidean_Geometry

4. 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
http://www.fact-index.com/e/eu/euclidean_geometry.html
Main Page See live article Alphabetical index
##### 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 This system is an axiomatic system , which hoped to prove all the "true statements" as theorems in geometry from a set of finite number of axioms The five postulates/axioms of the Euclidean system are:
• Any two points can be joined by a straight line Any straight line segment can be extended indefinitely in a straight line. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. All right angles are congruent If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate
Euclidean geometry is distinguished from other geometries by the parallel postulate , which is more easily 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.

5. Euclidean Geometry - Simple English Wikipedia, The Free Encyclopedia
Euclidean geometry is a system in mathematics. People think Euclid was the first person who described it; therefore, it bears his name.
http://simple.wikipedia.org/wiki/Euclidean_geometry
##### Euclidean geometry
From Wikipedia, the free encyclopedia Jump to: navigation search Euclidean geometry is a system in mathematics . People think Euclid was the first person who described it; therefore, it bears his name. He first described it in his textbook Elements . The book was the first systematic discussion of geometry as it was known at the time. In the book, Euclid first assumes a few axioms . These form the base for later work. They are intuitively clear. Starting from those axioms, other theorems can be proven In the 19th century other forms of geometry were found. These are non-Euclidean. Carl Friedrich Gauss János Bolyai , and Nikolai Ivanovich Lobachevsky were some people that developed such geometries.
##### change The axioms
Euclid makes the following assumptions. These are axioms, and need not be proved.
• Any two points can be joined by a straight line Any straight line segment can be made longer (extended) to infinity, so it becomes a straight line. With a straight line segment it is possible to draw a circle, so that one endpoint of the segment is the center of the circle, and the other endpoint lies on the circle. The line segment becomes the radius of the circle. All right angles are congruent Parallel postulate . If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
• 6. Euclidean Geometry - Definition
In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. Mathematicians sometimes use the term to encompass
http://www.wordiq.com/definition/Euclidean_geometry
##### Euclidean geometry - Definition
In mathematics Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. Mathematicians sometimes use the term to encompass higher dimensional geometries with similar properties. Euclidean geometry sometimes means geometry in the plane which is also called plane geometry . Plane geometry is the topic of this article. Euclidean Geometry is also based off of the Point-Line-Plane postulate. Euclidean geometry in three dimensions is traditionally called solid geometry . For information on higher dimensions see Euclidean space Plane geometry is the kind of geometry usually taught in high school . Euclidean geometry is named after the Greek mathematician Euclid . Euclid's text Elements is an early systematic treatment of this kind of geometry Contents showTocToggle("show","hide") 1 Axiomatic approach
2 Modern introduction to Euclidean geometry

2.1 The construction

3 Classical theorems
...
##### Axiomatic approach
The traditional presentation of Euclidean geometry is as an axiomatic system , setting out to prove all the "true statements" as theorems in geometry from a set of finite number of axioms The five postulates of the Elements are:
• Any two points can be joined by a straight line Any straight line segment can be extended indefinitely in a straight line.
• 7. Mathwords: Euclidean Geometry
Jul 29, 2008 Note Euclidean geometry is named for Euclid, a Greek who lived 2500 years ago and wrote Elements, a book that has survived to the present
http://www.mathwords.com/e/euclidean_geometry.htm
 index: click on a letter A B C D ... A to Z index index: subject areas sets, logic, proofs geometry algebra trigonometry ... entries www.mathwords.com about mathwords website feedback Euclidean Geometry The main area of study in high school geometry . This is the geometry of axioms theorems , and two-column proofs. It includes the study of points lines triangles quadrilaterals , other polygons circles spheres prisms ... cylinders , etc. Note: Euclidean geometry is named for Euclid, a Greek who lived 2500 years ago and wrote Elements , a book that has survived to the present day as the standard source book for Euclidean geometry. See also Plane geometry solid geometry analytic geometry non-Euclidean geometry this page updated 29-jul-08 Mathwords: Terms and Formulas from Algebra I to Calculus written, illustrated, and webmastered by Bruce Simmons

8. Non-Euclidean Geometry References
A bibliographic reference list of books and articles on non-Euclidean geometries, part of the MacTutor History of Mathematics archive.
http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/References/Non-Euclid
##### References for: Non-Euclidean geometry
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• 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.
• 9. Non-Euclidean Geometry
The two most important types of nonEuclidean geometry are hyperbolic geometry and elliptical geometry. The different models of non-Euclidean geometry can
http://www.daviddarling.info/encyclopedia/N/non-Euclidean_geometry.html
 GEOMETRY SPACE AND TIME GRAVITATIONAL PHYSICS A ... CONTACT entire Web this site non-Euclidean geometry Any geometry in which Euclid's fifth postulate, the so-called parallel postulate , doesn't hold. (One way to say the parallel postulate is: Given a straight line and a point A not on that line, there is only one exactly straight line through A that never intersects the original line.) The two most important types of non-Euclidean geometry are hyperbolic geometry and elliptical geometry . The different models of non-Euclidean geometry can have positive or negative curvature . The sign of curvature of a surface is indicated by drawing a straight line on the surface and then drawing another straight line perpendicular to it: both these lines are geodesics . If the two lines curve in the same direction, the surface has a positive curvature; if they curve in opposite directions, the surface has negative curvature. Elliptical (and spherical) geometry has positive curvature whereas hyperbolic geometry has negative curvature. The discovery of non-Euclidean geometry had immense consequences. For more than 2,000 years, people had thought that

10. Non-Euclidean Geometry
A historical account with links to biographies of some of the people involved.
http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Non-Euclidean_geometr
##### Non-Euclidean geometry
Geometry and topology index History Topics Index
Version for printing
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. Proclus (410-485) wrote a commentary on The Elements where he comments on attempted proofs to deduce the fifth postulate from the other four, in particular he notes that
•  11. Euclidean_geometry Encyclopedia Topics | Reference.com Encyclopedia article of euclidean_geometry at Reference.com compiled from comprehensive and current sources.http://www.reference.com/browse/Euclidean_geometry

12. Topic:Euclidean Geometry - Wikiversity
Aug 18, 2010 Welcome to the Euclidean Geometry Learning Project, part of the School of Mathematics. The purposes of this learning project are to
http://en.wikiversity.org/wiki/Topic:Euclidean_geometry
##### 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

 13. Euclidean Geometry Euclidean Geometry from WN Network. WorldNews delivers latest Breaking news including World News, US, politics, business, entertainment, science,http://wn.com/euclidean_geometry

14. Euclidean Geometry: Facts, Discussion Forum, And Encyclopedia Article
Alexandria , with a population of 4.1 million, is the secondlargest city in Egypt, and is the country's largest seaport, serving about 80% of Egypt's imports and exports.
http://www.absoluteastronomy.com/topics/Euclidean_geometry
Home Discussion Topics Dictionary ... Login Euclidean geometry
##### Euclidean geometry
Overview Euclidean geometry is a mathematical system attributed to the Alexandria Alexandria Alexandria , with a population of 4.1 million, is the second-largest city in Egypt, and is the country's largest seaport, serving about 80% of Egypt's imports and exports. Alexandria is also an important tourist resort...
n Greek mathematician Greek mathematics Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 4th century AD around the Eastern shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to...
Euclid
Euclid Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry." He was active in Alexandria during the reign of Ptolemy I...
, whose Elements Euclid's Elements Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
is the earliest known systematic discussion of geometry Geometry Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....

15. Non-Euclidean Geometry - Wikipedia, The Free Encyclopedia
A nonEuclidean geometry is the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system, characterized by a non-vanishing Riemann
http://en.wikipedia.org/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 A non-Euclidean geometry is the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system, characterized by a non-vanishing Riemann curvature tensor . Examples of non-Euclidean geometries include the hyperbolic and elliptic geometry , which are contrasted with a Euclidean geometry The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid 's fifth postulate, the parallel postulate , is equivalent to Playfair's postulate , which states that, within a two-dimensional plane, for any given line and a point A , which is not on , there is exactly one line through A that does not intersect . In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting , while in elliptic geometry, any line through A intersects (see the entries on hyperbolic geometry elliptic geometry , and absolute geometry for more information).

 16. Euclidean Geometry Geometry of the type described originally by Euclid in his Elements (13 books written c.300 BC) and based on five axioms, one of which is the controversialhttp://www.daviddarling.info/encyclopedia/E/Euclidean_geometry.html

17. Euclidean Geometry
Euclidean geometry is a mathematical wellknown system attributed to the Greek mathematician Euclid of Alexandria. Euclid s text Elements was the first
http://www.sciencedaily.com/articles/e/euclidean_geometry.htm
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##### Euclidean geometry

 18. Euclidean Geometry In Encyclopedia Euclidean geometry in Encyclopedia in Encyclopediahttp://www.tutorgig.com/ed/Euclidean_geometry

19. Non-Euclidean Geometry
Saccheri then studied the hypothesis of the acute angle and derived many theorems of nonEuclidean geometry without realising what he was doing.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.ht
##### Non-Euclidean geometry
Geometry and topology index History Topics Index
Version for printing
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. Proclus (410-485) wrote a commentary on The Elements where he comments on attempted proofs to deduce the fifth postulate from the other four, in particular he notes that
• 20. Euclidean Geometry - Encyclopedia Article - Citizendium
Mar 18, 2010 Euclidean geometry is a form of geometry first codified by Euclid in his series of thirteen books, The Elements.
http://en.citizendium.org/wiki/Euclidean_geometry
##### From Citizendium, the Citizens' Compendium
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