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21. Euclidean Geometry
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
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A representation of Euclid from The School of Athens by Raphael Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of 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 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. For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. It also is no longer taken for granted that Euclidean geometry describes physical space. An implication of

22. Models/Non-Euclidean_Geometry - Electronic Geometry Models
models//Noneuclidean_geometry ..
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 models//Non-Euclidean_Geometry

23. Database Error - Free Net Encyclopedia
ImageEuklid2.jpg. Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic
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 24. Non-Euclidean Geometry - Geometry - Math Dictionary A NonEuclidean Geometry is a branch of geometry which does not hold parallel postulate. The Non-Euclidean Geometry generally deals in hyperbolic geometryhttp://www.icoachmath.com/Sitemap/Non-Euclidean_Geometry.html

25. Non-Euclidean Geometry - Wiktionary
Sep 27, 2010 (geometry) Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the threedimensional space of
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non-Euclidean geometry
Definition from Wiktionary, the free dictionary Jump to: navigation search Wikipedia has an article on: Non-Euclidean geometry Wikipedia
Contents

26. Wapedia - Wiki: Euclidean Geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, whose Elements is the earliest known systematic
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 Wiki: Euclidean geometry Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid , whose Elements is the earliest known systematic discussion of geometry axioms , and deducing many other propositions theorems Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system The Elements begins with plane geometry , still taught in secondary school as the first axiomatic system and the first examples of formal proof . It goes on to the solid geometry of three dimensions . Much of the Elements states results of what are now called algebra and number theory , couched in geometrical language. A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of

 27. What Does Euclidean Geometry Mean? Definition And Meaning (Free English Language Definition of Euclidean geometry in the AudioEnglish.net Dictionary. Meaning of Euclidean geometry. What does Euclidean geometry mean?http://www.audioenglish.net/dictionary/euclidean_geometry.htm

28. Euclidean Geometry - Mathematics
Euclidean geometry is a type of geometry that most people assume when they think of geometry. It has its origins in ancient Greece, under the early geometer and mathematician Euclid
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Euclidean geometry
Edit Euclidean geometry is a type of geometry that most people assume when they think of geometry. It has its origins in ancient Greece, under the early geometer and mathematician Euclid. Euclidean geometry is, simply put, the geometry of Euclidean Space . Euclidean space, and Euclidean geometry by extension, is assumed to be flat and non-curved. Shapes on a piece of paper, for example, such as in a high school geometry course, is and example of two-dimensional Euclidean geometry, or in other words geometry in two-dimensional Euclidean space. The shapes themselves may be curved, both in terms of its edges and its faces and such; the shape itself may curve through space. But what distinguishes Euclidean space is the fact that the space itself does not curve. In the two-dimensional example of a piece of paper, the space itself is the piece of paper (not the shapes on them), and is Euclidean if on a flat desktop; the space becomes non-Euclidean when the piece of paper is bent or curved or folded in on itself. Euclidean space and its geometries can extend into three-dimensions (solid shapes such as polyhedrons ), four-dimensions, and beyond with no limit (hyper-solids such as arbitrary

 29. Euclidean Geometry Summary | BookRags.com Euclidean geometry. Euclidean geometry summary with 12 pages of encyclopedia entries, research information, and more.http://www.bookrags.com/wiki/Euclidean_geometry

30. * Euclidean Geometry - (GIS): Definition
Euclidean Geometry TopicGIS - Online Encyclopedia.
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Euclidean Geometry
InitAdv(0) Euclidean geometry has become closely connected with computational geometry computer graphics , convex geometry , discrete geometry , and some areas of combinatorics.
InitAdv(1) In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space
Contents
1 Types of triangles ...
InitAdv(2) The Cartesian co-ordinate system and the system of latitude and longitude of the earth are examples of coordinate system s based upon Euclidean geometry
InitAdv(3) 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(4) 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(5) Flat space has minimal (zero) curvature and obeys the precepts of Euclidean geometry . In flat space

31. 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.
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Non-Euclidean geometry
Geometry and topology index History Topics Index
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
• 32. Euclidean Geometry - Wiktionary
The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line
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Euclidean geometry
Definition from Wiktionary, the free dictionary Jump to: navigation search Wikipedia has an article on: Euclidean geometry Wikipedia
Contents

33. Introduction To Non-Euclidean Geometry - EscherMath
Mar 22, 2007 So far we have looked at what is commonly called Euclidean geometry. There are occasions where this type of geometry doesn t get one very
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From EscherMath
Jump to: navigation search So far we have looked at what is commonly called Euclidean geometry. There are occasions where this type of geometry doesn’t get one very far. Suppose we look at this sphere and want to measure the distance between the centers of two 5-pointed stars. You can’t just use a ruler, because you can’t put the ruler flat on the sphere to measure the length. If measuring length is already tricky, how would you find area?
Famous Early Geometers
• Pythagoras (ca. 540 BC) Showed that in a right triangle the sum of the squares of the sides equals the square of the hypotenuse. Plato (ca 380 BC) Laid the basis for formal geometry. His name is associated with the Platonic solids. Above the entrance to his school of Philosophy (the Academy) was engraved : “Let no one ignorant of geometry enter my doors” Aristotle (ca 340 BC) The tutor of Alexander the Great, also trained many of the great geometers of the time. Euclid (ca 300 BC) The first to write down the postulates for what is now known as Euclidean geometry. He was associated with the famous School of Alexandria. Archimedes (ca 225 BC) Pliny called him “the God of Mathematics”. He was also associated with the School of Alexandria. His name is now associated with the Archimedean solids. He was killed during the Siege of Syracuse. He was so immersed in his math that he supposedly did not notice the city being taken over by the Romans.
• 34. Non-Euclidean Geometry
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
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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
•  35. Answers.com - What Is The Difference Between Euclidean Geometry And Non-Euclidea Geometry question What is the difference between Euclidean Geometry and non Euclidean Geometry? In Euclidean geometry parallel lines are always the samehttp://wiki.answers.com/Q/What_is_the_difference_between_Euclidean_Geometry_and_

 36. Triangle Inequality : Euclidean Geometry Triangle inequality Euclidean Geometry images, discuss, define, news.http://www.servinghistory.com/topics/triangle_inequality::sub::Euclidean_Geometr

37. Kids.Net.Au - Encyclopedia > Euclidean Geometry
Kids.Net.Au is a search engine / portal for kids, children, parents, and teachers. The site offers a directory of child / kids safe websites, encyclopedia, dictionary
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Encyclopedia > Euclidean geometry
Article Content
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

38. "Non-euclidean Geometry" Related Terms, Short Phrases And Links
May 28, 2008 Noneuclidean Geometry - related terms, definitions and short phrases grouped together in the form of Encyclopedia article.
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Enter your search terms Submit search form Web keywen.com Non-Euclidean geometry History
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Review of Short Phrases and Links
This Review contains major "Non-euclidean Geometry"- related terms, short phrases and links grouped together in the form of Encyclopedia article. InitGlob('NON-EUCLIDEAN_GEOMETRY');
Definitions UpDw('Definitions','-Abz-');
• Non-Euclidean geometry was no more than a mathematical curiosity until Einstein applied it to physics. (Web site) UpDw('Definitions','c368283'); Non-Euclidean geometry is a type of geometry that is not based off the "postulates" (assumptions) that normal geometry is based off. UpDw('Definitions','b5dc72d'); Non-Euclidean geometry is a system built on not accepting this axiom as true. (Web site) UpDw('Definitions','4d6b0ba'); A non-Euclidean geometry is any geometry that contrasts the fundamental ideas of Euclidean geometry , especially with the nature of parallel lines. UpDw('Definitions','b94293e');
• 39. � Euclidean Geometry Specs �";
Euclidean geometry history by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandria n Greek mathematician Euclid, whose Elements is the earliest