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Euclidean Geometry:     more books (100)

Foundations of Three-dimensional Euclidean Geometry (Pure and Applied Mathematics) by I. Vaisman, 1980-08-01 Non-Euclidean Geometry: A Critical and Historical Study of its Development by Roberto Bonola, Nicholas Lobachevski, et all 2010-11-18 Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space by Jeremy J. Gray, 2004-06-01 Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause, 1987-01-01 Advanced Euclidean Geometry (Dover Books on Mathematics) by Roger A. Johnson, 2007-08-31 Geometry, Relativity and the Fourth Dimension by Rudolf v.B. Rucker, 1977-06-01 Problems and Solutions in Euclidean Geometry (Dover Books on Mathematics) by M. N. Aref, William Wernick, 2010-04-21 Advanced Euclidean Geometry by Alfred S. Posamentier, 2002-07-12 The Foundations of Geometry and the Non-Euclidean Plane by G.E. Martin, 1982-03-22 Plane and Solid Geometry (Universitext) by J.M. Aarts, 2008-10-08 Non-Euclidean Geometries: János Bolyai Memorial Volume (Mathematics and Its Applications) The Elements of Non-Euclidean Geometry (Classic Reprint) by Duncan M'Laren Young Sommerville, 2010-09-07 Elementary Differential Geometry (Springer Undergraduate Mathematics Series) by A.N. Pressley, 2010-03-18 Introductory Non-Euclidean Geometry by Henry Parker Manning, 2005-02-18

lists with details

21. Introduction To The Works Of Euclid
    Covers the life of Euclid and a discussion of euclidean geometry.  
    http://www.obkb.com/dcljr/euclid.html
    
    Extractions: (first posted to the web in 1995) jump to: outline of paper text of paper suggestions for further study bibliography ... anchor here Bibliography This is a paper I wrote in college for a History of Science course (although I've taken the liberty of modifying it slightly from time to time since I put it online). I know it's not publishable or anything, but it's still one of my favorite papers because it was so difficult to do. (I wrote it on a computer with about 12K of free RAM and only a cassette tape drive for storage!) In fact, the whole History of Science course was quite an experience. Students wishing to use this paper for their own reports on Euclid should know how to avoid plagiarism and how to cite online sources . In addition, I urge students to seek out the original printed sources yes, that means going to the library and not rely merely on what I say in this paper. (I'm always surprised by the number of junior high and high school students who e-mail me saying they can't find any information about Euclid!) Note that is used to denote square roots and all Greek letters used as symbols ( alpha beta , ...) are spelled out. Superscripts are implemented by using the appropriate HTML tags and may not display properly in some browsers. In this case, hopefully the meaning will be clear from the context.

22. Euclidean Geometry -- From MathWorld
    euclidean geometry. Twodimensional euclidean geometry is called plane geometry, and three-dimensional euclidean geometry is called solid geometry.  
    http://mathworld.wolfram.com/EuclideanGeometry.html
    
    Extractions: Euclidean Geometry A geometry in which Euclid's fifth postulate holds, sometimes also called parabolic geometry . Two-dimensional Euclidean geometry is called plane geometry , and three-dimensional Euclidean geometry is called solid geometry Hilbert proved the consistency of Euclidean geometry. Elements Elliptic Geometry Geometric Construction Geometry ... search Altshiller-Court, N. College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed., rev. enl. New York: Barnes and Noble, 1952. Casey, J. A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions with Numerous Examples, 2nd rev. enl. ed. Coxeter, H. S. M. and Greitzer, S. L.

23. Klein, Felix (1849-1925) -- From Eric Weisstein's World Of Scientific Biography
    Pl¼cker's assistant at Bonn who studied Analytic Geometry, describing geometry as the study of properties of figures which remain invariant under a Group of Transformations. He systemized Noneuclidean geometry.  
    http://www.treasure-troves.com/bios/KleinFelix.html
    
    Extractions: German mathematician who began his career as assistant at Bonn. Klein studied analytic geometry describing geometry as the study of properties of figures which remain invariant under a group of transformations He systemized non-Euclidean geometry and wrote a book on the icosahedron in 1884. He also worked on the development of group theory and collaborated with Lie in Erlanger Programm. He also is known in topology for the one-sided Klein bottle In addition to all his other work, he found time to write a classic history of mathematics. References Fricke, R. and Klein, F. Leipzig: B. G. Teubner, 1897-1912. Klein, F. Arithmetic, Algebra, Analysis. New York: Dover, N.D. Klein, F. Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis. New York: Dover. Klein, F. Famous Problems of Elementary Geometry. New York: Chelsea, 1956. Klein, F. Gesammelte Mathematische Abhandlungen. Berlin: Springer-Verlag, 1973.

24. Geometry From The Land Of The Incas
    Geometry from the land of the Incas This Internet site aims to interest students in euclidean geometry by offering a mix of Incan history with illustrated, animated stepby-step proofs of not  
    http://rdre1.inktomi.com/click?u=http://agutie.homestead.com/files/index.html&am

25. Discussion
    Noneuclidean geometry. This tutorial consists of html constructed constructed applet which demonstrates it visually. Development of euclidean geometry.  
    http://cvu.strath.ac.uk/courseware/msc/jgraves/
    
    Extractions: This tutorial consists of html constructed pages which explain non-Euclidean geometry, and a JAVA constructed applet which demonstrates it visually basic geometry ), and the more complicated ones which relied on axiom 5 in their proof ( Euclidean geometry Many mathematicians after Euclid (and even Euclid himself) where not comfortable with axiom five, it is quite a complicated statement and axioms are meant to be small, simple and straightforward. Axiom five is more like a theorem than an axiom, and as such it should have to be proved to be true and not assumed. The problem that Euclid and every mathematician after him found for 200 years was that it could not be proven from the 4 axioms before it. However, all the theorems that can be proved from it worked and many mathematicians were happy just to leave it. It is something that seems obviously true and yet was impossible to prove mathematically in a satisfactory way. Hyperbolic geometry is hard to describe. Its basic premise, that there can be multiple parallel lines through a point, is itself very hard to accept. In purely mathematical terms it is not so difficult. It consists of all Euclid's theorems that can be proved from the first four axioms (

26. Euclidean Geometry - Wikipedia, The Free Encyclopedia
    euclidean geometry. From Wikipedia, the free encyclopedia. In mathematics Modern Introduction to euclidean geometry. Today Euclidean  
    http://en.wikipedia.org/wiki/Euclidean_geometry
    
    Extractions: 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 usually refers to geometry in the plane which is also called plane geometry . It is plane geometry which is the topic of this article. 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 Table of contents 1 Axiomatic approach 2 Modern introduction to Euclidean geometry 2.1 The construction 3 Classical theorems ... edit 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.

27. 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
    
    Extractions: 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

28. Non-Euclidean Geometry - Wikipedia, The Free Encyclopedia
    Noneuclidean geometry. (Redirected from Non-euclidean geometry). External link. MacTutor Archive article on non-euclidean geometry. See also.  
    http://en.wikipedia.org/wiki/Non-euclidean_geometry
    
    Extractions: 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.

29. 51M05: General Euclidean Geometry
    Introduction. We use this category to hold files concerning nonplanar euclidean geometry topics. The files on this page are more  
    http://www.math.niu.edu/~rusin/known-math/index/51M05.html
    
    Extractions: POINTERS: Texts Software Web links Selected topics here We use this category to hold files concerning non-planar Euclidean geometry topics. The files on this page are more like samples of the techniques one may use for 3D problems (or n-dimensional: much of what is here is really independent of the number of dimensions.) The actions of the point groups among the crystallographic groups are the basis for the construction of the Platonic solids and the regular divisions of the sphere in R^3. For more information, consult the polyhedra and spheres pages. Parent field: 51M - Real and Complex Geometry For computational geometry see 68U05: Computer Graphics Pointer to Mesa , a 3-D graphics library (similar to OpenGL). A FAQ: Shortest distance between two lines in 3-dimensional space.

30. Non-Euclidean Geometry
    Resources in noneuclidean geometry.  
    http://www.westford.mec.edu/schools/tips/noneucld.html

31. 51M04: Elementary Euclidean Geometry (2-dimensional)
    links Selected topics here 51M04 Elementary euclidean geometry (2dimensional). Introduction. Ordinary plane geometry (such  
    http://www.math.niu.edu/~rusin/known-math/index/51M04.html
    
    Extractions: POINTERS: Texts Software Web links Selected topics here Ordinary plane geometry (such as is studied in US secondary schools) holds an irresistible appeal, although many results derive what appear to be unimaginative conclusions from tortured premises. Nonetheless, from time to time something catches our eye and gets us to think about ordinary triangles and circles. Constructibility with compass and straightedge is dealt with elsewhere Tilings and packings in the plane are part of Convex Geometry Many topics regarding polygons (e.g. decompositions into triangles and so on) are treated as part of polyhedral geometry Parent field: 51M - Real and Complex Geometry A compendium of plane curves For computational geometry see 68U05: Computer Graphics The Geometry Junkyard has a "pile" for planar geometry (and other related topics of interest!)

32. References For Non-Euclidean Geometry
    A bibliographic reference list of books and articles on nonEuclidean geometries.  
    http://www-groups.cs.st-and.ac.uk/~history/HistTopics/References/Non-Euclidean_g

33. What Is Non-Euclidean Geometry?
    What is noneuclidean geometry? Consequently, in a euclidean geometry every point has one and only one line parallel to any given line.  
    http://njnj.essortment.com/noneuclideange_risc.htm
    
    Extractions: What is non-Euclidean geometry? An introduction to the history and mathematics of non-Euclidean geometries. Euclid's geometrical thesis, "The Elements" (c. 300 B.C.E), proposed five basic postulates of geometry. Of these postulates, all were considered self-evident except for the fifth postulate. The fifth postulate asserted that two lines are parallel (i.e. non-intersecting) if a third line can intersect both lines perpendicularly. Consequently, in a Euclidean geometry every point has one and only one line parallel to any given line. For centuries people questioned Euclid's fifth postulate. Even Euclid seemed suspicious of the fifth postulate because he avoided solving problems with it until his 29th example. Mathematicians stumbled with ways to prove the validity of the fifth postulate from the first four postulates, which we now call the postulates of absolute geometry. Those mathematicians who didn't fail were soon seen to have fallacious errors in their reasoning. These errors usually occurred because a mathematician had made self-fulfilling assumptions pertaining to parallel lines, rather than working with the other postulates. Essentially, they were forcing a result through the application of faulty logic. bodyOffer(29808) Though many mathematicians questioned Euclidean geometry, Euclidean thought prevailed through school mathematical programs. "The Elements" became the most widely purchased non-religious work in the world, and it still remains the most widely received of mathematical texts. Furthermore, mathematical inquiries into the nature of non-Euclidean geometries were often devalued as frivolous. The philosopher Immanuel Kant (1724-1804) called Euclid's geometry, "the inevitable necessity of thought." Such philosophical opinions impeded mathematical progress in the field of geometry. Karl Friedrich Gauss (1777-1855), who began studying non-Euclidean geometries at the age of 15, never published any of his non-Euclidean works because he knew the mathematical precedent was against him.

34. COMPUTING IN EUCLIDEAN GEOMETRY
    Lecture Notes Series on Computing Vol. 4 COMPUTING IN euclidean geometry (2nd Edition) edited by Ding-Zhu Du (Univ. Minnesota Inst.  
    http://www.wspc.com/books/compsci/2463.html
    
    Extractions: This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.

35. Non-Euclidean Geometries, Models
    NonEuclidean Geometries As Good As Might Be. From our perspective, the situation was exactly the same as with euclidean geometry.  
    http://www.cut-the-knot.org/triangle/pythpar/Model.shtml
    
    Extractions: As Good As Might Be In 1823, Janos Bolyai wrote to his father: "Out of nothing I have created a new universe." By which he meant that starting from the first 4 of Euclid's postulates and a modified fifth, he developed an expansive theory that, although quite unusual, did not seem to lead to any logical contradiction. Gauss expressed his conviction in consistency of the theory he had in mind in a letter in 1824. However, hesitant of the public reaction to the idea that, by the side of Euclidean, there is another geometry, he never published anything on the subject. From our perspective, the situation was exactly the same as with Euclidean geometry. Euclid built an axiomatic theory by deriving a lot of theorems from his five postulates. No one had ever proved that continuing in Euclid's footstep would not lead to a contradiction. However, a 2000 year history elevated Elements on a pedestal of infallibility. Kant even stipulated that the universe had been built according to Euclid. Lobachevsky was quite aware of the problem and in later publications tried without success to redefine the notions of line and plane. A breakthrough came in 1868 with the publication of Saggio di interpretazoine della geometria non euclidea by the Italian mathematician Eugenio Beltrami (1835-1900). Beltrami discovered that Lobachevsky's geometry admits an interpretation in terms of Euclidean geometry. From here it follows that if Lobachevsky's geometry leads to a contradiction, Euclidean geometry is as well contradictory. In other words, consistency of Euclidean geometry implies consistency of the geometry of Lobachevsky. The construction is now known as Beltrami-Klein model of Lobachevsky geometry. Sometimes it's called the

36. Non-Euclidean Geometry
    Noneuclidean geometry Taxicab Geometry This site is an introduction to non-euclidean geometry with real world examples. http//www2  
    http://westford.mec.edu/schools/tips/noneucld.html

37. Question Corner -- Euclidean Geometry In Higher Dimensions
    euclidean geometry in Higher Dimensions. I would like to know where I can find out a little more than high school maths on euclidean geometry.  
    http://www.math.toronto.edu/mathnet/questionCorner/eucgeom.html
    
    Extractions: Question Corner and Discussion Area Asked by Victor Humberstone on February 10, 1997 I would like to know where I can find out a little more than high school maths on Euclidean Geometry. In particular, I would like to understand n -dimensional symmetrical `solids' (esp 4, 5 dimensions.) My son has recently been asking about a drawing of a `hypercube' (a 4-D cube) in an old book by George Gamov in which such an object was drawn and wants to understand how to extend the concept. I can't help! Can you help me to help him? Euclidean Geometry in higher dimensions is best understood in terms of coordinates and vectors. In fact, it is these which even give meaning to geometric concepts in higher dimensions. So, let me start with a quick overview of those (which you, as a physics graduate, will know anyway and may want to skip, but others reading the page may not): In 3 dimensions, we all have an intuitive understanding of what length and angle mean, and it is not at all clear how to extend these concepts to higher dimensions.

38. Question Corner -- Non-Euclidean Geometry
    Noneuclidean geometry. Asked by Brent Potteiger on April 5, 1997 Being as curious as I am, I would like to know about non-euclidean geometry. Thanks!!!  
    http://www.math.toronto.edu/mathnet/questionCorner/noneucgeom.html
    
    Extractions: Question Corner and Discussion Area Asked by Brent Potteiger on April 5, 1997 I have recently been studying Euclid (the "father" of geometry), and was amazed to find out about the existence of a non-Euclidean geometry. Being as curious as I am, I would like to know about non-Euclidean geometry. Thanks!!! All of Euclidean geometry can be deduced from just a few properties (called "axioms") of points and lines. With one exception (which I will describe below), these properties are all very basic and self-evident things like "for every pair of distinct points, there is exactly one line containing both of them". This approach doesn't require you to get into a philosophical definition of what a "point" or a "line" actually is. You could attach those labels to any concepts you like, and as long as those concepts satisfy the axioms, then all of the theorems of geometry are guaranteed to be true (because the theorems are deducible purely from the axioms without requiring any further knowledge of what "point" or "line" means). Although most of the axioms are extremely basic and self-evident, one is less so. It says (roughly) that if you draw two lines each at ninety degrees to a third line, then those two lines are parallel and never intersect. This statement, called

39. Key Curriculum Press | Advanced Euclidean Geometry
    Supplementals Advanced euclidean geometry. Advanced euclidean geometry Excursions for Secondary Teachers and Students. Alfred S  
    http://www.keypress.com/catalog/products/supplementals/Prod_AdvancedEuclidean.ht
    
    Extractions: Supplementals Advanced Euclidean Geometry Advanced Euclidean Geometry provides a thorough review of the essentials of the high school geometry course and then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created with software and includes a Windows/Macintosh CD-ROM containing over 100 interactive sketches. User must have access to Advanced Euclidean Geometry

40. Read This: Non-Euclidean Geometry
    Read This! The MAA Online book review column review of Non-euclidean geometry, by HSM Coxeter. Read This! Non-euclidean geometry by HSM Coxeter.  
    http://www.maa.org/reviews/coxeterneg.html
    
    Extractions: by H. S. M. Coxeter Coxeter's Non-Euclidean Geometry begins with a wonderful historical overview of the development of non-Euclidean geometry in the first chapter. Only a few proofs are given or sketched in this chapter. They flow with the prose and play an integral part in the understanding of the beginnings of hyperbolic, spherical, elliptic and differential geometry, among others. The mathematician, as well as the non-mathematician, is able to gain insights into these various types of geometry by the end of this chapter. For the remainder of the book, the historical aspects are never far from the mathematics. Many chapters begin with an introduction which puts the contents of the chapter into historical perspective. Coxeter uses comparisons, especially to Euclidean geometry, to aid in the understanding of other geometries. An example is found in chapter 8 where descriptive geometry (described as "high school geometry with congruence and parallelism left out") is compared to projective geometry. Coxeter takes us through the developments of real projective geometry, elliptic geometry in one, two and three dimensions, descriptive geometry and hyperbolic geometry in one and two dimensions. Though he introduces the elliptic metric "by means of absolute polarity" and could have introduced the hyperbolic metric in a similar fashion, he chose to "reverse the process" in order to "follow the historical development more closely". This not only gives the reader a different perspective, but once again reminds us of the historical perspective.

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