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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

Non-Euclidean Geometry - Mathematics And The Liberal Arts
A resource for student research projects and for teachers interested in using the history of mathematics Category Science Math Geometry Non-EuclideanNoneuclidean geometry - Mathematics and the Liberal Arts.
http://math.truman.edu/~thammond/history/NonEuclideanGeometry.html

Extractions: See the page The Parallel Postulate . To expand search, see Geometry . Laterally related topics: Symmetry Analytic Geometry Trigonometry Pattern ... Tilings , and The Square The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Make comment on this category Make comment on this project
Euclidean Geometry
euclidean geometry. euclidean geometry given line. The development of Euclideangeometry extends at least from 10,000 BC to the 20th century.
http://pratt.edu/~arch543p/help/euclidean_geometry.html

Extractions: Note: the following has been abstracted from the Grolier Encyclopedia. Euclidean geometry is the study of points, lines, planes, and other geometric figures, using a modified version of the assumptions of Euclid (c.300 BC). The most controversial assumption has been the parallel postulate: there is one and only one line that contains a given point and is parallel to a given line. The development of Euclidean geometry extends at least from 10,000 BC to the 20th century. In the 4th century BC, Plato founded an Academy in Athens, emphasized geometry, and used the five regular Polyhedrons in his explanation of the scientific phenomena of the universe. Aristotle, a student of Plato at the Academy, identified the rules for logical reasoning. The 13 books of Euclid's Elements are based on the mathematics that was considered at Plato's Academy. The geometry in the Elements was a logical system based on ten assumptions. Five of the assumptions were called common notions (Axioms, or self-evident truths), and the other five were postulates (required conditions). The resulting logical system was taken as a model for deductive reasoning and had a profound effect on all branches of knowledge. Although it has been necessary to refine the postulates as concepts of existence, continuity, order, and other aspects of Geometry have changed, the resulting geometry is still called Euclidean geometry. Modifications of Euclid's parallel postulate provide the basis for
Non-Euclidean Geometry
Noneuclidean geometry. Non-euclidean geometry refers to two geometrieshyperbolicgeometry and elliptic geometry. These geometries
http://pratt.edu/~arch543p/help/non-euclidean_geometry.html

Extractions: Note: the following has been abstracted from the Grolier Encyclopedia. Non-Euclidean Geometry The sum of the measures of the angles of a triangle is 180 deg in Euclidean Geometry , less than 180 deg in hyperbolic geometry, and more than 180 deg in elliptic geometry. The area of a triangle in hyperbolic geometry is proportional to the deficiency of its angle sum from 180 deg, while the area of a triangle in elliptic geometry is proportional to the excess of its angle sum over 180 deg. In Euclidean geometry all triangles have an angle sum of 180 deg irrespective of area. Thus, similar triangles with different areas can exist in Euclidean geometry. This kind of occurrence is not possible in hyperbolic or elliptic geometry. In two-dimensional geometries, lines that are perpendicular to the same given line are parallel in Euclidean geometry, are neither parallel nor intersecting in hyperbolic geometry, and intersect at the pole of the given line in elliptic geometry. The appearance of the lines as straight or curved depends on the postulates for the space. Euclid postponed the use of his parallel postulate as long as possible and probably was a bit uneasy about it. For the next 2,000 years numerous attempts were made to prove the statement as a theorem. Many of the attempts involved statements that are now recognized as equivalent to the parallel postulate. These statements include the following: (1) Parallel lines exist, and any two lines cut by a transversal are no more parallel on one side of the transversal than on the other side (2d century AD). (2) Parallel lines exist, and if a line intersects one of two parallel lines, it will intersect the other also (5th century). (3) The sum of the measures of the angles of any triangle is equal to a straight angle (13th century). (4) Given any triangle, a similar triangle of any size whatever may be constructed (17th century).
Euclidean Geometry
euclidean geometry. This site provides as motivational introduction to geometryin a form (Euclidean) which is more accessible than nonEuclidean geometries.
http://www.geom.umn.edu/~crobles/hyperbolic/eucl/

Extractions: Up: The Hyperbolic Geometry Exhibit This site provides as motivational introduction to geometry in a form (Euclidean) which is more accessible than non-Euclidean geometries. Here we will establish definitions and concepts that we can apply, via analogy, to our discussion of hyperbolic geometry. This overview includes: Isometries as products of reflections Table of Contents Up: The Hyperbolic Geometry Exhibit
Non-Euclidean Geometry
Noneuclidean geometry. Mathematicians Many manifolds are naturally suitedfor hyperbolic or spherical, rather than Euclidean, geometry. Although
http://www.geom.umn.edu/docs/research/ieee94/node12.html

Extractions: Next: Minimal Surfaces Up: Manifolds Previous: Viewing with 4D Mathematicians in the nineteenth century showed that it was possible to create consistent geometries in which Euclid's Parallel Postulate was no longer true- Absence of parallels leads to spherical, or elliptic, geometry; abundance of parallels leads to hyperbolic geometry. By mid-century the English mathematician Arthur Cayley had constructed analytic models of these three geometries that had a common descent from projective geometry, which one may think of as the formalization of the renaissance theory of perspective. Cayley's construction is in fact ideal for programming interactive navigations of nonEuclidean geometries Many manifolds are naturally suited for hyperbolic or spherical, rather than Euclidean, geometry. Although the formulas for computing distance and angles in these geometries differ from Euclidean geometry, they can be built into mathematical visualization systems by hand. Translations, rotations, and dot-products for shaders and illumination must also be handled differently in the non-Euclidean geometries. In Figure , we see a partial tessellation of regular right-angled dodecahedra in the three built-in Geomview models of hyperbolic 3-space. In the virtual model shown in Figure
NonEuclid - Hyperbolic Geometry Article & Applet
Plane. Basic Concepts What is Noneuclidean geometry - EuclideanGeometry, Spherical Geometry, Hyperbolic Geometry, and others.
http://www.cs.unm.edu/~joel/NonEuclid/
NonEuclid: Non-Euclidean Geometery
NonEuclid What is Noneuclidean geometry. 1.1 euclidean geometry he Geometrywith which we are most familiar is called euclidean geometry.
http://www.cs.unm.edu/~joel/NonEuclid/noneuclidean.html

Extractions: he Geometry with which we are most familiar is called Euclidean Geometry. Euclidean Geometry was named after Euclid, a Greek mathematician who lived in 300 BC. His book, called "The Elements", is a collection of axioms, theorems and proofs about squares, circles acute angles, isosceles triangles, and other such things. Most of the theorems which are taught in high schools today can be found in Euclid's 2000 year old book. Euclidean Geometry was of great practical value to the ancient Greeks as they used it (and we still use it today) to design buildings and survey land. non-Euclidean Geometry is any geometry that is different from Euclidean Geometry. One of the most useful non-Euclidean geometries is Spherical Geometry which describes the surface of a sphere. Spherical Geometry is used by pilots and ship captains as they navigate around the world. Working in Spherical Geometry has some non intuitive results. For example, did you know that the shortest flying distance from Florida to the Philippine Islands is a path across Alaska? The Philippines are South of Florida - why is flying North to Alaska a short-cut? The answer is that Florida, Alaska, and the Philippines are collinear locations in Spherical Geometry (they lie on a "Great Circle"). Another odd property of Spherical Geometry is that
Non-Euclidean Geometry
Resources in non-euclidean geometry.Category Science Math Geometry Non-EuclideanNoneuclidean geometry Taxicab Geometry This site is an introductionto non-euclidean geometry with real world examples. http//www2
http://westford.mec.edu/schools/tips/noneucld.html
Non-Euclidean Geometry -- From MathWorld
Noneuclidean geometry, It was not until 1868 that Beltrami proved that non-Euclideangeometries were as logically consistent as euclidean geometry.
http://mathworld.wolfram.com/Non-EuclideanGeometry.html

Extractions: In three dimensions, there are three classes of constant curvature geometries . All are based on the first four of Euclid's postulates , but each uses its own version of the parallel postulate . The "flat" geometry of everyday intuition is called Euclidean geometry (or parabolic geometry ), and the non-Euclidean geometries are called hyperbolic geometry (or Lobachevsky-Bolyai-Gauss geometry ) and elliptic geometry (or Riemannian geometry). Spherical geometry is a non-Euclidean two-dimensional geometry. It was not until 1868 that Beltrami proved that non-Euclidean geometries were as logically consistent as Euclidean geometry Absolute Geometry Elliptic Geometry Euclid's Postulates ... Spherical Geometry References . "Welcome to the Non-Euclidean Geometry Homepage." http://members.tripod.com/~noneuclidean/ Bolyai, J. "Scientiam spatii absolute veritam exhibens: a veritate aut falsitate Axiomatis XI Euclidei (a priori haud unquam decidenda) indepentem: adjecta ad casum falsitatis, quadratura circuli geometrica." Reprinted as "The Science of Absolute Space" in Bonola, R. Non-Euclidean Geometry, and The Theory of Parallels by Nikolas Lobachevski, with a Supplement Containing The Science of Absolute Space by John Bolyai.
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: 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 ... Plane Geometry References 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. Geometry Revisited. Washington, DC: Math. Assoc. Amer., 1967 Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, 1969. Gallatly, W. The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, 1913. Greenberg, M. J. Euclidean and Non-Euclidean Geometries: Development and History, 3rd ed.
What Is Non-Euclidean Geometry?
What is noneuclidean geometry? Euclid's geometrical full terms. Reviewthe full terms by clicking here. non euclidean geometry what is.
http://njnj.essortment.com/noneuclideange_risc.htm

Extractions: What is non-Euclidean geometry? 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.
The Math Forum - Math Library - Non-Euclidean Geom.
This page contains sites relating to Noneuclidean geometry. KSEG - Ilya BaranKSEG is a Linux program for dynamically exploring euclidean geometry.
http://mathforum.org/library/topics/noneuclid_g/
Math Forum - Ask Dr. Math Archives: High School Non-Euclidean Geometry
Browse High School Noneuclidean geometry. Stars indicate Non-EuclideanGeometry 10/22/2001 What is non-euclidean geometry? What two
http://mathforum.org/library/drmath/sets/high_non_euclid.html
Euclidean Geometry
Similar pages euclidean geometry WikipediaOther languages Deutsch. euclidean geometry. From Wikipedia, the free encyclopedia.euclidean geometry is the geometry described by Euclid in the Elements.
http://whyslopes.com/etc/ComplexNumbers/videosEuclideanGeometryEtc.html

Extractions: Site Areas: Volume 1, Elements of Reason Volume 1A, Pattern Based Reason Volume 1B, Mathematics Curriculum Notes Volume 2, Three Skills For Algebra Volume 3, Why Slopes and More Math 4 Lecons (Mathematiques et Logique) Complex Numbers Revisited Help Your Child Learn LaTeX2HotEqn Automation Order above Volumes via DoubleHook Book Store Order Volumes via PayPal (Credit Card) Order Volumes via OrderForm (Check/Money Order) Order Volumes (or contact author) via Email D9 3rd Distributive Law D1 to D6 give an easy intro to vectors. From Euclidean Geometry to Vectors and Complex Numbers These videos give a derivation of the properties of complex numbers from Euclidean Geometry instead of Algebra. The text version of this derivation does exist. But the local references describe the main ideas.
Non-Euclidean Geometry - Wikipedia
Noneuclidean geometry. (Redirected from Non-euclidean geometry). Non Thefifth postulate produced the familiar euclidean geometry. Its
http://www.wikipedia.org/wiki/Non-euclidean_geometry

Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help (Redirected from Non-euclidean geometry Non-Euclidean geometries are those geometries obtained by relaxing 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. This is not the way in which Euclid originally defined his fifth postulate, but it is equivalent to his definition. In fact, geometers were troubled by the disparate complexity of the fifth postulate, and thought that it could perhaps be proved as a theorem from the other four. One attempt to prove that the fifth postulate was in fact a theorem was to assume its inverse, and derive a logical fallacy from it. This exercise did just the opposite of its goal: rather than prove that the fifth postulate was provable from the other four, it proved that you could assume either the fifth postulate or its inverse, and either assumption would produce a complete, self-consistent geometry. The fifth postulate produced the familiar Euclidean geometry. Its converse produced non-euclidean geometries.
Question Corner -- Non-Euclidean Geometry
Question Corner and Discussion Area. Noneuclidean geometry. Being as curiousas 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
Question Corner -- Euclidean Geometry In Higher Dimensions
euclidean geometry in Higher Dimensions. euclidean geometry in higherdimensions is best understood in terms of coordinates and vectors.
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.
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.
COMPUTING IN EUCLIDEAN GEOMETRY
1 COMPUTING IN euclidean geometry edited by DingZhu Du (University of Minnesota) Frank Hwang (AT T Bell Laboratories) This book is a collection of surveys
http://www.wspc.com/books/compsci/1657.html

Extractions: This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a 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. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.
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!)

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