Download or read book The Foundations of Geometry and the Non Euclidean Plane written by G.E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
Download or read book The Foundations of Geometry and the Non Euclidean Plane written by George Edward Martin and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Geometry and Non Euclidean Plane written by George E. Martin and published by . This book was released on 1972 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Geometry written by David Hilbert and published by . This book was released on 1902 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Plane Geometry written by Harvey I. Blau and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unified--yet straightforward and accessible --exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme--the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes--with a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topic--The axiomatic development of the absolute plane--which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the "gap" plane. Gradually presents axioms for absolute plane geometry.
Download or read book Euclidean Plane and Its Relatives written by Anton Petrunin and published by . This book was released on 2016-09-13 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book grew from my lecture notes. It is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.
Download or read book Foundations of Geometry written by C. R. Wylie and published by Courier Corporation. This book was released on 2009-05-21 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains geometric theories and shows many examples.
Download or read book Foundations of Euclidean and Non Euclidean Geometry written by Ellery B. Golos and published by . This book was released on 1968 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Geometry written by Clarence Raymond Wylie and published by . This book was released on 1964 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Geometry written by David Hilbert and published by Prabhat Prakashan. This book was released on 1950-01-01 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Geometry written by David Hilbert and published by . This book was released on 1910 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Euclidean Geometry written by Roberto Bonola and published by Courier Corporation. This book was released on 1955-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams.
Download or read book Euclidean and Non Euclidean Geometry International Student Edition written by Patrick J. Ryan and published by Cambridge University Press. This book was released on 2009-09-04 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Download or read book The Foundation of Geometry and the Non euclidean Plane written by George E. Martin and published by . This book was released on 1975 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Euclidean and Non euclidean Geometries written by Maria Helena Noronha and published by . This book was released on 2002 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a self-contained treatment of classical Euclidean geometry through both axiomatic and analytic methods. Concise and well organized, it prompts readers to prove a theorem yet provides them with a framework for doing so. Chapter topics cover neutral geometry, Euclidean plane geometry, geometric transformations, Euclidean 3-space, Euclidean n-space; perimeter, area and volume; spherical geometry; hyperbolic geometry; models for plane geometries; and the hyperbolic metric.
Download or read book The Elements of Non Euclidean Geometry written by Julian Lowell Coolidge and published by . This book was released on 1909 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundation of Euclidean and Non Euclidean Geometries according to F Klein written by L. Redei and published by Elsevier. This book was released on 2014-07-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.
