Download or read book The Foundations of Geometry Works on Non Euclidean Geometry written by Nikolai I. Lobachevsky and published by . This book was released on 2019-10-02 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neither general relativity (which revealed that gravity is merely manifestation of the non-Euclidean geometry of spacetime) nor modern cosmology would have been possible without the almost simultaneous and independent discovery of non-Euclidean geometry in the 19th century by three great mathematicians - Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss (whose ideas were later further developed by Georg Friedrich Bernhard Riemann).This volume contains three works by Lobachevsky on the foundations of geometry and non-Euclidean geometry: "Geometry", "Geometrical investigations on the theory of parallel lines" and "Pangeometry". It will be of interest not only to experts and students in mathematics, physics, history and philosophy of science, but also to anyone who is not intimidated by the magnitude of one of the greatest discoveries of our civilization and would attempt to follow (and learn from) Lobachevsky's line of thought, helpfully illustrated by over 130 figures, that led him to the discovery.
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 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 A History of Non Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
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 Bibliography of Non Euclidean Geometry Including the Theory of Parallels the Foundations of Geometry and Space of N Dimensions written by Duncan M'Laren Young Sommerville and published by . This book was released on 1911 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 Non Euclidean Geometry written by Roberto Bonola and published by Courier Corporation. This book was released on 2012-08-15 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. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.
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 The Foundations of Geometry written by David Hilbert and published by Read Books Ltd. This book was released on 2015-05-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Download or read book Foundations of Euclidean and Non Euclidean Geometry written by Richard L. Faber and published by CRC Press. This book was released on 1983-01-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Mathematics written by Paul Carus and published by . This book was released on 1908 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Essay on the Foundations of Geometry written by Bertrand Russell and published by . This book was released on 1897 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Simple Non Euclidean Geometry and Its Physical Basis written by I.M. Yaglom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
Download or read book Bibliography of Non Euclidean Geometry written by Duncan M. Y. Sommerville and published by Forgotten Books. This book was released on 2017-11-21 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Bibliography of Non-Euclidean Geometry: Including the Theory of Parallels, the Foundations of Geometry, and Space of N Dimensions The classification is indicated in square brackets after the title. The names of journals are abbreviated according to the system adopted for the International Catalogue. Figures in heavy type are volume-numbers or years, the figures in brackets which sometimes precede these are the numbers of the series, the figures after the volume-numbers are the page-numbers. There are numerous references from one title to another which is closely connected with it. When the name of an author is in small capitals, simply followed by the date, as chasles, 1856, this indicates a reference to the Chronological Catalogue under the year and author mentioned. The sign indicates a reference to the Appendix, where some additional information is given which has been received too late for insertion without over-running of the pages. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
