[PDF] A Simple Non Euclidean Geometry And Its Physical Basis eBook

Author : I.M. Yaglom
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 37,87 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146126135X

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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.

Author : Marina Gavrilova
Publisher : Springer Science & Business Media
Page : 1272 pages
File Size : 18,26 MB
Release : 2006
Category : Computers
ISBN : 354034070X

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The five-volume set LNCS 3980-3984 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2006, held in Glasgow, UK in May 2006.The five volumes present a total of 664 papers selected from over 2300 submissions. The papers present a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the refereed papers are structured according to the five major conference themes: computational methods, algorithms and applications high performance technical computing and networks advanced and emerging applications geometric modelling, graphics and visualization information systems and information technologies.Moreover, submissions from 31 Workshops and technical sessions in the areas, such as information security, mobile communication, grid computing, modeling, optimization, computational geometry, virtual reality, symbolic computations, molecular structures, Web systems and intelligence, spatial analysis, bioinformatics and geocomputations, contribute to this publication.

Author : Harold E. Wolfe
Publisher : Courier Corporation
Page : 274 pages
File Size : 12,29 MB
Release : 2012-01-01
Category : Mathematics
ISBN : 0486498506

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One of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition

Author : Leo Dorst
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 26,15 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146120089X

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Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Author : Boris A. Rosenfeld
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 43,67 MB
Release : 2012-09-08
Category : Mathematics
ISBN : 1441986804

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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.

Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 237 pages
File Size : 26,21 MB
Release : 2009-09-04
Category : Mathematics
ISBN : 0521127076

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This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.

Author : Marvin J. Greenberg
Publisher : Macmillan
Page : 512 pages
File Size : 33,3 MB
Release : 1993-07-15
Category : Mathematics
ISBN : 9780716724469

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This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.

Author : A.S. Weber
Publisher : Broadview Press
Page : 518 pages
File Size : 23,90 MB
Release : 2000-03-10
Category : Science
ISBN : 9781551111650

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Nineteenth-Century Science is a science anthology which provides over 30 selections from original 19th-century scientific monographs, textbooks and articles written by such authors as Charles Darwin, Mary Somerville, J.W. Goethe, John Dalton, Charles Lyell and Hermann von Helmholtz. The volume surveys scientific discovery and thought from Jean-Baptiste Lamarck’s theory of evolution of 1809 to the isolation of radium by Marie and Pierre Curie in 1898. Each selection opens with a biographical introduction, situating each scientist and discovery within the context of history and culture of the period. Each entry is also followed by a list of further suggested reading on the topic. A broad range of technical and popular material has been included, from Mendeleev’s detailed description of the periodic table to Faraday’s highly accessible lecture for young people on the chemistry of a burning candle. The anthology will be of interest to the general reader who would like to explore in detail the scientific, cultural, and intellectual development of the nineteenth-century, as well as to students and teachers who specialize in the science, literature, history, or sociology of the period. The book provides examples from all the disciplines of western science-chemistry, physics, medicine, astronomy, biology, evolutionary theory, etc. The majority of the entries consist of complete, unabridged journal articles or book chapters from original 19th-century scientific texts.