Spherical Geometry And Its Applications

Author : Marshall Whittlesey
Publisher : CRC Press
Page : 348 pages
File Size : 55,8 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781000617542

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Spherical Geometry and Its Applications by Marshall Whittlesey Pdf

Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Author : Marshall A. Whittlesey
Publisher : CRC Press
Page : 262 pages
File Size : 43,5 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781000627527

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Spherical Geometry and Its Applications by Marshall A. Whittlesey Pdf

Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Author : Walter J. Meyer
Publisher : CRC Press
Page : 422 pages
File Size : 41,5 Mb
Release : 2022-06-19
Category : Mathematics
ISBN : 9780429582264

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Geometry and Its Applications by Walter J. Meyer Pdf

This unique textbook combines traditional geometry presents a contemporary approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, introduces axiomatic, Euclidean and non-Euclidean, and transformational geometry. The text integrates applications and examples throughout. The Third Edition offers many updates, including expaning on historical notes, Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. The Third Edition streamlines the treatment from the previous two editions Treatment of axiomatic geometry has been expanded Nearly 300 applications from all fields are included An emphasis on computer science-related applications appeals to student interest Many new excercises keep the presentation fresh

Author : Marshall A. Whittlesey
Publisher : Unknown
Page : 335 pages
File Size : 51,7 Mb
Release : 2020
Category : MATHEMATICS
ISBN : 042932880X

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Spherical Geometry and Its Applications by Marshall A. Whittlesey Pdf

Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world - but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Author : H. Groemer
Publisher : Cambridge University Press
Page : 343 pages
File Size : 42,8 Mb
Release : 1996-09-13
Category : Mathematics
ISBN : 9780521473187

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Geometric Applications of Fourier Series and Spherical Harmonics by H. Groemer Pdf

This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Author : George A. Jennings
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208556

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Modern Geometry with Applications by George A. Jennings Pdf

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

Author : Walter A. Meyer
Publisher : Elsevier
Page : 560 pages
File Size : 50,6 Mb
Release : 2006-02-21
Category : Mathematics
ISBN : 9780080478036

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Geometry and Its Applications by Walter A. Meyer Pdf

Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. Realistic applications integrated throughout the text, including (but not limited to): Symmetries of artistic patterns Physics Robotics Computer vision Computer graphics Stability of architectural structures Molecular biology Medicine Pattern recognition Historical notes included in many chapters

Author : William J. M'Clelland,Thomas Preston
Publisher : Unknown
Page : 184 pages
File Size : 50,5 Mb
Release : 1886
Category : Geometry
ISBN : HARVARD:32044091916569

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A Treatise on Spherical Trigonometry by William J. M'Clelland,Thomas Preston Pdf

Author : I.M. Yaglom
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261353

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A Simple Non-Euclidean Geometry and Its Physical Basis by I.M. Yaglom Pdf

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 : Horatio Nelson Robinson
Publisher : Unknown
Page : 264 pages
File Size : 45,9 Mb
Release : 2008-06-01
Category : Electronic
ISBN : 1436832632

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Elements of Geometry, Plane and Spherical by Horatio Nelson Robinson Pdf

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Author : Albert Ensign Church
Publisher : Unknown
Page : 70 pages
File Size : 54,7 Mb
Release : 1864
Category : Geometry, Descriptive
ISBN : UCSC:32106013584492

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Elements of Descriptive Geometry by Albert Ensign Church Pdf

Author : Albert Ensign Church
Publisher : Unknown
Page : 212 pages
File Size : 47,6 Mb
Release : 1864
Category : Geometry, Descriptive
ISBN : NYPL:33433024468286

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Elements of Descriptive Geometry by Albert Ensign Church Pdf

Author : William J. McClelland,Thomas Preston
Publisher : Unknown
Page : 160 pages
File Size : 44,5 Mb
Release : 2008-06-01
Category : Electronic
ISBN : 1436553504

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A Treatise on Spherical Trigonometry, Part by William J. McClelland,Thomas Preston Pdf

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Author : Glen Van Brummelen
Publisher : Princeton University Press
Page : 218 pages
File Size : 52,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780691148922

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Heavenly Mathematics by Glen Van Brummelen Pdf

Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegent proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries. -- Jacket.

Author : Thomas E. Cecil
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 50,8 Mb
Release : 2007-11-26
Category : Mathematics
ISBN : 9780387746555

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Lie Sphere Geometry by Thomas E. Cecil Pdf

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.