Spherical Geometry And Its Applications
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Spherical Geometry And Its Applications
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Author : Marshall Whittlesey
language : en
Publisher: CRC Press
Release Date : 2019-11-14
Spherical Geometry And Its Applications written by Marshall Whittlesey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
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
Spherical Geometry And Its Applications
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Author : Marshall Whittlesey
language : en
Publisher: CRC Press
Release Date : 2019-11-14
Spherical Geometry And Its Applications written by Marshall Whittlesey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
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
Geometric Applications Of Fourier Series And Spherical Harmonics
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Author : H. Groemer
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-13
Geometric Applications Of Fourier Series And Spherical Harmonics written by H. Groemer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-13 with Mathematics categories.
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.
Geometry And Its Applications
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Author : Walter A. Meyer
language : en
Publisher: Elsevier
Release Date : 2006-02-21
Geometry And Its Applications written by Walter A. Meyer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-21 with Mathematics categories.
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
Geometry And Its Applications In Arts Nature And Technology
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Author : Georg Glaeser
language : en
Publisher: Springer Nature
Release Date : 2020-12-18
Geometry And Its Applications In Arts Nature And Technology written by Georg Glaeser and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Mathematics categories.
This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.
Modern Geometry With Applications
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Author : George A. Jennings
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-12
Modern Geometry With Applications written by George A. Jennings and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-12 with Mathematics categories.
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.
Spherical Geometry And Its Applications
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Author : Marshall A. Whittlesey
language : en
Publisher:
Release Date : 2020
Spherical Geometry And Its Applications written by Marshall A. Whittlesey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with MATHEMATICS categories.
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
Heavenly Mathematics
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Author : Glen Van Brummelen
language : en
Publisher: Princeton University Press
Release Date : 2017-04-04
Heavenly Mathematics written by Glen Van Brummelen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-04 with Mathematics categories.
"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."--Jacket.
Circles Spheres And Spherical Geometry
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Author : Hiroshi Maehara
language : en
Publisher: Springer Nature
Release Date : 2024-08-09
Circles Spheres And Spherical Geometry written by Hiroshi Maehara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-09 with Mathematics categories.
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics. The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton’s 13-balls-problem, Casey’s theorem (an extension of Ptolemy’s theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere. The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided. This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike.
A Treatise On Spherical Trigonometry And Its Application To Geodesy And Astronomy With Numerous Examples
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Author : John Casey
language : en
Publisher: Read Books Ltd
Release Date : 2013-01-03
A Treatise On Spherical Trigonometry And Its Application To Geodesy And Astronomy With Numerous Examples written by John Casey and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-03 with Mathematics categories.
This early work on spherical trigonometry is both expensive and hard to find in its first edition. It contains a comprehensive account of the subject and includes numerous examples and exercises. This is a fascinating work and highly recommended for anyone interested in learning spherical trigonometry. Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.