Circles Spheres And Spherical Geometry
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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 The Circle And The Sphere
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Author : Julian Lowell Coolidge
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
A Treatise On The Circle And The Sphere written by Julian Lowell Coolidge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with History categories.
Circles and spheres are central objects in geometry. Mappings that take circles to circles or spheres to spheres have special roles in metric and conformal geometry. An example of this is Lie's sphere geometry, whose group of transformations is precisely the conformal group. Coolidge's treatise looks at systems of circles and spheres and the geometry and groups associated to them. It was written (1916) at a time when Lie's enormous influence on the field was still widely felt. Today, there is a renewed interest in the geometry of special geometric configurations. Coolidge has examined many of the most intuitive: linear systems of circles, circles orthogonal to a given sphere, and so on. He also examines the differential and projective geometry of the space of all spheres in a given space.Through the simple vehicles of circles and spheres, Coolidge makes contact with diverse areas of mathematics: conformal transformations and analytic functions, projective and contact geometry, and Lie's theory of continuous groups, to name a few. The interested reader will be well rewarded by a study of this remarkable book.
Menelaus Spherics
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Author : Roshdi Rashed
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-10-23
Menelaus Spherics written by Roshdi Rashed and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Philosophy categories.
Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.
Divided Spheres
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Author : Edward S. Popko
language : en
Publisher: CRC Press
Release Date : 2021-08-18
Divided Spheres written by Edward S. Popko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-18 with Mathematics categories.
Praise for the previous edition [. . .] Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include Computer-Aided Design and applications, which I would never have imagined when I started down this fascinating and rewarding path. His lovely illustrations bring the subject to life for all readers, including those who are not drawn to the mathematics. This book demonstrates the scope, beauty, and utility of an art and science with roots in antiquity. [. . .] Anyone with an interest in the geometry of spheres, whether a professional engineer, an architect or product designer, a student, a teacher, or simply someone curious about the spectrum of topics to be found in this book, will find it helpful and rewarding. – Magnus Wenninger, Benedictine Monk and Polyhedral Modeler Ed Popko's comprehensive survey of the history, literature, geometric, and mathematical properties of the sphere is the definitive work on the subject. His masterful and thorough investigation of every aspect is covered with sensitivity and intelligence. This book should be in the library of anyone interested in the orderly subdivision of the sphere. – Shoji Sadao, Architect, Cartographer and lifelong business partner of Buckminster Fuller Edward Popko's Divided Spheres is a "thesaurus" must to those whose academic interest in the world of geometry looks to greater coverage of synonyms and antonyms of this beautiful shape we call a sphere. The late Buckminster Fuller might well place this manuscript as an all-reference for illumination to one of nature's most perfect inventions. – Thomas T. K. Zung, Senior Partner, Buckminster Fuller, Sadao, & Zung Architects. This first edition of this well-illustrated book presented a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explained the principles of spherical design and the three classic methods of subdivision based on geometric solids (polyhedra). This thoroughly edited new edition does all that, while also introducing new techniques that extend the class concept by relaxing the triangulation constraint to develop two new forms of optimized hexagonal tessellations. The objective is to generate spherical grids where all edge (or arc) lengths or overlap ratios are equal. New to the Second Edition New Foreword by Joseph Clinton, lifelong Buckminster Fuller collaborator A new chapter by Chris Kitrick on the mathematical techniques for developing optimal single-edge hexagonal tessellations, of varying density, with the smallest edge possible for a particular topology, suggesting ways of comparing their levels of optimization An expanded history of the evolution of spherical subdivision New applications of spherical design in science, product design, architecture, and entertainment New geodesic algorithms for grid optimization New full-color spherical illustrations created using DisplaySphere to aid readers in visualizing and comparing the various tessellations presented in the book Updated Bibliography with references to the most recent advancements in spherical subdivision methods
A Treatise On Spherical Trigonometry With Applications To Spherical Geometry Numerous Examples
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Author : William J. M'Clelland
language : en
Publisher:
Release Date : 1887
A Treatise On Spherical Trigonometry With Applications To Spherical Geometry Numerous Examples written by William J. M'Clelland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1887 with Spherical trigonometry categories.
A Treatise On Spherical Trigonometry With Applications To Spherical Geometry And Numerous Examples
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Author : William J. M'Clelland
language : en
Publisher:
Release Date : 1897
A Treatise On Spherical Trigonometry With Applications To Spherical Geometry And Numerous Examples written by William J. M'Clelland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1897 with Spherical trigonometry categories.
Symbols In Arts Religion And Culture
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Author : Farrin Chwalkowski
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2016-12-14
Symbols In Arts Religion And Culture written by Farrin Chwalkowski and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-14 with Art categories.
We are a product of nature. Every single cell of our body is made of, and depends, on nature. Our inner soul is heavily influenced by nature. We feel sad if the sun is not shining for a few days, and feel pleasure when drawn to the wonder of flowers and uplifted by the song of birds. We came from nature; we are part of nature. In short, we are nature. Nature has been an intimate part of the human experience from the earliest times. Different religions and cultures, from all corners of the world, have honoured and worshipped nature in art, ritual and literature in their own unique ways. This book shows how we learn about our own human nature, our own sense of identity and how we fit into the larger scheme of life and spirit when we come to better understand how our human ancestors, through art, symbol and myth, expressed their relationship with the natural world.
Twists Tilings And Tessellations
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Author : Robert J. Lang
language : en
Publisher: CRC Press
Release Date : 2017-12-22
Twists Tilings And Tessellations written by Robert J. Lang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-22 with Mathematics categories.
Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.
The Annotated Flatland
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Author : Ian Stewart
language : en
Publisher: Basic Books
Release Date : 2008-07-31
The Annotated Flatland written by Ian Stewart and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-31 with Science categories.
Flatland is a unique, delightful satire that has charmed readers for over a century. Published in 1884 by the English clergyman and headmaster Edwin A. Abbott, it is the fanciful tale of A. Square, a two-dimensional being who is whisked away by a mysterious visitor to The Land of Three Dimensions, an experience that forever alters his worldview. Like the original, Ian Stewart's commentary takes readers on a strange and wonderful journey. With clarity and wit, Stewart illuminates Abbott's numerous Victorian references and touches on such diverse topics as ancient Babylon, Karl Marx, Mary Shelley's Frankenstein, Mt. Everest, H.G. Wells, and phrenology. The Annotated Flatland makes fascinating connections between Flatland and Abbott's era, resulting in a classic to rival Abbott's own, and a book that will inspire and delight curious readers for generations to come.