Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere

Author:   Edward S. Popko
Publisher:   Taylor & Francis Inc
ISBN:  

9781466504295


Pages:   532
Publication Date:   16 July 2012
Replaced By:   9780367680039
Format:   Hardback
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere


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Overview

This well-illustrated book is the first comprehensive yet accessible introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome fifty years ago, which paved the way for a flood of practical applications in construction and other areas. Geodesic applications now encompass everything from product and packaging design, civil engineering, virology, nanotechnology, computer graphics, climate modeling, supercomputer architecture, wireless mobile networks, virtual reality gaming, astronomy, and computer-aided design (CAD).

Full Product Details

Author:   Edward S. Popko
Publisher:   Taylor & Francis Inc
Imprint:   A K Peters
Dimensions:   Width: 19.10cm , Height: 2.50cm , Length: 23.50cm
Weight:   1.247kg
ISBN:  

9781466504295


ISBN 10:   1466504293
Pages:   532
Publication Date:   16 July 2012
Audience:   College/higher education ,  College/higher education ,  Tertiary & Higher Education ,  Tertiary & Higher Education
Replaced By:   9780367680039
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Divided Spheres Working with Spheres Making a Point An Arbitrary Number Symmetry and Polyhedral Designs Spherical Workbenches Detailed Designs Other Ways to Use Polyhedra Summary Additional Resources Bucky's Dome Synergetic Geometry Dymaxion Projection Cahill and Waterman Projections Vector Equilibrium Icosa's The First Dome NC State and Skybreak Carolina Ford Rotunda Dome Marines in Raleigh University Circuit Radomes Kaiser's Domes Union Tank Car Covering Every Angle Summary Additional Resources Putting Spheres to Work Tammes Problem Spherical Viruses Celestial Catalogs Sudbury Neutrino Observatory Climate Models and Weather Prediction Cartography Honeycombs for Supercomputers Fish Farming Virtual Reality Modeling Spheres Dividing Golf Balls Spherical Throwable Panoramic Camera Hoberman's MiniSphere Rafiki's Code World Art and Expression Additional Resources Circular Reasoning Lesser and Great Circles Geodesic Subdivision Circle Poles Arc and Chord Factors Where Are We? Altitude-Azimuth Coordinates Latitude and Longitude Coordinates Spherical Trips Loxodromes Separation Angle Latitude Sailing Longitude Spherical Coordinates Cartesian Coordinates , , Coordinates Spherical Polygons Excess and Defect Summary Additional Resources Distributing Points Covering Packing Volume Summary Additional Resources Polyhedral Frameworks What Is a Polyhedron? Platonic Solids Symmetry Archimedean Solids Additional Resources Golf Ball Dimples Icosahedral Balls Octahedral Balls Tetrahedral Balls Bilateral Symmetry Subdivided Areas Dimple Graphics Summary Additional Resources Subdivision Schemas Geodesic Notation Triangulation Number Frequency and Harmonics Grid Symmetry Class I: Alternates and Ford Class II: Triacon Class III: Skew Covering the Whole Sphere Additional Resources Comparing Results Kissing-Touching Sameness or Nearly So Triangle Area Face Acuteness Euler Lines Parts and T . 257 Convex Hull Spherical Caps Stereograms Face Orientation King Icosa Summary Additional Resources Computer-Aided Design A Short History CATIA Octet Truss Connector Spherical Design Three Class II Triacon Designs Panel Sphere Class II Strut Sphere Class II Parabolic Stellations Class I Ford Shell 31 Great Circles Class III Skew Additional Resources Advanced CAD Techniques Reference Models An Architectural Example Spherical Reference Models Prepackaged Reference and Assembly Models Local Axis Systems Assembly Review Design-in-Context Associative Geometry Design-in-Context versus Constraints Mirrored Enantiomorphs Power Copy Power Copy Prototype Macros Publication Data Structures CAD Alternatives: Stella and Antiprism Antiprism Summary Additional Resources Spherical Trigonometry Basic Trigonometric Functions The Core Theorems Law of Cosines Law of Sines Right Triangles Napier's Rule Using Napier's Rule on Oblique Triangles Polar Triangles Additional Resources Stereographic Projection Points on a Sphere Stereographic Properties A History of Diverse Uses The Astrolabe Crystallography and Geology Cartography Projection Methods Great Circles Lesser Circles Wulff Net Polyhedra Stereographics Polyhedra as Crystals Metrics and Interpretation Projecting Polyhedra Octahedron Tetrahedron Geodesic Stereographics Spherical Icosahedron Summary Additional Resources Geodesic Math Class I: Alternates and Fords Class II: Triacon Class III: Skew Characteristics of Triangles Storing Grid Points Additional Resources Schema Coordinates Coordinates for Class I: Alternates and Ford Coordinates for Class II: Triacon Coordinates for Class III: Skew Coordinate Rotations Rotation Concepts Direction and Sequences Simple Rotations Reflections Antipodal Points Compound Rotations Rotation around an Arbitrary Axis Polyhedra and Class Rotation Sequences Icosahedron Classes I and III Icosahedron Class Octahedron Classes I and III Octahedron Class Tetrahedron Classes I and III Tetrahedron Class Dodecahedron Class Cube Class Implementing Rotations Using Matrices Rotation Algorithms An Example Summary Additional Resources

Reviews

<p>Edward Popko 's Divided Spheres is the definitive source for the many varied ways a sphere can be divided and subdivided. From domes and pollen grains to golf balls, every category and type is elegantly described in these pages. The mathematics and the images together amount to a marvelous collection, one of those rare works that will be on the bookshelf of anyone with an interest in the wonders of geometry.<br> Kenneth Snelson, renowned inventor of Tensegrity sculpture <p>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. Spherical subdivision is relevant today and useful for the futur


Edward Popko's Divided Spheres is the definitive source for the many varied ways a sphere can be divided and subdivided. From domes and pollen grains to golf balls, every category and type is elegantly described in these pages. The mathematics and the images together amount to a marvelous collection, one of those rare works that will be on the bookshelf of anyone with an interest in the wonders of geometry. --Kenneth Snelson, renowned inventor of Tensegrity sculpture 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. Spherical subdivision is relevant today and useful for the future. 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, author of Spherical Models Dr. Popko shows you how to solve practical design problems based on spherical polyhedra. Novices and experts will understand the challenges and classic techniques of spherical design just by looking at the many beautiful illustrations. --Steve Waterman, mathematician


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