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New Book on Geodesics and the Orderly Subdivision of the Sphere
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.
● Presents a thorough introduction to the mathematics of the geodesic dome
● Covers many modern science, engineering, medical, and biological applications
● Explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra)
● Compares geodesic methods
● Illustrates how basic and advanced CAD techniques apply to spherical subdivision
Praise for Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere
I have loved the beauty and symmetry of polyhedra and spherical divisions for many years. My own efforts have been concentrated on making both simple and complex spherical models using classical methods and simple tools. 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, Benedictine Monk and Polyhedral Modeler
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, Sculptor and Photographer
Edward Popko’s Divided Spheres is a ‘thesaurus’
—Thomas T.K. Zung, Senior Partner, Buckminster Fuller, Sadao & Zung Architects
My own discovery, Waterman Polyhedra, was my way to see hidden patterns in ordered points in space. Ed's book Divided Spheres is about patterns and points too but on spheres. He shows you how to solve practical design problems based 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
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
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ISBN 9781466504295, June 2012, 532 pp, $69.95