Divided Spheres: Geodesics and the Orderly Subdivision of the SpherePraise for the previous edition [. . .] Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include ComputerAided 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. 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. 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 allreference for illumination to one of nature's most perfect inventions. This first edition of this wellillustrated 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

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Contents
1 Divided Spheres  1 
2 Buckys Dome  13 
3 Putting Spheres to Work  59 
4 Circular Reasoning  101 
5 Distributing Points  147 
6 Polyhedral Frameworks  157 
7 Golf Ball Dimples  203 
8 Subdivision Schemas  213 
10 SelfOrganizing Grids  293 
A Stereographic Projection  337 
B Coordinate Rotations  359 
C Geodesic Math  389 
411  
439  
About the Authors  453 
9 Comparing Results  267 
Other editions  View all
Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere Edward Popko,Chrisopher J. Kitrick No preview available  2021 
Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere Edward S. Popko,Christopher J. Kitrick No preview available  2021 