{"product_id":"divided-spheres-edward-s-popko-9780367680749","title":"Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere","description":"\u003cp\u003e\u003cstrong\u003ePraise for the previous edition\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e[. . .] 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. \u003c\/p\u003e\u003cp\u003eHis 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.\u003cbr\u003e\u003cb\u003e\u003ci\u003e- Magnus Wenninger, Benedictine Monk and Polyhedral Modeler\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eEd 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. \u003cbr\u003e\u003cb\u003e\u003ci\u003e- Shoji Sadao, Architect, Cartographer and lifelong business partner of Buckminster Fuller\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eEdward Popko's \u003cem\u003eDivided Spheres\u003c\/em\u003e 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. \u003cbr\u003e\u003cb\u003e\u003ci\u003e- Thomas T. K. Zung, Senior Partner, Buckminster Fuller, Sadao, \u0026amp; Zung Architects. \u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eThis 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). \u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003eNew to the Second Edition\u003c\/p\u003e\u003cul\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eNew Foreword by Joseph Clinton, lifelong Buckminster Fuller collaborator\u003c\/li\u003e \u003cli\u003eA 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\u003c\/li\u003e \u003cli\u003eAn expanded history of the evolution of spherical subdivision\u003c\/li\u003e \u003cli\u003eNew applications of spherical design in science, product design, architecture, and entertainment\u003c\/li\u003e \u003cli\u003eNew geodesic algorithms for grid optimization\u003c\/li\u003e \u003cli\u003eNew full-color spherical illustrations created using \u003ci\u003eDisplaySphere \u003c\/i\u003eto aid readers in visualizing and comparing the various tessellations presented in the book\u003c\/li\u003e \u003cli\u003eUpdated Bibliography with references to the most recent advancements in spherical subdivision methods\u003c\/li\u003e \u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Edward S. Popko,Christopher J. Kitrick\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0367680742\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780367680749\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e A K PETERS\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/25\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 454\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.84lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.00h x 7.00w x 0.98d","brand":"Edward S. Popko","offers":[{"title":"Paperback","offer_id":48437895889151,"sku":"9780367680749","price":66.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_341f0084-1a99-4189-a4ca-df2dd61fbdaa.jpg?v=1777167506","url":"https:\/\/www.whiterainbookhouse.com\/products\/divided-spheres-edward-s-popko-9780367680749","provider":"WR Book House","version":"1.0","type":"link"}