We use cookies to make your experience better. By continuing to browse our site you are agreeing to our use of cookies. Learn more.
Divided Spheres by Edward Popko
£45.99
Available
Product Ref. (e.g. ISBN, SKU)
9780367680749
Published:
25 Sep 2023
Format:
Paperback
Number of pages:
454 pages
Dimensions:
254x255x27mm
Weight:
0.453kgs
Author:
This well-illustrated book presents 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.
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
About the Author: Edward S. Popko is a graduate of the University of Detroit's School of Architecture and has both Masters and PhD degrees from Massachusetts Institute of Technology. He is a registered architect and former Fulbright Scholar. In the 1960s, he was an apprentice in Buckminster Fuller's affiliate office, Geometrics, Inc., in Cambridge, Massachusetts, and later authored Geodesics, a primer on geodesic domes, and Transitions, a documentary of urban settlements in developing countries. For the past 25 years, he has held research, product development, and marketing positions for Computer Aided Design and Geographic Information Systems technology within IBM. He has managed software development teams in computer mapping and CAD solutions for architects, industrial buildings, high‐tech plants, and shipbuilding.He is retired from IBM and lives with his wife, Geraldine, in Woodstock, New York. They have a daughter Ellen and a son Gerald.Christopher J. Kitrick is a graduate of the University of Cincinnati with a bachelor's in Architecture and a masters in Structural Engineering. In the late 1970s he interned for 3 years at Buckminster Fuller's professor emeritus office on the campus of the University of Philadelphia. During that tenure he was involved in Fuller's Synergetics II book, multiple dome developments, tensegrity research, and the first computerized version edition of the Dymaxion Air‐Ocean map.For the past 36 years he has been involved with graphics software and hardware development from mainframe to mobile devices enabling the rapid advancement of visual technology. Independently he has authored and presented numerous technical papers on spherical geometry at international conferences on space structures.He is still working and resides in La Jolla, California, with his wife Tomoko. They have two sons Francis and Ian, and one daughter, Eileen.
| Number of pages | 454 |
|---|
We will despatch your order as quickly as we can. If, for whatever reason, a product is out of stock we will contact you to discuss the likely delivery time or an alternative product.
| First Item | 2 Items & Over | |
|---|---|---|
| UK | £3.75 | £5.00 |
| EU | £15.00 | £30.00 |
| USA & Canada | £30.00 | £50.00 |
| Rest of the World | £45.00 | £60.00 |
| Collect in Store | free | free |
Additional Delivery Information (and some really important bits):
UK Delivery
Orders for delivery in the UK are despatched by Courier and Signed For delivery services and will normally be delivered to you within a few days of placing your order. Signed Books are shipped in our specially made book mailing cartons, with the books themselves wrapped in paper to protect them. Sometimes we may ship your order in several parts, particularly if you have 'Pre-Order' titles in your order or titles which are held in stock with our publishing partners.
The Really Important Bit: Because we use courier and signed for delivery services, please use an address at which your parcel can be signed for during the normal working day, for example, you may want to have your order delivered to your work address if you're not at home during the day.
First Item @ £3.75 (sometimes a shipping supplement may be added for particularly heavy books or specific postcodes*)
2 Items & over @ £5.00 in total
Another Really Important Bit: There are a number of Postcodes in the UK for which we will need to charge a shipping supplement, this will be calculated once we know the size and weight of the shipment. For these orders we will contact customers to agree a suitable and economic method of shipping. There may also be additional time required for delivery to some areas of the United Kingdom. Where possible, we will ship single book orders (under 2kg) by Royal Mail to all UK postcodes. Multiple book orders and books over 2kg are shipped via APC Overnight, regardless of Postcode.
Overseas Delivery
Shipments to EU countries:
First Item @ £15.00 (sometimes a shipping supplement will be added for particularly heavy books)
2 Items & over @ £30.00 in total
A really, really important Brexit bit: From 1st January 2021 shipments to EU addresses may incur additional costs which could be requested by Fed Ex at the time of delivery. These costs may vary from country to country and are not within our control and will be in addition to the costs paid to us for your delivery. If in any doubt, please check with your local Fed Ex office what, if any, additional costs will be applicable to your order - https://www.fedex.com
From 1st July 2021, VAT will be applicable to those EU countries where VAT is applied to books - this additional charge will be collected by Fed Ex (or the Royal Mail) at the time of delivery.
Shipments to the USA & Canada:
First Item @ £30.00
2 Items & over @ £50.00 in total
Shipments to the Rest of the World:
First Item @ £45.00
2 Items & over @ £60.00 in total
All overseas orders are shipped using a 'signed for' courier service - please provide an address at which your parcel can be signed for on receipt. We use the same packaging materials for our overseas deliveries as we do those in the UK. In some cases, particularly large and heavy books, or books being shipped to remote areas, may incur an additional shipping charge - if this is the case with your order, we'll notify you as quickly as possible of these charges and to arrange the additional payment. You can of course cancel your order with an immediate refund should you not wish to accept these additional costs. Shipments to overseas territories may incur additional Duty & Tax costs which could be requested by Fed Ex at the time of delivery. These costs may vary from country to country and are not within our control and will be in addition to the costs paid to us for your delivery. If in any doubt, please check with your local Fed Ex office what, if any, additional Tax & Duty costs will be applicable to your order - https://www.fedex.com
Collect in Person at Coles Books
We're open Monday - Saturday, 9:00am - 5:30pm. If you're collecting your order, please wait until you get the text, phone call or email from us, just to be on the safe side and to ensure we have your order ready for you on arrival (we'll use the contact information provided during checkout). Not everything on our website is available for immediate collection, please do wait for the text, call or email - if time is of the essence, we'd suggest you call us on 01869 320779 and check availability prior to placing your order. You can pick up your order from the till, please bring a copy of your email receipt (electronic or printed is fine).
Coming by Car
If you're coming to Coles by car, why not take advantage of the 2 hours free parking at Sainsbury's Pioneer Square - just follow the signs for Pioneer Square as you drive into Bicester and park in the multi-storey car park above the supermarket. Come down the travelators, exit Sainsbury's, turn right and follow the pedestrianised walkway to Crown Walk and turn right - and Coles will be right in front of you. You don't need to shop in Sainsbury's to get the free parking!
Where to Find Us
Coles Books
22 Crown Walk
Pioneer Square
Bicester, Oxfordshire
OX26 6HY, United Kingdom
It was the most impressive packaging that I have EVER SEEN!!! The books were in perfect condition!!!!!
Super fast delivery and well packaged. Quality item and service!