rayjraz's Full Review: Hugh Kenner - Geodesic Math and How to Use It
A brief introduction on what this book covers: "Geodesics" use the principles of the triangle & arch which take great advantage of tension & compression forces on building materials. The Romans took advantage of the arch & nature has been building “circular” for millions of years (from birds nests to bee hives) - natural selection just wouldn't let them build otherwise. In the wake of recent disasters, even people that use brick or concrete buildings realize we need a 4th little pig (as the fairy tale goes)...
With geodesics, you can build all kinds of structures ranging in size from dog houses to Dymaxion cars & houses (by R. Buckminster Fuller) to stadiums. You can also build real cool looking models made from just about any material - “paper origami”, ice cream sticks, straws & tacks... Many model kits are available like Legos or something else cool called K'NEX. There are also superbly illustrated books for children or adults for making all kinds models - which I see a lot mentioned in reviews as “my favorite book”. Some other good books are listed below...
“GEODESIC MATH AND HOW TO USE IT” (as the title's written) can get very technical (though it's mostly all trigonometry). It does give you tables for results already calculated for many types & sizes of domes, so you can start building in “no time”...
Oh, if you want to see a really nice PICTURE of the book, copy & paste this link in your browser address bar (it's after "http://" only - the "www." is left out): images.amazon.com/images/P/0520239318.01._SCLZZZZZZZ_.jpg
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This is an excellent technical compendium on geodesics, though in a somewhat dated format. It seemed over-technical at 1st for what I wanted (just chord factors or lengths of segments before applying radius of dome). Chord factors are listed in tables at the end to 7 decimals for various domes (octahedral, icosahedral & tetrahedral). If you're familiar with trigonometry for solving these & others on your own, it will let you jump around chapters that are of more interest.
Originally copyrighted in 1976, but not edited for this 2nd paperback 2003 Edition (semi-gloss color cover). The author, Hugh Kenner (1923-2003), has compiled a very thorough book. Very well written & explained in orderly fashion with excellent general layout & (especially for the time) detailed diagrams plus cross page-references. IMO there is very little that I would change except for replacing current diagrams with modern CAD generated illustrations, that's about it.
The book has 172 pages with several blank pages for notes (I note in the wide margins instead) & is 8.7 x 8.7 x 0.5 inches. It's not a small book, but not a big bulky one either. It has a lot of information handy to store just about anywhere...
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I found many formulas & shortcuts throughout the book. From Chapter 12 I plotted a 16 frequency (# of divisions making total # of triangles) icosahedron (the typical geodesic polyhedron shape) dome with 3,880 chords or “struts”. Even made them into arcs for a perfectly round sphere. Chapter 12 has “Using the Tables” with a simple symmetric triangle xyz-grid on a spreadsheet. Each chord calculated does not rely on another chord's result, so chance of error is greatly reduced. Chapter 14 “Truncations” has "Truncation by Rotation", which saves time on calculating the rest of the chords in dome, or moving chords by their symmetry.
This "still nicely" bound book after a lot of use covers tension & tensegrities, subdivisions, great circles, symmetry & breakdowns, choosing a polyhedron, spherical coordinate system, ellipses & superellipses, truncations, space frames & many kinds of angles - plus charts & other resources at the end.
A free program on the web called Windome is useful to 8 decimals, but lacks input parameters like radius... So I use it to verify chord factors. From 2-16 frequency domes involving about 12,240 chords plotting all verified (to 15 digits) on 1st try. Besides spreadsheets, formulas can be used in programming like "The R Project", formulas & programs are also written for old Hewlett-Packard HP-35, 21 & 45 series calculators & programs filed with the HP-65 library (circa mid-1970's). I guess it also goes to show Hewlett-Packard has a history in the PC & hardware programming business, as NASA & Apollo missions back then found these calculators "indispensable"...
One thing - spherical coordinate symbols for Theta & Phi are switched, though referenced in correct order (check Mathworld). It's easy to correct for, in the book just read the "Phi symbol" as Theta & "Theta symbol" as Phi - references & formulas will be in order. This book was written in mid-1970's, guess more? people then used this as convention.
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There are many good free sources on the web for geodesic domes & math plotting through Cartesian x,y,z and/or spherical Theta, Phi coordinates using basic trigonometry. This book cost me $13.57 shipped free brand new & is WELL worth it, even after searching the web...
Besides lots of information on the web, here are some good books on the subject:
Shapes, Space and Symmetry by Alan Holden
Spherical Models by Magnus J. Wenninger
Polyhedron Models by Magnus J. Wenninger
Build Your Own Polyhedra by Peter Hilton
Bucky Works : Buckminster Fuller's Ideas for Today by J. Baldwin
A final word of caution on building materials for domes in general: if you use wood make sure you take extra fireproofing precautions, unless it's a temporary frame. 2 domes that were successively (not to say “successfully”) built out of wood on the same lot here in town burnt down before the fire department got to them - plus they were right down the street! The intense heat from both fires left nothing except the slab & melted everything.
So, when they start to burn there is very little time to exit the structure. As energy efficient as they are, the same design allows for a very efficient combustion, especially with wood stud frames & panels. Other problems arise as well with ventilating interior wood frames to help prevent condensation.
There are many other materials that will not burn that could make up the panels (like from American Ingenuity, Inc.), or even a monolithic concrete pour over a temporary plastic covered geodesic wood frame. Another method that doesn't use geodesics is a “monolithic shotcreted airform dome” (from a company called Monolithic Dome Institute).
Another popular material for geodesic frames is metal conduit pipe. Both ends are flattened & a hole drilled near each flattened end, then joined at each end by a bolt forming the hubs/connectors. Those are also the kind seen on kid's playgrounds, sometimes painted a nice bright or gaudy color.
One company, Pacific Domes, sells pre-made kits with durable powder coated paint already applied. There's also a lot of information on DIY for this at “Burning Man Festival” sites (held once a year out in the desert of Black Rock City, Nevada) - so the dome built under “the symbolic burning man” does not dangerously collapse from the fire....
This is THE most requested UCP out-of-print title! It describes in detail how to arrive at the correct dimensions to build your very own geodesic dome...More at Buy.com Marketplaces
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