Geodesic Math and How to Use It [Englisch] [Taschenbuch]

Hugh Kenner's book is the bible of geodesy. While other books provide you with tables and some of the rudiments of the theory of geodesic domes, 'Geodesic Math and How to Use it' gives you a first-principle look at how domes are developed from a mathematical/geometrical point of view. Most importantly, Kenner introduces the reader to a novel metric for both describing the location of geodesic points in space and calculating their exact positions, so you can develop your own chord factors rather than relying on tables without understanding the underlying math.

Seemed over-technical at 1st, but after about a year has been my reference book on geodesics & making all kinds of geodesic domes... It lists chord factors (lengths of segments before applying radius of dome) on tables to 7 decimals for various domes @ the end of the book if you don't want do calculate w/formulas provided. If your familiar with trigonometry, it will let you jump around chapters that are of more interest.

This book was originally copyrighted in 1976, but not edited for this 2nd paperback 2003 Edition (glossy 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.

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. Not a small book but not a big bulky one either. Makes for a lot of information handy to store just about anywhere...
____________________________________________________________________________________

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 3880 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 @ 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 2-16v 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...

One thing - spherical coordinate symbols for Theta & Phi are switched, though referenced in correct order (check Mathworld). Easy to correct, just read "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.
____________________________________________________________________________________

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...

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 here in town (on same lot) burnt down before fire department got to them - and 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).

I have been researching geodesics for a while and have found this book valuable in understanding the subject, however, I would suggest downloading some of the NASA tech briefs about geodesic math (and its free) before spending this amount of money on a book. There are several online sources of info to help the novice.