Geodesic Math - AAA Home Page for Jay Salsburg（测地线的数学Jay Salsburg AAA主页）.pdf

Geodesic Math All Artwork, Graphics and Illustrations were created or made by: Jay Salsburg, Design Scientist, jay@ excerpt of an article by Joe Clinton 1 Geodesic Math Producing geodesics from the icosahedron. The following article is an excerpt of an article by Joe Clinton on the different methods of producing geodesics from the icosahedron. Formatted by Jay Salsburg, Design Scientist Using analytical geometry (Fuller used spherical trigonometry), calculated on a computer: General procedure 1. find the 3-dimensional coordinates of the vertices of the grid on the spherical surface 2. find geometry using the different Methods 3. calculate the chord lengths, angles etc. with these coordinates and analytical formulas. Joe worked with Fuller on his programs and was funded by NASA on a project called “Structural Design Con- cepts for Future Space Missions.” The specific motivation for developing these methods was to have a variety of forms to combine in large space frame domes. For example the Expo dome in Montreal is a combination of a: 32-frequency regular triacon (Class II, method 3) and a 16-frequency truncatable alternate (Class I, method 3) With known parameters and sophisticated analysis, large structures can be optimized by different combinations and different methods; however, for small structures (up to 40) they are not generally relevant. What was called “alternate” breakdown, Joe classifies as “Class I’’; what was called ‘’triacon’’ he classifies as ‘’Class II’’. Joe wrote this section mainly with the intent of communicating the state of development of geodesic geometries and the hope that it would be an aid to those interested in exploring and expanding this field. Geodesic Math DEFINITIONS Axial angle (omega Ω ) = an angle formed by an element and a radius from the center