## Response from Prof. B.

Thanks for the information and the links on the golden ratio, one of the favorite topics of generations of mathematicians. Thanks also for the Kepler link, which enabled me to find a much better bibliographical reference to Edmund Laguerre for my document on Laguerre geometry.

With respect to the organic reasons for the appearance of the golden ratio in plant and animal forms, a good reference is the work of D'Arcy Thompson, "On Growth and Form".

With respect to three-dimensional modeling programs, it is true that many of the commercially available ones use what is called "constructive solid geometry" to manipulate primitive forms such as spheres and cylinders, and some of my colleagues have used these successfully in mathematical research as well as art. We used a program like that for the two basic images in the picture "The Temple of Viviani" in my show at the Providence Art Club, although the golden tube surrounding the intersection curve was generated by an entirely different sort of program that uses formulas. I generally prefer such a program since abstract objects defined by formulas are ordinarily my starting point. Applied mathematicians have a different viewpoint (one of the features that often can be used to distinguish pure from applied mathematicians).