Jeffrey Stewart Ely
I am interested in applying computer graphical techniques to
illuminate mathematical processes and
objects. Ideally, this can lead to a deeper understanding or at least
to an increased appreciation
and/or awareness of the process or object. Some of my projects are
implemented as billions of particles, others use the ray-tracing
technique and hundreds of millions of rays. In either case, I do not
use "canned" software, preferring to write the code myself to first
principles.
This is my response to a request to make a ball and stick model of
the buckyball carbon molecule.
After deciding that a strict interpretation of the molecule lacked
artistic flair, I proceeded to use it
as a theme. Here, the overall structure is a 60-node truncated
icosahedron (buckyball), but each
node is itself a buckyball. The center sphere reflects this model
in its surface and also recursively
reflects the whole against a mirror that is behind the observer.
I was recently surprised to read in David Richeson's book, Euler's
Gem, that Legendre proved
Euler's Formula, V - E + F = 2, by projecting a polyhedron onto a
sphere and then summing the
areas of the various spherical polygons. I think this fact
resonates rather well with this design.