gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/29/85)
> And why is floating point not a proper subject for net.math?
Floating-point processors may have some interesting
mathematical properties, but this wasn't being discussed.
Suggested NEW topic with some mathematical interest:
Someone came by the other day and told us of a theorem
that went roughly as follows:
Consider a closed (not necessarily convex) smooth (C-2) surface
in 3-D, an external point light source, and an external point
observer. As the light source and/or observer are moved around,
the number of specular reflections seen by the observer always
has the same parity (remainder modulo 2). In other words, new
reflections of the light source come and go in pairs.
As told, the theorem postulated a translucent surface, so that
reflections from the rear surface were also visible, and also
that the light source was sufficiently far away. But I don't
think these conditions are necessary.
In investigating this subject, one rediscovers "caustics" and
other interesting things that are related to dynamical systems
theory.
A good, clear proof of the theorem and a demonstration of the
necessity of its conditions would be useful.