## Common Transversals and TangentsFrank
SottileUniversity of Masssachusetts, AmherstSymbolic Computational Algebra 2002 University of Western Ontario |

We describe some interesting symbolic computations that arose while studying the following simple geometric problem:

Consider *k* lines and 4-*k* spheres in **R**^{3}.

- When the given lines and spheres are general, how many lines are there
that meet the fixed lines and are tangent to the spheres.
Call these
*common tangents and transversals*. - For which arrangements of lines and spheres are there infinitely many cmmon tangents and transversals?

Besides the interesting geometry, computation, and pictures, we feel that the
study of geometry in 3-space is a fertile area for potential applications of
symbolic and computational algebra.
The results in this talk represent joint work with
Gabor Megyesi and
Thorsten Theobald.

A
web page
featuring many, many pictures from this study.