The envelope of lines meeting a fixed line that are tangent to two spheres

Details The envelope of lines meeting a fixed line that are tangent to two spheres The envelope of lines meeting a fixed line that are tangent to two spheres

2003-04-23

arxiv.org/abs/math/0304346v2

Discrete and Computational Geometry, 33, Number 4, (2005) 617--644.

Mathematics

Algebraic Geometry

24 pages, 13 .eps pictures

Scientific paper

We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. All such configurations are degenerate. The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex algebraic geometry, explicit computation and graphics.

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