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

Megyesi, Gàbor and Sottile, Frank (2005) The envelope of lines meeting a fixed line and tangent to two spheres. Discrete and Computational Geometry, 33 (4). pp. 617-644. ISSN 1432-0444

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Abstract

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 projective algebraic geometry, explicit computation and graphics.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 51 Geometry (See also algebraic geometry)
MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
Depositing User: Ms Lucy van Russelt
Date Deposited: 17 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/543

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