The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres Academic Article

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. 2005 Springer Science+Business Media, Inc.

authors

• Sottile, Frank

published proceedings

• Discrete & Computational Geometry

author list (cited authors)

• Megyesi, G., & Sottile, F.

citation count

• 7

complete list of authors

• Megyesi, Gábor||Sottile, Frank

publication date

• April 2005

publisher

• Springer Nature  Publisher

published in

• Discrete and Computational Geometry: an international journal of mathematics and computer science  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00454-005-1160-8

start page

• 617

end page

• 644

volume

• 33

issue

• 4

URL

• http://dx.doi.org/10.1007/s00454-005-1160-8