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How to realize a given number of tangents to four unit balls in ℝ3

Part of: Projective and enumerative geometry

Published online by Cambridge University Press:  26 February 2010

Thorsten Theobald
Thorsten Theobald
Affiliation:
Zentrum Mathematik, Technische Universitat München, Boltzmannstr. 3, D-85747 Garching bei München, Germany. E-mail: theobald@ma.tum.de.
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Abstract

By a recent result, the number of common tangent lines to four unit balls in ℝ3 is bounded by 12 unless the four centres are collinear. In the present paper, this result is complemented by showing that indeed every number of tangents k ∈ {0, …, 12} can be established in real space. The constructions combine geometric and algebraic aspects of the tangent problem.

MSC classification

Secondary: 14N10: Enumerative problems (combinatorial problems)
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 51 - 62
Copyright
Copyright © University College London 2001

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