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How to realize a given number of tangents to four unit balls in ℝ 3
Author(s) -
Theobald Thorsten
Publication year - 2001
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014352
Subject(s) - tangent , mathematics , unit (ring theory) , bounded function , algebraic number , unit sphere , space (punctuation) , geometry , combinatorics , mathematical analysis , mathematics education , computer science , operating system
By a recent result, the number of common tangent lines to four unit balls in ℝ 3 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.