Balancing unit vectors

Details Balancing unit vectors Balancing unit vectors

2008-03-04

arxiv.org/abs/0803.0460v1

Journal of Combinatorial Theory, Series A 89 (2000) 105-112

Mathematics

Metric Geometry

7 pages

Scientific paper

10.1006/jcta.1999.3011

Theorem A. Let $x_1,...,x_{2k+1}$ be unit vectors in a normed plane. Then there exist signs $\epsi_1,...,\epsi_{2k+1}\in\{\pm 1\}$ such that $\norm{\sum_{i=1}^{2k+1}\epsi_i x_i}\leq 1$. We use the method of proof of the above theorem to show the following point facility location result, generalizing Proposition 6.4 of Y. S. Kupitz and H. Martini (1997). Theorem B. Let $p_0,p_1,...,p_n$ be distinct points in a normed plane such that for any $1\leq i

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