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Balancing unit vectors

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A. Letx1, …, x2k+1be unit vectors in a normed plane. Then there exist signs1, …, 2k+1{±1} such that ∑2k+1i=1 ixi1. 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). B. Letp0, p1, …, pnbe distinct points in a normed plane such that for any 1i

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