Cutting convex curves

We show that for any two convex curves C-1 and C-2 in R-d parametrized by [0, 1] with opposite orientations, there exists a hyperplane H with the following property: For any t is an element of [0, 1] the points C-1 (t) and C-2(t) are never in the same open half space bounded by H. This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes. (C) 2016 Elsevier Ltd. All rights reserved.
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Issue Date
2016-11
Language
ENG
Citation

EUROPEAN JOURNAL OF COMBINATORICS, v.58, pp.34 - 37

ISSN
0195-6698
DOI
10.1016/j.ejc.2016.04.011
URI
http://hdl.handle.net/10203/213201
Appears in Collection
MA-Journal Papers(저널논문)
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