REAL

A lower bound on opaque sets

Kawamura, A. and Moriyama, S. and Otachi, Y. and Pach, János (2016) A lower bound on opaque sets. In: Coloring Points with Respect to Squares. Leibniz International Proceedings in Informatics (LIPIcs) . Schloss Dagstuhl Leibniz-Zentrum für Informatik, Dagstuhl, 46.1-46.10. ISBN 978-3-95977-009-5

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Abstract

It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle. © Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, and János Pach.

Item Type: Book Section
Additional Information: N1 Funding Details: 200020-144531, SNSF, Swiss National Science Foundation N1 Funding Details: 200021-137574, SNSF, Swiss National Science Foundation A4 et al.; National Science Foundation (NSF); Princeton University; The Center for Geometry and its Applications (SRC-GAIA); The Fields Institute for Research in Mathematical Sciences; Tufts University
Uncontrolled Keywords: Computational geometry; Unit squares; Total length; LOWER BOUNDS; Convex set; Cauchy-Crofton formulae; Set theory; Opaque sets; lower bound; Cauchy-Crofton formula; BARRIERS
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 03 Jan 2017 14:03
Last Modified: 03 Jan 2017 14:03
URI: http://real.mtak.hu/id/eprint/44222

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