A lower bound on opaque sets

Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach

Research output: Contribution to journal › Article

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 known since 1964. A similar bound is proved for all convex sets U other than a triangle.

Original languageEnglish
Pages (from-to)13-22
Number of pages10
JournalComputational Geometry: Theory and Applications
Volume80
DOIs
Publication statusPublished - Jul 2019

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Intersect
Straight Line
Convex Sets
Triangle
Union
Lower bound
Curve
Unit

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

A lower bound on opaque sets. / Kawamura, Akitoshi; Moriyama, Sonoko; Otachi, Yota; Pach, János.

In: Computational Geometry: Theory and Applications, Vol. 80, 07.2019, p. 13-22.

Research output: Contribution to journal › Article

Kawamura, A, Moriyama, S, Otachi, Y & Pach, J 2019, 'A lower bound on opaque sets', Computational Geometry: Theory and Applications, vol. 80, pp. 13-22. https://doi.org/10.1016/j.comgeo.2019.01.002
Kawamura A, Moriyama S, Otachi Y, Pach J. A lower bound on opaque sets. Computational Geometry: Theory and Applications. 2019 Jul;80:13-22. https://doi.org/10.1016/j.comgeo.2019.01.002
Kawamura, Akitoshi ; Moriyama, Sonoko ; Otachi, Yota ; Pach, János. / A lower bound on opaque sets. In: Computational Geometry: Theory and Applications. 2019 ; Vol. 80. pp. 13-22.
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