A lower bound on opaque sets

Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach

Research output: Contribution to journalArticlepeer-review

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

All Science Journal Classification (ASJC) codes

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

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