A lower bound on opaque sets

2014/03/16 by Akitoshi Kawamura, Sonoko Moriyama, Kawamura, Akitoshi +5 · 2 citations
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1403.3894

openalex publication_date 2014/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 established by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.

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• Explicit lower bounds for opaque sets of unit square and unit disc
• Errata and Addenda to Mathematical Constants

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