A Lower Bound on Opaque Sets

Authors Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach

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Akitoshi Kawamura
Sonoko Moriyama
Yota Otachi
János Pach

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Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, and János Pach. A Lower Bound on Opaque Sets. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 46:1-46:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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.
  • barriers; Cauchy-Crofton formula; lower bound; opaque sets


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