### 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 language | English |
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Pages (from-to) | 13-22 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 80 |

DOIs | |

Publication status | Published - Jul 2019 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Computational Geometry: Theory and Applications*,

*80*, 13-22. https://doi.org/10.1016/j.comgeo.2019.01.002

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

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 80, pp. 13-22. https://doi.org/10.1016/j.comgeo.2019.01.002

}

TY - JOUR

T1 - A lower bound on opaque sets

AU - Kawamura, Akitoshi

AU - Moriyama, Sonoko

AU - Otachi, Yota

AU - Pach, János

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85061302923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061302923&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2019.01.002

DO - 10.1016/j.comgeo.2019.01.002

M3 - Article

AN - SCOPUS:85061302923

VL - 80

SP - 13

EP - 22

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

ER -