TY - JOUR

T1 - A lower bound on opaque sets

AU - Kawamura, Akitoshi

AU - Moriyama, Sonoko

AU - Otachi, Yota

AU - Pach, János

N1 - Funding Information:
The work presented here was supported in part by the JSPS KAKENHI (Grant-in-Aid for Challenging Research (Exploratory)) JP17K19960; by the MEXT KAKENHI (Grants-in-Aid for Scientific Research on Innovative Areas) JP24106002, JP24106004, JP25106505 under the ELC project; by OTKA under EUROGIGA projects GraDR and ComPoSe 10-EuroGIGA-OP-003; and by Swiss National Science Foundation Grants 200020-162884 and 200021-165977. A preliminary version was presented at the 32nd Annual Symposium on Computational Geometry (SoCG 2016) [10]. We are grateful to Gábor Tardos for many interesting discussions on the subject. In particular, the present proof of Lemma 4 is based on his idea.
Publisher Copyright:
© 2019

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.

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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 -