Kawamura, Akitoshi and Moriyama, Sonoko and Otachi, Yota and Pach, János (2019) A lower bound on opaque sets. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 80. pp. 13-22. ISSN 0925-7721
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Official URL: http://doi.org/10.1016/j.comgeo.2019.01.002
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. (C) 2019 Published by Elsevier B.V.
| Item Type: | Article |
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| Additional Information: | Funding Agency and Grant Number: JSPS KAKENHI [JP17K19960]; MEXT KAKENHI [JP24106002, JP24106004, JP25106505, 10-EuroGIGA-OP-003]; Swiss National Science Foundation [200020-162884, 200021-165977] Funding text: 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)110]. Kyushu University, Japan Nihon University, Japan Kumamoto University, Japan EPFL, Switzerland Rényi Institute, Budapest, Hungary Export Date: 18 October 2019 CODEN: CGOME Correspondence Address: Kawamura, A.; Kyushu UniversityJapan; email: kawamura@inf.kyushu-u.ac.jp Funding Agency and Grant Number: JSPS KAKENHIMinistry of Education, Culture, Sports, Science and Technology, Japan (MEXT)Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research (KAKENHI) [JP17K19960]; MEXT KAKENHIMinistry of Education, Culture, Sports, Science and Technology, Japan (MEXT)Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research (KAKENHI) [JP24106002, JP24106004, JP25106505, 10-EuroGIGA-OP-003]; Swiss National Science FoundationSwiss National Science Foundation (SNSF) [200020-162884, 200021-165977] Funding text: 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)110]. |
| Uncontrolled Keywords: | Covering; Cauchy-Crofton formula; Mathematics, Applied; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 19 Oct 2019 04:34 |
| Last Modified: | 19 Oct 2019 04:34 |
| URI: | http://real.mtak.hu/id/eprint/102414 |
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