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.
@InProceedings{kawamura_et_al:LIPIcs.SoCG.2016.46, author = {Kawamura, Akitoshi and Moriyama, Sonoko and Otachi, Yota and Pach, J\'{a}nos}, title = {{A Lower Bound on Opaque Sets}}, booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)}, pages = {46:1--46:10}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-009-5}, ISSN = {1868-8969}, year = {2016}, volume = {51}, editor = {Fekete, S\'{a}ndor and Lubiw, Anna}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.46}, URN = {urn:nbn:de:0030-drops-59386}, doi = {10.4230/LIPIcs.SoCG.2016.46}, annote = {Keywords: barriers; Cauchy-Crofton formula; lower bound; opaque sets} }
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