Work

A lower bound on opaque sets

Year: 2014

Type: preprint

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 established by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1403.3894

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

Institutions: Kyushu University, Nihon University, Kumamoto University, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950610752

Cites: 3

Cited by: 3

Related to: 10