UNIT SQUARES INTERSECTING ALL SECANTS OF A SQUARE

Authors
VALTR P
Citation
P. Valtr, UNIT SQUARES INTERSECTING ALL SECANTS OF A SQUARE, Discrete & computational geometry, 11(2), 1994, pp. 235-239
Citations number
5
Categorie Soggetti
Computer Sciences, Special Topics","Mathematics, General","Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
11
Issue
2
Year of publication
1994
Pages
235 - 239
Database
ISI
SICI code
0179-5376(1994)11:2<235:USIASO>2.0.ZU;2-K
Abstract
Let S be a square of side length s > 0. We construct, for any sufficie ntly large s, a set of less than 1.994s closed unit squares whose side s are parallel to those of S such that any straight line intersecting S intersects at least one square of S. It disproves L. Fejes Toth's co njecture that, for integral s, there is no such configuration of less than 2s - 1 unit squares.