Unit squares intersecting all secants of a square
Copyright policy )Unit squares intersecting all secants of a square
Let S be a square of side length s > 0. We construct, for any sufficiently large s, a set of less than 1.994 s closed unit squares whose sides are parallel to those of S such that any straight line intersecting S intersects at least one square of S. It disproves L. Fejes Tòth's conjecture that, for integral s, there is no such configuration of less than 2s -1 unit squares.
- Charles University Czech Republic
- Freie Universität Berlin Germany
- DigiZeitschriften Germany
discrete geometry, geometrical construction, Article, Erdős problems and related topics of discrete geometry, 510.mathematics, intersecting problem, line cover, minimal problem, 000 Informatik, Informationswissenschaft, allgemeine Werke::000 Informatik, Wissen, Systeme::004 Datenverarbeitung; Informatik, squares
discrete geometry, geometrical construction, Article, Erdős problems and related topics of discrete geometry, 510.mathematics, intersecting problem, line cover, minimal problem, 000 Informatik, Informationswissenschaft, allgemeine Werke::000 Informatik, Wissen, Systeme::004 Datenverarbeitung; Informatik, squares
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