Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a conjecture of Danzer and Grünbaum


Authors: Meir Katchalski and David Nashtir
Journal: Proc. Amer. Math. Soc. 124 (1996), 3213-3218
MSC (1991): Primary 52A35
DOI: https://doi.org/10.1090/S0002-9939-96-03806-3
MathSciNet review: 1376992
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of the paper is that if $A$ is a family of homothetic triangles in the plane such that any 9 of them can be pierced by two points, then all members of $A$ can be pierced by two points. This is best possible in more than one sense: (1) the number 9 cannot be replaced by 8; (2) no similar statement is true for homothetic copies (or even translates) of a symmetric convex hexagon.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 52A35

Retrieve articles in all journals with MSC (1991): 52A35


Additional Information

Meir Katchalski
Affiliation: Department of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel
Email: meirk@tx.technion.ac.il

David Nashtir
Affiliation: Department of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel

DOI: https://doi.org/10.1090/S0002-9939-96-03806-3
Received by editor(s): July 18, 1994
Additional Notes: The first author’s research was supported by the Fund for Promotion of Research at the Technion (grant 100-806) and the Technion V. P. R. Fund (grant 100-934)
Communicated by: Jeffry N. Kahn
Article copyright: © Copyright 1996 American Mathematical Society