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INFINITE PATHS WITH NO SMALL ANGLES

Part of:Discrete geometry

Published online by Cambridge University Press:  10 December 2009

Imre Bárány and
Attila Pór
Imre Bárány
Affiliation:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, HungaryDepartment of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K. (email: barany@renyi.hu)
Attila Pór
Affiliation:
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, U.S.A. (email: apor@math.wku.edu)

Abstract

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It is shown here that given a discrete (and infinite) set of points in the plane, it is possible to arrange them on a polygonal path so that every angle on the polygonal path is at least 9∘. This has been known to hold for finite sets (with 20∘). The main result holds for discrete sets in higher dimensions as well, with a smaller bound on the angle.

MSC classification

Secondary:52C10: Erdős problems and related topics of discrete geometry52C30: Planar arrangements of lines and pseudolines

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010, pp. 26 - 34
Copyright
Copyright © University College London 2010

References

[1]Bárány, I., Pór, A. and Valtr, P., Paths without small angles. SIAM J. Discrete Math. (2009), to appear.Google Scholar
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