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On a Question of Erdős and Ulam.
- Source :
-
Discrete & Computational Geometry . Feb2010, Vol. 43 Issue 2, p393-401. 9p. - Publication Year :
- 2010
-
Abstract
- Ulam asked in 1945 if there is an everywhere dense rational set, i.e., 1 a point set in the plane with all its pairwise distances rational. Erdős conjectured that if a set S has a dense rational subset, then S should be very special. The only known types of examples of sets with dense (or even just infinite) rational subsets are lines and circles. In this paper we prove Erdős’ conjecture for algebraic curves by showing that no irreducible algebraic curve other than a line or a circle contains an infinite rational set. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01795376
- Volume :
- 43
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Discrete & Computational Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 47481422
- Full Text :
- https://doi.org/10.1007/s00454-009-9179-x