On a Question of Erdos and Ulam
نویسندگان
چکیده
Ulam asked in 1945 if there is an everywhere dense rational set, i.e. 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.
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 43 شماره
صفحات -
تاریخ انتشار 2010