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Transactions of the American Mathematical Society

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The limiting curve of Jarník's polygons


Author: Greg Martin
Journal: Trans. Amer. Math. Soc. 355 (2003), 4865-4880
MSC (2000): Primary 52C05; Secondary 11H06
DOI: https://doi.org/10.1090/S0002-9947-03-03219-7
Published electronically: July 28, 2003
MathSciNet review: 1997588
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Abstract | References | Similar Articles | Additional Information

Abstract: In 1925, Jarník defined a sequence of convex polygons for use in constructing curves containing many lattice points relative to their curvatures. Properly scaled, these polygons converge to a certain limiting curve. In this paper we identify this limiting curve precisely, showing that it consists piecewise of arcs of parabolas, and we discuss the analogous problem for sequences of polygons arising from generalizations of Jarník's construction.


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

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Additional Information

Greg Martin
Affiliation: Department of Mathematics, University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
Email: gerg@math.ubc.ca

DOI: https://doi.org/10.1090/S0002-9947-03-03219-7
Received by editor(s): June 20, 2002
Published electronically: July 28, 2003
Article copyright: © Copyright 2003 American Mathematical Society