The limiting curve of Jarník’s polygons

Martin, Greg

doi:10.1090/S0002-9947-03-03219-7

The limiting curve of Jarník’s polygons
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Trans. Amer. Math. Soc. 355 (2003), 4865-4880 Request permission

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.

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