The Limiting Curve of Jarnik's Polygons

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dc.creatorMartin, Greg
dc.date2002-06-17
dc.date.accessioned2026-07-07T04:49:10Z
dc.date.available2026-07-07T04:49:10Z
dc.descriptionIn 1925, Jarnik 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 Jarnik's construction.
dc.description16 pages; 11 figures
dc.identifierhttps://arxiv.org/abs/math/0206168
dc.identifierhttp://arxiv.org/abs/math/0206168
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64322
dc.subjectNumber Theory
dc.subject52C05 (11H06)
dc.titleThe Limiting Curve of Jarnik's Polygons
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