The maximal angular gap among rectangular grid points

Z. Füredi, Bruce Reznick

Research output: Contribution to journalArticle

Abstract

Let A - {a1,...,am} and β -{b1,...,bn} be two sots of real numbers. Consider the (at, most) mn rays from the origin to the points (aibj), and define the aperture Ap(A, B) to bo the largest angular gap between consecutive rays. Clearly, Ap(A, B) ≥ 2π/mn. Let f(m, n) denote the minimum aperture of any m × n rectangular array, as defined above. In this paper, we show, that for sufficiently large n, f(n, n) <220/n2, so that f(n,n) = Ω(n-2). We also show that f(m,n) = 2π/mnonly when m = 2, or n = 2 or (m, n) = (4, 4), (4, G) or (6,4).

Original languageEnglish
Pages (from-to)119-137
Number of pages19
JournalPeriodica Mathematica Hungarica
Volume36
Issue number2-3
Publication statusPublished - 1998

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Keywords

  • Approximation by fractions
  • Discrepancy
  • Even distribution
  • Geometry of numbers
  • Lattice
  • Trigonometric identities

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The maximal angular gap among rectangular grid points. / Füredi, Z.; Reznick, Bruce.

In: Periodica Mathematica Hungarica, Vol. 36, No. 2-3, 1998, p. 119-137.

Research output: Contribution to journalArticle

Füredi, Z. ; Reznick, Bruce. / The maximal angular gap among rectangular grid points. In: Periodica Mathematica Hungarica. 1998 ; Vol. 36, No. 2-3. pp. 119-137.
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