The rectangular spiral or the n1 × n2 × … × nk Points Problem

Marco Ripà
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 1, Pages 59–71
Full paper (PDF, 589 Kb)

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Authors and affiliations

Marco Ripà
Economics – Institutions and Finance, Roma Tre University
Rome, Italy

Abstract

A generalization of Ripà’s square spiral solution for the n × n × … × n Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the k-dimensional n1 × n2 × … × nk Points Problem. In this way, we can build a range in which, with certainty, all the best possible solutions to the problem we are considering will fall. Finally, we provide a few characteristic numerical examples in order to appreciate the fineness of the result arising from the particular approach we have chosen.

Keywords

  • Dots
  • Straight line
  • Inside the box
  • Outside the box
  • Plane
  • Upper bound
  • Lower bound
  • Topology
  • Graph theory
  • Segment
  • Points

AMS Classification

  • Primary: 91A44
  • Secondary: 37F20, 91A46

References

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Related papers

  1. Ripà, Marco. “The n × n × n Points Problem Optimal Solution.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 36-43.

Cite this paper

Ripà, M. (2014). The rectangular spiral or the n1 × n2 × … × nk Points Problem. Notes on Number Theory and Discrete Mathematics, 20(1), 59-71.

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