Marco Ripà

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 1, Pages 59—71

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## Details

### 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 *n*_{1} × *n*_{2} × … × *n _{k}* 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

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## Related papers

- 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

APARipà, M. (2014). The rectangular spiral or the *n*_{1} × *n*_{2} × … × *n _{k}* Points Problem. Notes on Number Theory and Discrete Mathematics, 20(1), 59-71.

Ripà, Marco. “The Rectangular Spiral or the *n*_{1} × *n*_{2} × … × *n _{k} *Points Problem.” Notes on Number Theory and Discrete Mathematics 20, no. 1 (2014): 59-71.

Ripà, Marco. “The Rectangular Spiral or the *n*_{1} × *n*_{2} × … × *n _{k} *Points Problem.” Notes on Number Theory and Discrete Mathematics 20.1 (2014): 59-71. Print.