A1 Refereed original research article in a scientific journal
Formulas for the number of gridlines
Authors: Ernvall-Hytonen AM, Matomaki K, Haukkanen P, Merikoski JK
Publisher: SPRINGER WIEN
Publication year: 2011
Journal: Monatshefte für Mathematik
Journal name in source: MONATSHEFTE FUR MATHEMATIK
Journal acronym: MONATSH MATH
Number in series: 2
Volume: 164
Issue: 2
First page : 157
Last page: 170
Number of pages: 14
ISSN: 0026-9255
DOI: https://doi.org/10.1007/s00605-010-0236-6
Abstract
Let l(n) be the number of lines through at least two points of an n x n rectangular grid. We prove recursive and asymptotic formulas for it using respectively combinatorial and number theoretic methods. We also study the ratio l(n)/l(n - 1). All this originates from Mustonen's experimental results.
Let l(n) be the number of lines through at least two points of an n x n rectangular grid. We prove recursive and asymptotic formulas for it using respectively combinatorial and number theoretic methods. We also study the ratio l(n)/l(n - 1). All this originates from Mustonen's experimental results.
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