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Formulas for the number of gridlines
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 164, no 2, 157-170 p.Article in journal (Refereed) Published
Abstract [en]

Let l(n) be the number of lines through at least two points of an n × 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.

Place, publisher, year, edition, pages
Springer, 2011. Vol. 164, no 2, 157-170 p.
Keyword [en]
Asymptotic formulas, Euler φ-function, Lattice points, Rectangular grid, Recursive formulas
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-150740DOI: 10.1007/s00605-010-0236-6ISI: 000295176000003Scopus ID: 2-s2.0-80053097673OAI: oai:DiVA.org:kth-150740DiVA: diva2:745736
Funder
Swedish Research Council, 2009-721
Note

QC 20140911

Available from: 2014-09-11 Created: 2014-09-09 Last updated: 2017-12-05Bibliographically approved

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