Formulas for the number of gridlines



: Ernvall-Hytonen AM, Matomaki K, Haukkanen P, Merikoski JK

Publisher: SPRINGER WIEN

: 2011

: Monatshefte für Mathematik

: MONATSHEFTE FUR MATHEMATIK

: MONATSH MATH

: 2

: 164

: 2

: 157

: 170

: 14

: 0026-9255

DOI: https://doi.org/10.1007/s00605-010-0236-6


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.



Last updated on 2024-26-11 at 16:34