Hostname: page-component-6d856f89d9-vrt8f Total loading time: 0 Render date: 2024-07-16T07:18:42.654Z Has data issue: false hasContentIssue false
  • English
  • Français

On convex lattice polygons

Published online by Cambridge University Press:  17 April 2009

P.R. Scott
P.R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let π be a convex lattice polygon with b boundary points and c (≥ 1) interior points. We show that for any given c, the number b satisfies b ≤ 2c + 7, and identify the polygons for which equality holds.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 395 - 399
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Nosarzewska, M., “Évaluation de la différence entre l'aire d'une région plane convexe et le nombre des points aux coordonnées entières couvertes par elle”, Colloq. Math. 1 (1947/1948), 305–311.CrossRefGoogle Scholar
[2]Pick, G., “Geometrisches zur Zahlenlehre”, Sitzungsber Lotos Prag. (2) 19 (1900), 311–319. [Quoted from [3], p. 324, and Zentralblatt über die Fortschritte der Mathematik 31 (1899), p. 215, ]Google Scholar
[3]Steinhaus, H., Mathematical snapshots, new edition, revised and enlarged (Oxford University Press, Oxford, London, New York, 1960).Google Scholar
[4]Wills, J.M., “Über konvexe Gitterpolygone”, Comment. Math. Helv. 48 (1973), 188–194.CrossRefGoogle Scholar