Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-20T02:06:56.091Z Has data issue: false hasContentIssue false
  • English
  • Français

Covering a polygon with triangles: a Caratheodory-type theorem

Published online by Cambridge University Press:  09 April 2009

M. J. C. Baker
M. J. C. Baker
Affiliation:
Royal Australian Air Force Academy Point Cook Victoria 3029, 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.

Generalizations are proved for theorems of Carathéodory (1907), Kirchberger (1903) and Watson (1973), the theme of these results being how thickly the convex hull of a family of points is covered by simplexes whose vertices are chosen from the points of the family.

Subject classification (Amer. Math. Soc. (MOS) 1970): 52A35.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 229 - 234
Copyright
Copyright © Australian Mathematical Society 1979

References

Baker, M. J. C. (1978), ‘Covering with triangles’, A sequence of notes in James Cook Mathematical Notes (University of North Queensland Mathematics Department), Nos. 15, 16, 17. Townsville.Google Scholar
Birch, B. J. (1959), ‘On 3n points in a plane’, Proc. Cambridge Phil. Soc. 55, 289–293.CrossRefGoogle Scholar
Carathéodory, C. (1907), Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen’, Math. Ann. 64, 95–115.CrossRefGoogle Scholar
Helly, E. (1923), ‘Über Mengen konvexen Körper mit gemeinschaftlichen Punkten’, Jber. Deutsch. Math. Verein. 32, 175–176.Google Scholar
Katchalski, M. (1977), ‘A Helly type theorem on a sphere’, Proc. Amer. Math. Soc. 66, 119–122.CrossRefGoogle Scholar
Kirchberger, P. (1903), ‘Über Tschebyschefsche Annäherungsmethoden’, Math. Ann. 57, 509–540.CrossRefGoogle Scholar
Watson, D. R. (1973), ‘A refinement of theorems of Kirchberger and Carathéodory’, J. Austral. Math. Soc. 15, 190–192.CrossRefGoogle Scholar