On plane coverings with convex domains

Bambah, R. P. ; Woods, A. C. (1971) On plane coverings with convex domains Mathematika, 18 (1). pp. 91-97. ISSN 0025-5793

Full text not available from this repository.

Official URL: http://journals.cambridge.org/production/action/cj...

Related URL: http://dx.doi.org/10.1112/S002557930000841X


The following theorem has been proved by Bambah, Rogers and Zassenhaus [1], Theorem A. Let K be a closed convex domain with a centre. Let A0 A1,..., An = A0, An+1,....., An+m, be points such that: (i) the polygon A0 A1 ... An is a Jordan polygon bounding a closed domain π of area a(π ); (ii) for each r, 0 ≤ r ≤ n, there is a point common to K + An-1 and K + Ar; (iii) the points An+1, .... An+m are in the interior of π (iv) for each point X of π, there exists an Ar, 1 ≤ r ≤ n + m, such that X ∈ K + Ar and the line segment XAr is in π. Then α(π) ≤ (2m+n-2)t(k), where t(K) is the area of the largest triangle contained in K.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:52A45; Convex sets; Covering
ID Code:71955
Deposited On:19 Jun 2012 13:38
Last Modified:19 Jun 2012 13:38

Repository Staff Only: item control page