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

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

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

## Abstract

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 A_{0} A_{1},..., A_{n} = A_{0}, A_{n+1},....., A_{n+m}, be points such that: (i) the polygon A_{0} A_{1} ... A_{n} 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 + A_{n-1} and K + A_{r}; (iii) the points A_{n+1}, .... A_{n+m} are in the interior of π (iv) for each point X of π, there exists an A_{r}, 1 ≤ r ≤ n + m, such that X ∈ K + A_{r} and the line segment XA_{r} 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 |
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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 |

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