On the equipartition of plane convex bodies and convex polygons |
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Authors: | Roser Guàrdia Ferran Hurtado |
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Institution: | (1) Dept. de Matemàtica Aplicada III, Univ. Politècnica de Catalunya, Terrassa, Spain;(2) Dept. de Matemàtica Aplicada II, Univ. Politècnica de Catalunya, Barcelona, Spain |
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Abstract: | In this paper we consider the problem of partitioning a plane compact convex body into equal-area parts, i.e., an equipartition,
by means of chords. We prove two basic results that hold with some specific exceptions: (a) When chords are pairwise non-crossing,
the dual tree of the partition has to be a path, (b) A convex n-gon admits no equipartition produced by more than n chords having a common interior point. |
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Keywords: | 52A10 52A38 52C45 |
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