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Smallest Universal Covers for Families of Triangles

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Abstract

A universal cover for a family T of triangles is a convex shape that contains a congruent copy of each triangle T ∈ T. We conjecture that for any family T of triangles (of bounded area) there is a triangle that forms a universal cover for T of smallest possible area. We prove this conjecture for all families of two triangles, and for the family of triangles that fit in the unit circle.
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Dates and versions

hal-02972966 , version 1 (20-10-2020)

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  • HAL Id : hal-02972966 , version 1

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Ji-Won Park, Otfried Cheong. Smallest Universal Covers for Families of Triangles. EuroCG 2020 - 36th European Workshop on Computational Geometry, Mar 2020, Würzburg, Germany. ⟨hal-02972966⟩
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