Smallest Universal Covers for Families of Triangles
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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