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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
Covering families of triangles by convex sets
 Krajči, Samuel ; Kynčl, Jan (advisor) ; Soukup, Jan (referee)
A convex universal cover of a family M of sets in the plane is a convex set that contains a congruent copy of every element of M. Park and Cheong conjecture that for every family of triangles with bounded diameter there exists a triangle that is a smallest universal cover of this family. We prove this conjecture for every family of all triangles with the lengths of their two sides fixed, every family of all triangles with the length of a side and the size α of the opposite angle fixed (where α is from an interval (0, λ]∩[3π/7, π) with λ being approximately 0.396π), every finite subfamily of a family of all triangles with the length of a side and the size α of the opposite angle fixed (where α ≥ π/2). 1
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