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arXiv · 1012.3106

Cutting Mutually Congruent Pieces from Convex Regions

R. Nandakumar
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Abstract

What is the shape of the 2D convex region P from which, when 2 mutually congruent convex pieces with maximum possible area are cut out, the highest fraction of the area of P is left over? When P is restricted to the set of all possible triangular shapes, our computational search yields an approximate upper bound of 5.6% on the area wasted when any triangle is given its best (most area utilizing) partition into 2 convex pieces. We then produce evidence for the general convex region which wastes the most area for its best convex 2-partition not being a triangle and briefly discuss some further generalizations of the question.

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R. Nandakumar. 2011-02-23. Cutting Mutually Congruent Pieces from Convex Regions. https://arxiv.org/abs/1012.3106

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