Cutting Mutually Congruent Pieces from Convex Regions

Details Cutting Mutually Congruent Pieces from Convex Regions Cutting Mutually Congruent Pieces from Convex Regions

2010-12-14

arxiv.org/abs/1012.3106v3

Mathematics

Combinatorics

8 pages, 3 figures. 'v-3' slightly modified from earlier versions

Scientific paper

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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