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Abstract
We show that every packing of regular pentagons in the Euclidean plane has density less than 0.9611. Our proof is computerassisted. We also give a detailed strategy for proving the KuperbergKuperberg conjecture, which asserts that the optimal packing of regular pentagons in the plane is a double lattice, formed by aligned vertical columns of upward pointing pentagons alternating with aligned vertical columns of downward pointing pentagons. The strategy is based on estimates of the areas of Delaunay triangles. Our strategy reduces the Kuperberg conjecture to area minimization problems that involve at most four acute Delaunay triangles.
Original language  English 

Journal  arXiv.org ePrint archive 
Publication status  In preparation  23 Feb 2016 
Keywords
 math.MG
ASJC Scopus subject areas
 Geometry and Topology
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Activities
 1 Workshop, seminar or course (Participation in/Organisation of)

ICERM: Phase Transitions and Emergent Properties
Woden Barnard Kusner (Participant)2 Feb 2015 → 8 May 2015Activity: Participation in or organisation of › Workshop, seminar or course (Participation in/Organisation of)