The Honeycomb Conjecture
Copyright policy )The Honeycomb Conjecture
The classical honeycomb conjecture asserts that any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Pappus discusses this problem in his preface to Book V. This paper gives the first general proof of the conjecture. The revision is the published version, which allows disconnected honeycomb cells and gaps between cells.
24 pages
- University of Michigan–Flint United States
- University of Michigan United States
- University of Michigan–Ann Arbor United States
partition of the plane, Science, Metric Geometry (math.MG), Tilings in \(2\) dimensions (aspects of discrete geometry), Mathematics - Metric Geometry, Legacy, honeycomb conjecture, regular hexagonal honeycomb tiling, FOS: Mathematics, Packing and covering in \(2\) dimensions (aspects of discrete geometry), Mathematics
partition of the plane, Science, Metric Geometry (math.MG), Tilings in \(2\) dimensions (aspects of discrete geometry), Mathematics - Metric Geometry, Legacy, honeycomb conjecture, regular hexagonal honeycomb tiling, FOS: Mathematics, Packing and covering in \(2\) dimensions (aspects of discrete geometry), Mathematics
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