The Honeycomb Conjecture
Thomas C. Hales
Abstract
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.
Create a lesson
Related papers
Each simplex in R4 has a point with at least 14 emanating normals to its boundary
Ivan Nasonov, Gaiane Panina
Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞
Emin Abdullaev
Embedding large subsets of Wasserstein spaces into Banach spaces
Cyril Letrouit, Quentin Mérigot
A Smooth Covariogram and the Transition Between Projection Bodies
J. Haddad, C. H. Jiménez, M. Resende Guedes
Intermediate coverings, random images, and projections
Yunhao Zhao, Yingyu Zhao, Chen Zhou et al.
On the Graph Corresponding to Center of Distances of Metric Space
Oleksiy Dovgoshey, Olga Rovenska