The Honeycomb Conjecture

Preprint

20 May 2002

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9906042

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.

Keywords

DISCONNECTED HONEYCOMB
HONEYCOMB CONJECTURE
CLASSICAL HONEYCOMB
ALLOWS DISCONNECTED
CONJECTURE ASSERTS
CELLS AND GAPS
PARTITION
REGULAR

All Related Versions

Version 1, 1999-06-08, ArXiv
Version 2, 2002-05-20, ArXiv

This publication has 0 references indexed in Scilit: