The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter. The first record of the conjecture dates back to 36BC, from Marcus Terentius Varro, but is often attributed to Pappus of Alexandria (c. 290 – c. 350). The conjecture was proven in 1999 by mathematician Thomas C. Hales, who mentions in his work that there is reason to believe that the conjecture may have been present in the minds of mathematicians before Varro.
- Weaire–Phelan structure, a counter-example to the Kelvin conjecture on the solution of the similar problem in 3D.
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