The Honeycomb Conjecture

From Neatorama:

In 36 B.C., Roman scholar Marcus Terentius Varro came up with the answer of why honeycomb cells are hexagons, in what since has been called the Honeycomb Conjecture. Varro guessed that hexagon is the best way to divide a surface into regions of equal area with the least total perimeter - basically, it's the most compact (and therefore efficient) structure - but he couldn't prove it mathematically.

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