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Why do Bees love hexagons?

Bees can be extremely intelligent and also brilliant mathematicians. But, bees after all could build honeycombs from rectangles or squares or triangles … But for some reason, bees choose hexagons.  Always hexagons. And not just your basic six-sided hexagon. They like “perfect” hexagons, meaning all six sides are of equal length. The question is why?

There are many theories for example maybe a honeycomb built of hexagons can hold more honey, maybe hexagons require less building wax.  But what is the real reason?  Roman soldier/scholar/writer, Marcus Terentius Varro, proposed an answer, called “The Honeybee Conjecture”

 “It is a mathematical truth,” Alan Lightman writes, “that there are only three geometrical figures with equal sides that can fit together on a flat surface without leaving gaps: equilateral triangles, squares and hexagons.”

So which to choose? The triangle? The square? Or the hexagon? Which one is best? Here’s where our Roman, Marcus Terentius Varro made his great contribution. His “conjecture” — and that’s what it was, a mathematical guess — proposed that a structure built from hexagons is probably a wee bit more compact than a structure built from squares or triangles. A hexagonal honeycomb, he thought, would have “the smallest total perimeter.” He couldn’t prove it mathematically, but that’s what he thought.

Compactness matters. The more compact your structure, the less wax you need to construct the honeycomb. Wax is expensive. A bee must consume about eight ounces of honey to produce a single ounce of wax. So if you are watching your wax bill, you want the most compact building plan you can find.

And guess what?             

A mathematician at the University of Michigan, Thomas Hales, solved the riddle. It turns out, Varro was right. A hexagonal structure is indeed more compact. In 1999, Hales produced a mathematical proof that said so.

As Charles Darwin himself once wrote, the honeycomb is a masterpiece of engineering. It is “absolutely perfect in economizing labor and wax.”

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