Lately I’ve been quite taken with the honeybee. What an amazing creature!
Consider just the honeycomb, the foundation upon which the bee colony is built. I’m sure you know it’s for storing honey and pollen, receiving the queen’s eggs, and raising their offspring. And you’re probably aware that each individual cell of the honeycomb is in the shape of a hexagon. Always hexagons. Never squares, triangles, or circles.
But not just any hexagon. A perfect hexagon. Each side is of equal length, and always joined to its adjacent sides at an angle of 120 degrees. And always tipped up at between 9 and 14° towards the open ends, presumably so the honey doesn’t drip out. Throughout the colony, teams of bees are working independently to build their perfectly shaped hexagon cells to be joined to other teams’ perfectly shaped hexagons… in the dark, upside down, while clinging to a partner above.
And why a hexagon? A circle has a better ratio of perimeter to area than a hexagon, for the same perimeter. But when circles fit together there will be gaps between them, which would mean wasted space and duplication of cell walls, for with a hexagon, each wall is a wall for two separate chambers. “It is a mathematical truth 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.”1 So why do bees always choose the hexagon?
Over 2000 years ago, a Roman scholar named Marcus Terentius Varro proposed an answer, which ever since has been called “The Honeybee Conjecture.” Varro conjectured that a honeycomb built of hexagons could hold more honey and require less building wax. But he couldn’t prove it mathematically, so it was just a conjecture. Until 1999, when mathematician Thomas Hales at the University of Michigan solved the riddle. It turns out, Varro was right.2
The honeybee has a brain the size of a grass seed, but she has confounded computerless mathematicians for thousands of years as to her choice of the hexagon for her honeycomb.
All I can say is… all praise to her Maker!
1 See Alan Lightman’s “The Symmetrical Universe.”
2 Read Thomas Hales’ 24-page proof here.