## Busy Bee Geometry

April 6, 2014 § Leave a comment

“When there is no honey, the Pooh takes his tummy wherever the honey will be,” sang Pooh.

But, whilst poking his paw into the nearest beehive, did he ever stop to think about the ingenuity of the humble honey bee? Let’s hope not, a mathematical analysis surely wouldn’t make for a good Winnie the Pooh episode!

We are all used to the hexagonal shape of the cells within a beehive. But, why do the bees choose hexagons?

It was way back in the 4^{th} century that Pappus, an Ancient Greek geometer, started to think that maybe there was more to it than just being pretty . . . it’s actually a very efficient building technique. To make the most efficient use of space, they need to use shapes that tessellate – that means shapes that fit neatly together without leaving gaps.

But, you may say, why not use other shapes that tessellate, like squares or triangles? Well, for one thing, regular hexagons have a smaller overall perimeter than squares and triangles – once they have built one hexagon, they have already built one of the walls for 6 other hexagons, so it makes the workload much quicker and easier. Plus, the regular hexagon pattern has now been proved to be the most efficient pattern for curved walls. This means that the individual cells can bulge with honey and still make the most efficient use of the space.

So, next time you are using a protractor to measure an angle, spare a thought for the worker bees that are instinctively setting the walls in their beehives at exactly 120 degrees without so much as a spirit level!