MARCUS DU SAUTOY:'Here in California, beekeeper Steve Godling 'is taking me to see one of the greatest mysteries in nature.'
MARCUS DU SAUTOY:That's one of the wonders of the natural world, it's beautiful.
MARCUS DU SAUTOY:This almost looks man-made, manufactured, I mean it doesn't look like something from the natural world. The precision, the fine straight lines that they've created. 'The bees' honeycomb is a marvel of natural engineering.
MARCUS DU SAUTOY:'It's a place to raise their young and to store their food, 'and it's all made from wax. 'A substance that takes a huge amount of energy for them to produce.
MARCUS DU SAUTOY:'Every cell is identical - six walls, all the same length, 'meeting at exactly 120 degrees. 'The cross-section is a perfect six sided polygon - the hexagon.
MARCUS DU SAUTOY:'With a myriad of natural shapes to choose from, 'why have the bees selected this complex geometric structure?
MARCUS DU SAUTOY:'The answer comes from the bees' need to economise.
MARCUS DU SAUTOY:'The problem they have to solve 'is how to create their comb using as little precious wax as possible.'
MARCUS DU SAUTOY:If they want to produce a network of regular shapes which fit together neatly, then you've really only got three options. You can do equilateral triangles, or you could do squares, or you can do the bees' hexagons.
MARCUS DU SAUTOY:'But why of those three, does the bee choose the hexagons?
MARCUS DU SAUTOY:Well it turns out that the triangles actually use much more wax than any of the other shapes. Squares are a little better, but it's the hexagons which use the least amount of wax. 'It took human mathematicians until 1999 'to prove that the hexagonal array 'was the most efficient possible solution to this problem.
MARCUS DU SAUTOY:'Yet with a little help from evolution, 'the bees worked it out for themselves millions of years ago.
MARCUS DU SAUTOY:'It's easy to see why the hexagon is important to the bees, 'but how on earth do these hard working creatures, 'with a brain smaller than a sesame seed, 'create the shapes with such precision?
MARCUS DU SAUTOY:'For that we need to have a look 'at some of the laziest structures around.'
MARCUS DU SAUTOY:The soap bubble reveals something fundamental about nature. It's lazy. It tries to find the most efficient shape, the one using the least energy and the least amount of space. The sphere is one surface, no corners, infinitely symmetrical.
MARCUS DU SAUTOY:'When bubbles are on their own, they always try to be spheres. 'But when you start packing them together, their geometry changes.'
MARCUS DU SAUTOY:The bubbles are incredibly dynamic. They're always trying to assume the most efficient shape. The one that uses the least energy.
MARCUS DU SAUTOY:But if we in fact make each of the bubbles the same size a rather magical shape start to appear
MARCUS DU SAUTOY:The hexagon.
MARCUS DU SAUTOY:'This leaves the bees with a very simple way to build their honeycomb. 'All they need to do is build a cylinder of wax 'and nature will do the rest.
MARCUS DU SAUTOY:'It's thought that the wax, warmed by their bodies, 'pulls itself into the most efficient configuration.
MARCUS DU SAUTOY:'So when we see that pattern at the heart of the bee hive, 'it is in fact echoing some of the fundamental laws of the universe.
MARCUS DU SAUTOY:'This drive to efficiency can be seen written throughout nature.
MARCUS DU SAUTOY:'It's this hidden geometric force 'that makes the world the shape it is.'
Marcus du Sautoy visits a bee-keeper and explores how bees create their honeycombs.
If they are going to tessellate they have a limited number of regular polygons they could choose from, but the hexagon is the most efficient – giving the maximum storage area for the least amount of wax.
In fact, the bees do not create hexagons, but circular cells which, as is shown using bubble arrays, pull together to make hexagons due to surface tension.
This same principle is behind other polygon formations in the natural world too.
This clip is from the series The Code.
Teacher Notes
Use as an enrichment clip as part of a series of lessons on tessellation.
The bubble examples can, with a little practice, be replicated in the classroom using glycerin bubble mixture on a piece of transparency on an overhead projector.
Curriculum Notes
These clips will be relevant for teaching Maths at KS4 and GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.
The topics discussed will support OCR, Edexcel, AQA, WJEC in England and Wales, CCEA in Northern Ireland and SQA in Scotland.
