The shapes and curves we learn to identify as children take on new significance when we see them in the wild. The forces of nature converge to produce spirals and polygons and a multitude of other forms in both living and non-living things, on scales ranging from the microscopic to the galactic.
The hexagon is the most common observable shape on Earth. This six-sided polygon appears in everything from animals and the structures that they build to crystalline formations and bubbles.
Hexagonal shapes appear again and again in nature due in large part to their efficiency. A flat surface covered by hexagons encloses equal areas using less total wall length than any other regular shape – as demonstrated by the cells in a honeycomb.
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By constructing the cells containing their eggs, larvae and honey in hexagonal form, bees can maximise the space inside their hives.
Known as the honeycomb theorem, this dates back to 36BC, when Roman polymath Marcus Terentius Varro first proposed it – although he couldn’t prove it. The theorem was eventually proven by the mathematician Thomas C. Hales, in 1999.
So, too, the keratinous scutes of a turtle shell, which cover its bony carapace, take a hexagonal form. They cover the shell efficiently from the start and allow it to grow in a stable way – the scutes keep pace with the growth of the bone beneath, expanding and leaving no gaps.
The hexagon shows its utility in the compound eyes of arthropods as well.
Tiny hexagonal facets, known as ommatidia, cover the dome-like surface of the eye, allowing for maximum field of vision.
Strangely, as the arthropod grows, each facet starts out as a square at the edge of the dome and later becomes a hexagon, slotting into the array of others preceding it.
Hexagons appear in inanimate objects as well.
Many crystals take hexagonal forms because the process requires the least amount of energy and results in the greatest structural stability. Of course, crystals take many other shapes, due to chemical structures and the forces acting upon them.
But many recognisable crystals do take the shape of hexagons – from snowflakes and the quartz crystal spears found in gift shops to basalt resulting from cooling lava.
Even the froth of bubbles in your bath skews hexagonal.
While not every junction between a bubble is hexagonal, most of them are – for the same reasons that honeycombs and crystals are six-sided.
The forces between the air inside the bubbles and the surface tension of the soap are most evenly and stably supported in this shape.
Top image: a bee on a flower. Credit: David Labat Seguin/500px/Getty Images
