Well, compare a 13-year life cycle and a 12-year life cycle. Suppose there are predators with life cycles of 2, 3, 4, 5, 6, 7, 8 and 9 years. The cicadas need to come out of the ground when their predators are lying dormant.
Imagine the cicadas have a range of predators that also spend most of their lives in the ground. One explanation appeals to the fact that 13 and 17 are prime numbers. Why is it 13 and 17 years? Why not 12 and 14? Or 16 and 18? Then, every 13 or 17 years (depending on the subspecies), the cicadas emerge in great swarms for a period of around two weeks. There are two subspecies of North American periodical cicadas that live most of their lives in the ground. The honeycomb conjecture was first proposed in ancient times, but was only proved in 1999 by mathematician Thomas Hales.
If you want to fully cover a surface using tiles of a uniform shape and size, while keeping the total length of the perimeter to a minimum, hexagons are the shape to use.Ĭharles Darwin reasoned that bees have evolved to use this shape because it produces the largest cells to store honey for the smallest input of energy to produce wax. Why?Īccording to the honeycomb conjecture in mathematics, hexagons are the most efficient shape for tiling the plane.
More than 2,000 years later, philosophers and physicists are starting to take this idea seriously.Īs I argue in a new paper, mathematics is an essential component of nature that gives structure to the physical world.īees in hives produce hexagonal honeycomb.
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