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5 December 2013 11:26 am ,
Vol. 342 ,
Researchers have been hot on the trail of the elusive Denisovans, a type of ancient human known only by their DNA and...
Thousands of scientists in the Russian Academy of Sciences (RAS) are about to lose their jobs as a result of the...
Dyslexia, a learning disability that hinders reading, hasn't been associated with deficits in vision, hearing, or...
Exotic, elusive, and dangerous, snakes have fascinated humankind for millennia. They can be hard to find, yet their...
Researchers have sequenced and analyzed the first two snake genomes, which represent two evolutionary extremes. The...
Snake venoms are remarkably complex mixtures that can stun or kill prey within minutes. But more and more researchers...
At age 30, Dutch biologist Freek Vonk has built up a respectable career as a snake scientist. But in his home country,...
Since arriving on the island of Guam in the 1940s, the brown tree snake ( Boiga irregularis ) has extirpated native...
- 5 December 2013 11:26 am , Vol. 342 , #6163
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Bees Do It Best
24 August 1999 5:30 pm
Honey may be sweet, but honeybees' engineering is even sweeter. A mathematician has proved that a comb's hexagonal lattice allows bees to store the most honey for the least amount of beeswax. The proof, presented last month at the Turán Workshop in Mathematics, Convex and Discrete Geometry in Budapest, ends centuries of speculation--and confirms the intuition of human engineers, who use honeycombed materials to produce light but strong panels for cars, planes, and spacecraft.
Since at least the first century, researchers have theorized that a hexagonal lattice is the most economical design for a honeycomb's single layer of equal-sized cells. Until this summer, however, no one could mathematically confirm the hunch.
Now, Thomas Hales of the University of Michigan, Ann Arbor, has shown that a hexagonal honeycomb has walls with the shortest total length, per unit area, of any design that divides a plane into equal-sized cells. The proof, which Hales began working on last year, builds on his earlier work showing that equal-volume bubbles in a wet foam will form a regular lattice. But no one knew if that result applied to a honeycomb, which Hales says is more like a dry foam in which the bubbles squeeze one another's shape, leading to tradeoffs in volume. In the most efficient dry foam, the cells might have different shapes. Hales, however, showed that a beehive's hexagonal compartments optimize the gains and losses when the effect of each cell on its neighbors is taken into account, giving the most efficient overall arrangement.
While other mathematicians had made progress on the problem, Hales is the first to propose a method which correctly accounts for the costs and benefits of making the sides of a cell curved or using more than 6 sides in a cell, says John Sullivan of the University of Illinois at Urbana-Champaign. "Hales's bright idea was that no single cell can do better than a hexagon if appropriately penalized," he says. And he and other geometers are pleased that the proof, unlike similar solutions, does not require elaborate computer calculations. "There should be an easy reason for a pattern this simple," Sullivan says, "and I think Hales has found it."