Bees and wasps build space-efficient and strong nests using hexagonal cells

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The question of why honey bees adapted to building their nests from hexagonal cells has been debated for centuries. In On the Origin of Species, Darwin theorized that natural selection led to “an economy of wax.” Being frugal with wax is wise work for a honey bee given they need to consume approximately eight pounds of honey to produce one pound of wax.

But it took mathematicians studying the hexagon shape to make a beeline to the truth. Around 36 B.C., a scholar by the name of Marcus Terentius Varro first wrote about this particular math problem, later dubbed the “the honeycomb conjecture,” by stating that, compared to other shapes such as a triangle or a square, a “hexagon inscribed in a circular figure encloses the greatest amount of space.”

In a 2019 interview, Thomas Hales—the mathematician who finally proved the conjecture—said that ultimately, “A hexagonal honeycomb is the way to fit the most area with the least perimeter.” From a bee’s perspective, that means storing more honey in a larger volume while spending less energy building a structure to contain it. In other words, Darwin was right.

And space-efficiency isn’t the only benefit of building with hexagons. Stacked together, hexagons fill spans in an offset arrangement with six short walls around each “tube,” giving structures a high compression strength. Beehives also dissipate heat well, preventing the waxy structure from melting on hot days. Though few species of wasps store honey, they too build nests using hexagonal cells, taking advantage of these same benefits. Efficiency, strength, and controlled heat loss are all important for human structures as well, so it’s no wonder that honeycombs inspire human design.

Scientists and engineers have incorporated hexagonal designs into seemingly endless applications, including light-weight building materials, flexible panels for bridge construction, sound absorption, light diffusion, catalyst design, magnetic shielding, tissue engineering, and even building better surfboards.

“He must be a dull man who can examine the exquisite structure of a comb, so beautifully adapted to its end, without enthusiastic admiration,” wrote Darwin. As we examine these structures more than a century and a half later, we’re still finding new things to admire and emulate.

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“Through thousands of years of exploration, we have gone beyond the traditional awareness of the exceptionally high mechanical strength as the only characteristic of honeycomb structures, and have gradually deepened our understanding of multifunctional design principles for honeycomb structures.”

Journal article
Bioinspired engineering of honeycomb structure – Using nature to inspire human innovationProgress in Materials ScienceQiancheng Zhang, Xiaohu Yang, Peng Li, Guoyou Huang, Shangsheng Feng, Cheng Shen, Bin Han, Xiaohui Zhang, Feng Jin, Feng Xu, Tian Jian Lu

“In part because of the isoperimetric property of the honeycomb, there is a vast literature through the centuries mentioning the bee as a geometer. . . During the 18th century, the mathematical architecture of the honeycomb was viewed as evidence of a great teleological tendency of the universe.”

Journal article
The Honeycomb ConjectureDiscrete Computational GeometryThomas C. Hales

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