The mysterious Golden Ratio is an incommensurable number which occurs organically throughout the universe. Beginning as 1.61803, the Golden Ratio continues forever without repeating, similar to Pi. Artists and architects have employed the number to guide design, and in the natural world the Golden Ratio often appears in the shape of a spiral. For example, think of a snail shell, a photo of a galaxy, or even some flowers. Better yet, watch this video:

Researchers at Kent State University observed that the coiling action of the butterfly proboscis — the tube-like mouthpart that many butterflies and moths use to feed on fluids — resembled a spiral similar to that of the Golden Ratio, and they decided to investigate. Their study, “The Golden Ratio Reveals Geometric Differences in Proboscis Coiling Among Butterflies of Different Feeding Habits,” appears in American Entomologist.

A galaxy, a nautilus shell, and the partially uncoiled proboscis of a red-spotted purple butterfly (Limenitis arthemis astyanax).

For their experiment, they collected six butterfly species with different feeding habits (nectar feeders, sap feeders, and puddle feeders) and used a high-speed camera to record proboscis-coiling configurations. The videos were then analyzed to isolate the frame that showed closeness to the Golden Ratio spiral.

Though proboscis geometry did not show a trend that matched the evolutionary relationships among the studied species, it was discovered that the Golden Ratio did relate to butterfly feeding habits, and sap-feeding butterflies have proboscis conformations that closely resemble the Golden Ratio. The researchers suggest that the differences in proboscis coiling conformations might relate to the substrates from which butterflies feed.

“This trend fits a pattern where nectar feeders primarily feed on fluids confined in floral tubes, sap feeders feed on exposed fluids of porous surfaces, and puddle feeders feed from both,” they wrote.

The researchers suggest that these findings can be used to predict the feeding habits of unstudied moths and butterflies, and they could provide the basis for further research on the connection between the structural configuration of proboscis coiling patterns and butterfly feeding habits.

“Although coincidental, it is fascinating that a mathematical occurrence can be used to reveal a widespread pattern at radically different scales, from galaxies to butterfly proboscises,” said lead author Matthew S. Lehnert.

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– The Golden Ratio Reveals Geometric Differences in Proboscis Coiling Among Butterflies of Different Feeding Habits