Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio

Avian eggs represent a striking evolutionary adaptation for which shell thickness is crucial. An understudied eggshell property includes the neutral axis, a line that is drawn through any bent structure and whose precise location is characterized by the k-factor. Previous studies have established that, for chicken eggs, mean k corresponds to the golden ratio (phi = 1.618, or 0.618 in its reciprocal form). We hypothesized whether such an arrangement of the neutral axis conforms to the eggshell of any bird or only to eggshells with a certain set of geometric parameters. Implementing a suite of innovative methodological approaches, we investigated variations in k of 435 avian species, exploring which correspond to phi. We found that mean k is highly variable among birds and does not always conform to phi, being much lower in spherical and ellipsoid eggs and higher in pyriform eggs. While 21 species had k values within 0.618 +/- 0.02 (including four falcon species) and the Falconinae subfamily (six species) revealed a mean of 0.618, it is predominantly domesticated species (chicken, ducks, and geese) that lay eggs whose neutral axis corresponds to the golden ratio. Thus, the study of the mathematical secrets of the eggshell related to the golden ratio of its neutral axis suggests its species-specific signatures in birds.

Automated summary

This study investigates the variation in the k factor of the neutral axis in avian eggs and finds that not all bird species conform to the golden ratio. The neutral axis in eggs of domesticated species, such as chicken, ducks, and geese, corresponds to the golden ratio, while spherical and ellipsoid eggs have lower k values and pyriform eggs have higher k values.