Skip to main content
Kent Academic Repository

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

Narushin, Valeriy G., Griffin, Alexander W., Romanov, Michael N, Griffin, Darren K. (2022) Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio. Annals of the New York Academy of Sciences, 1517 (1). pp. 143-153. ISSN 0077-8923. (doi:10.1111/nyas.14895) (KAR id:96707)


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 (Φ = 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 Φ. We found that mean k is highly variable among birds and does not always conform to Φ, 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.

Item Type: Article
DOI/Identification number: 10.1111/nyas.14895
Uncontrolled keywords: avian egg, eggshell, evolution, golden ratio, neutral axis
Subjects: Q Science > QA Mathematics (inc Computing science) > QA440 Geometry
Q Science > QH Natural history > QH324.2 Computational biology
Q Science > QL Zoology
S Agriculture > SF Animal culture
Divisions: Divisions > Division of Natural Sciences > Centre for Interdisciplinary Studies of Reproduction
Divisions > Division of Natural Sciences > Biosciences
Funders: University of Kent (
SWORD Depositor: JISC Publications Router
Depositing User: Mike Romanov
Date Deposited: 02 Sep 2022 14:50 UTC
Last Modified: 08 Sep 2023 18:04 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.