# Egg and math: introducing a universal formula for egg shape

Narushin, Valeriy G., Romanov, Michael N, Griffin, Darren K. (2021) Egg and math: introducing a universal formula for egg shape. Annals of the New York Academy of Sciences, 1505 (1). pp. 169-177. ISSN 0077-8923. (doi:10.1111/nyas.14680) (KAR id:89885)

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## Abstract

The egg, as one of the most traditional food products, has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view. As a main parameter in oomorphology, the shape of a bird's egg has, to date, escaped a universally applicable mathematical formulation. Analysis of all egg shapes can be done using four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have a clear mathematical definition, each derived from the expression of the previous, but a formula for the pyriform profile has yet to be derived. To rectify this, we introduce an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere—ellipsoid—Hügelschäffer's ovoid transformation, and it is applicable to any egg geometry. The required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical analysis and description represents the sought-for universal formula and is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications theoretically possible.

Item Type: Article 10.1111/nyas.14680 egg geometry; egg shape; pyriform ovoid; Hügelschäffer's model; oomorphology; universal formula Q Science > QA Mathematics (inc Computing science)Q Science > QA Mathematics (inc Computing science) > QA440 GeometryQ Science > QH Natural history > QH324.2 Computational biologyQ Science > QL ZoologyS Agriculture > SF Animal culture Divisions > Division of Natural Sciences > Centre for Interdisciplinary Studies of ReproductionDivisions > Division of Natural Sciences > Biosciences Food Systems, Natural Resources and Environment Mike Romanov 24 Aug 2021 05:27 UTC 09 Jan 2024 10:48 UTC https://kar.kent.ac.uk/id/eprint/89885 (The current URI for this page, for reference purposes)

## University of Kent Author Information

### Romanov, Michael N.

Creator's ORCID: https://orcid.org/0000-0003-3584-4644

### Griffin, Darren K..

Creator's ORCID: https://orcid.org/0000-0001-7595-3226