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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, . ISSN 0077-8923. (doi:10.1111/nyas.14680) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (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
DOI/Identification number: 10.1111/nyas.14680
Uncontrolled keywords: egg geometry; egg shape; pyriform ovoid; Hügelschäffer's model; oomorphology; universal formula
Subjects: Q Science > QA Mathematics (inc Computing science)
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 > Biosciences
Signature Themes: Food Systems, Natural Resources and Environment
Depositing User: Mike Romanov
Date Deposited: 24 Aug 2021 05:27 UTC
Last Modified: 28 Aug 2021 07:06 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/89885 (The current URI for this page, for reference purposes)
Narushin, Valeriy G.: https://orcid.org/0000-0001-6799-6605
Romanov, Michael N.: https://orcid.org/0000-0003-3584-4644
Griffin, Darren K.: https://orcid.org/0000-0001-7595-3226
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