# Mathematical progression of avian egg shape with associated area and volume determinations

Narushin, Valeriy G., Romanov, Michael N., Mishra, Birendra, Griffin, Darren K. (2022) Mathematical progression of avian egg shape with associated area and volume determinations. Annals of the New York Academy of Sciences, 1513 (1). pp. 65-78. ISSN 0077-8923. (doi:10.1111/nyas.14771) (KAR id:95513)

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## Abstract

Development of nondestructive techniques for estimating egg parameters requires a comprehensive approach based on mathematical theory. Basic properties used to solve theoretical and applied problems in this respect are volume (V) and surface area (S). There are respective formulae for calculating V and S of spherical, ellipsoidal, and ovoid eggs in classical egg geometry; however, the mathematical description and calculation of these parameters for pyriform eggs have remained elusive. In the present study, we derived the appropriate formulae and established that this would be not only applicable and valid for the category of pyriform eggs, but also universal and explicit for all other naturally occurring avian egg shapes. Thus, we have demonstrated “mathematical progression” of this natural object, considering the egg as a sequence of geometric figures that transform from one to another in the following sequence of shapes: sphere → ellipsoid → ovoid (whose profile corresponds to Hügelschäffer's model) → pyriform ovoid.

Item Type: Article 10.1111/nyas.14771 egg shape geometry, egg volume, surface area, nondestructive measurement, mathematical progression 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 Mike Romanov 21 Jun 2022 10:42 UTC 18 Nov 2022 04:34 UTC https://kar.kent.ac.uk/id/eprint/95513 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6799-6605 https://orcid.org/0000-0003-3584-4644 https://orcid.org/0000-0002-8786-3700 https://orcid.org/0000-0001-7595-3226