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Egg geometrical calculations that include estimations of volume and surface areas are important for the poultry industry and in biological studies, as they can be used in research on population and ecological morphology, and to predict chick weight, egg hatchability, shell quality characteristics, and egg interior parameters. The research reported here is directed at the prediction of egg volume and surface area, and develops a formula that could be both accurate and suitable for calculations. The objective of this research was to improve the accuracy of the calculations of egg volume and surface area based on the measurements of the egg length and breadth. The experiment was carried out with 90 fresh eggs from a flock of Hy-Line Brown chicks at the age of 65 wk. The resulting formula for egg volume, V, was V = (0.6057 - 0.0018B)LB2 in which L is the egg length in millimeters, and B is the egg maximum breadth in millimeters. Egg surface area, S, was calculated as S = (3.155 - 0.0136L + 0.0115B)LB, in which both L and B are taken in millimeters.

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.

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The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

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