The pros and cons of the Preston–Biggins egg shape model: A reconsideration case based on mathematical modeling and simulation

The Preston egg profile model developed from an interdisciplinary research over 70 years ago remains a popular mathematical tool among formulae to define geometric bird egg contours. Biggins and colleagues transformed this into a mathematical formula with broader applicability (Preston–Biggins model), now considered to be the most accurate in describing egg shapes. However, an important principle of universality of mathematics in egg shape computations is compliance with the properties of a geometric solid of revolution; we previously postulated this model as the Main Axiom of the Mathematical Formula of the Bird’s Egg. Here, we tested the conformity of the Preston–Biggins model with this Main Axiom. The theoretical verification failed, however, as it was impossible to solve theoretically the fourth-order polynomial. Using numerical and simulation methods, we examined geometric egg profiles with several variants of their linear dimensions. When applying the Preston–Biggins model, high accuracy of actual egg profiles was demonstrated. For example, the root mean square error (RMSE) calculated for a standard chicken egg was equal to 0.007. This value increased slightly when evaluating conical eggs (0.01), but the accuracy of reproducing such a contour was still at a fairly high level. The calculated values of the relative root mean square error (RRMSE) ranged between 0.003 and 0.007. However, the Main Axiom principle was violated, leading to discrepancy between the maximum breadth and the value of its distance from the egg center. The pros of this model thus lie in the fact that it is applicable to real-world egg profiles, the cons in that it does not conform to the universality principle encapsulated in the Main Axiom.

Highlights

• Preston–Biggins model is considered as the most accurate in describing egg shapes.

• We tested it against the Main Axiom of the Mathematical Formula of the Bird’s Egg.

• Using numerical and simulation methods, we examined various geometric egg profiles.

• The pros of this model lie in the fact that it is applied to real-world egg profiles.

• The cons are that that it does not adhere to the Main Axiom universality principle.