Discrete aggregate analysis of ovoid egg shapes in various bird species

Abstract

The shape from 16,491 eggs of 472 species of 19 groups of birds was studied. The analysis was carried out by photographing eggs using a specially written software. In parallel, profiles of different ovoids were built in the CorelDRAW software, by articulating circles of different diameters. Comparison of them with the profiles of real bird eggs showed complete identity. During further analysis, we found that the whole variety of shapes fits into a system of discrete aggregates described by the proportions: (a) ±√a±√b)/±√c: (a) ±√2±√1)/±√4 = (0.207; 1.207); (b) ±√3±√1)/±√4 = (0.366; 1.366); (c) ±√4±√1)/±√4 = (0.5; 1.5); (e) ±√5±√1)/±√4 = (0.618; 1.618). These proportions are universal constants of nature, similar to π and e (the base of the natural logarithm). Besides them, we realize another constant in eggs. This is the cross-ratio (or the double ratio or the wurf. The close connection between the shapes of bird eggs and the universal constants of nature allows us to solve the following problems. We therefore suggested that discussed patterns of the geometric model and the resulting form standards will contribute to the unification of egg analysis methods. We also believed that the suggested universal model and constants will resolve the question of quantitative expression of the optimal shape and incubation qualities of eggs.