Abstract
The general principles of ovoid shapes and their mathematical interpretation were considered concerning previous data and experience. Previously, bird egg description was carried out using the composite ovoid model. According to this model, an ovoid is considered as a set of arcs with a smooth transition between them. The studied group of eggs was named true ovoid. They differ from other forms in size of their infundibular zone radius (thick end) that is almost equal to half of the diameter (0.5D ± 0.01 ˂ ri = 0.5D).We suggested that this commonality, a priori, implies the presence of an abstract geometric model, which is a satisfactory solution and logical approach for analyzing the diversity of natural ovoids. Such a model is a system of circles passing into each other. This allows, within a single system, to assign a vendor code to each form, which involves the name, geometric shape, and quantitative parameters that can be implemented in bird taxonomy.Early, 0.01 D was chosen as the model difference value and the ratio of symmetrical eggs in the analyzed database was 1.1%. In this research, we extended the difference value to 0.05 D and this covered 6.0% of the egg shapes. This is the maximum interval at which the curvature of the polar zones does not visually differ. We revealed that the variability in the egg shapes depends on the radii of curvature of the lateral and polar arcs. The larger the radius of the lateral arches, the greater the degree of freedom for variation of the lateral arches. We supposed that our data could associate any form of bird egg with its biological content. In turn, many ovoid features relevant to other natural objects can be used in bird taxonomical study.
Highlights
We revealed that the variability in the egg shapes depends on the radii of curvature of the lateral and polar arcs
This communication is a continuation of the article “Mathematical interpretation of artificial ovoids and avian egg shapes
We concluded that it is necessary to create the standards for bird egg shapes
Summary
This communication is a continuation of the article “Mathematical interpretation of artificial ovoids and avian egg shapes. In previous articles (Mytiai & Matsyura 2017, 2019), we discussed the ovoid form as one that is manifested in bird eggs and other animals, in the structure of their body parts, in the form of seeds and plant organs, and various spheres of human activity: architecture, art, philosophy, religion, and mathematics (see Rosin, 2001, Sullivan, 2019, Kosloski, 2020). The essential point is that all the above-mentioned forms arise independently of each other, and are a manifestation of the same regularity: the transition of symmetry (sphere) into asymmetry (ovoid) This transition is accompanied by the appearance of the new properties, the essence of which has a common basis (Jung et al, 2017, Church et al, 2019). We presented the data on the remaining 80 % of the eggs and their shapes
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