Where the Shape of the Egg Comes From?

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.

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“…14-16). Cartesian ovals: а) with p = 1, q = 2 and c = 5; b) with p = 1, q = 3 and c = 5 (Beverlin, 2006); с) hyperbolic cone (Kirsh, 2010).…”

Section: Discussionmentioning

confidence: 99%