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Asymmetric rounded-typical pseudo-ovoids: 1, 9, 17) construction of ovoids in the shape matrix; 2), 10), 18) egg profile diagram; bird egg profiles: 3) Fringilla coelebs; 4) Tetrastes bonasia; 5) Chloris chloris; 6) Fulica atra; 7) Sturnus vulgaris; 8) Turdus merula; 11) Acrocephalus palustris; 12) Turdus viscivorus; 13) Cuculus canorus; 14) Oriolus oriolus; 15) Luscinia luscinia; 16) Dendrocopos major; 19) Haematopus ostralegus; 20) Remiz pendulinus; 21) Porzana porzana; 22) Anthropoides virgo; 23) Cygnus cygnus;24) Anas strepera.
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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...
Citations
... Alongside the initial applications of Hügelschäffer curves in aero-engineering (see [7], [11]), recently, there has been research on the applications of these curves in: architecture and civil engineering (see [30], [32]); poultry industry, ornithology and bioengineering (see [15], [23], [24], [25], [26], [27], [28]); traffic engineering (see [34]) and hydro-engineering (see [14], [33], [44]). To aid in the application of Hügelschäffer curves and the practical usage of the area formulae for these curves, we have developed the applet [21]. ...
In this paper, we give new Taylor approximative formulae for the area of the egg-shaped parts of Hügelschäffer curves. Based on a parametrization of the Hügelschäffer curve, a formula for the area of the egg-shaped part of such a curve is derived via elliptic integrals of the first and second kind. Furthermore, new approximative formulae for calculating this area derived from standard and double Taylor approximations are given. A representation of the value 1/π was also obtained using an appropriate series.
... These geometrical constructions fully coincide with the profiles of real eggs (Fig. 5). Previously, we made the same comparison with curves from various mathematicians, drawings of architectural structures, profiles of sewage pipes, works of art, and obtained similar results (Mytiai, Matsyura, 2019;Mytiai et al., 2020). ...
... The most surprising thing was that the geometrically constructed ovoids completely coincide with the profiles of the birds' eggs. Furthermore, as we noted previously (Mytiai and Matsyura, 2019;Mytiai et al., 2020), ovoids are widespread in human life. In construction, they are present in architectural structures -houses, temple domes (Rossi and Fiorillo, 2020;Petrovic et al., 2011;Dean, 2021) and egg-shaped architectural ornamentation (Craven, 2019). ...
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.
... Typically, there are various ways to develop formulas to describe shapes and phenomena. Various equations for bird eggs have been reviewed recently [20], and there are many more [18], [21]. The main goal should be to apply mathematics to the natural sciences in the best possible way. ...
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections
This paper presents the preface of the proceedings for the 4th International Conference on Sustainable Futures: Environmental, Technological, Social, and Economic Matters (ICSF 2023), a multidisciplinary event that explores the challenges and opportunities of sustainability in various domains. The preface outlines the conference’s objectives, themes, workshops, and topics, as well as its contribution to advancing sustainable development and global dialogue. It also acknowledges the efforts and inputs of various stakeholders who have made the conference possible, especially in light of the pandemic situation. Furthermore, it thanks IOP Publishing for its support and flexibility in facilitating open access publishing. The paper concludes by looking forward to future editions of ICSF and the ongoing quest for a more sustainable and interconnected world. The paper invites readers to delve into the rich and diverse content that shapes this influential conference.
The shape of birds' eggs has fascinated scientists for many years. It is now possible mathematically to describe shape accurately, allowing exploration of the physical and ecological factors driving the evolution of egg shape. However, there has been relatively little consideration of how egg shape is established in the oviduct or, given that even without an external calcitic layer eggs retain their shape, how shape is fixed in the isthmus. This paper proposes a hypothesis that attempts to explain how egg shape is established and fixed in the oviduct. The hypothesis suggests that as the egg mass (i.e. yolk and albumen) moves from the magnum into the isthmus, it is squeezed by the physical restriction imposed by the isthmus lumen and cannot easily move into the isthmus. As the leading edge of the egg mass enters the isthmus, the egg mass in the distal magnum is forced to bulge outwards, resulting in an asymmetrical shape. The various egg shapes observed in birds are, hence, produced by the interaction between the size of the egg mass relative to female body mass, and the degree of the restriction of the isthmus. Thus, a large egg mass, i.e. relative to female body mass, entering a narrow isthmus will produce a pointed egg shape. If the egg mass is relatively small, and the isthmus lumen wide, more of the egg mass could enter the isthmus and the degree of asymmetry would be reduced. It is further proposed that egg shape is fixed during the formation of the shell membranes in the isthmus because the constituent protein fibres permanently stick together as they are deposited. For the first time this hypothesis helps explain the pattern of deposition and characteristics of the calcitic egg in relation to the diversity of egg shapes in birds and reptiles.
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) a direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections.
