Research finally reveals ancient, universal equation for the shape of an egg

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Researchers from Vita-Market Ltd, the Research Institute for Environment Treatment, and the University of Kent have found the universal mathematical formula that can describe any bird egg in nature. This feat was previously unsuccessful.

The egg-shape is a long-standing topic of interest to engineers and mathematicians. It has been widely regarded as a key element in evolution, large enough to incubate an egg, small enough not to roll away once it is laid, and structurally sound enough that it can support weight. This shape was also the starting point of life for the 10,500 species that have survived the extinction of the dinosaurs. The egg is often referred to as the "perfect shape."

Analyzing all egg shapes required four geometric figures: sphere (ellipsoid), ovoid and pyriform. A mathematical formula for the latter is still to be determined.

Researchers created a mathematical model that could fit any geometric shape.

The new universal mathematical formula to determine the shape of eggs is based upon four parameters: egg length and maximum breadth, shift on the vertical axis, egg diameter, and one-quarter of the egg length.

This long-awaited universal formula is an important step in understanding the egg shape and how it evolved. It also allows for widespread biological and technological applications.

Mathematical descriptions for all basic egg shapes have been used in food research, mechanical engineering and agriculture, as well as aeronautics and biosciences. This formula can be used to engineer thin-walled vessels of egg shapes, which should be more robust than spherical ones.

This formula is a significant breakthrough that has multiple applications, including:

Competent scientific description of biological objects. The mathematical description of an egg will make it much easier to work in the fields of biological systemics, optimization of technological parameters and egg incubation. It is easy to determine the physical characteristics of biological objects. Engineers and researchers who create technologies to incubate, process, store, and sort eggs need to know the egg's external characteristics. This formula is an easy way to identify eggs by their volume, surface area, radius, curvature, and other indicators. Future engineering inspired by biology. The egg is a natural system that can be used to develop engineering systems and other state-of the-art technologies. This egg-shaped geometric figure can be used in architecture (e.g., London City Hall's roof or the Gherkin) and construction because it can withstand maximum loads while using minimal materials.

Professor of Genetics at the University of Kent, Darren Griffin is the PI of the research. He says "biological evolutionary processes like egg formation must be explored for mathematical description as a basis to research in evolutionary biology. As demonstrated by this formula. This universal formula is applicable across all fundamental disciplines, including the food and poultry industries, and can be used to stimulate further research using the egg as a research object.

Dr. Michael Romanov is Visiting Researcher at University of Kent. He says that this mathematical equation "underlines our understanding of a certain philosophical harmony among biology and mathematics, and from these two a path towards further comprehension of the universe, understood neatly as an egg."

Valeriy Narushin was a former visiting researcher at University of Kent. She said that they look forward to the "application of this formula across industries from art to technology to architecture to agriculture." This breakthrough shows why it is important to collaborate across disciplines.

The research was published in the Annals of the New York Academy of Sciences.

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More information: Valeriy Narushin and colleagues, Egg and mathematics: Introducing a universal formula to shape eggs, Annals of the New York Academy of Sciences (2021). Valeriy G. Narshin et al., Egg and Math: Introducing a universal formula to determine egg shape. (2021). DOI: 10.1111/nyas.14680