Behind the shape of an egg is a universal equation

This is a significant step in understanding how and why the shape evolved. Researchers have discovered a mathematical formula that can describe any bird egg that exists in nature.

The egg shape has long attracted the attention of mathematicians, engineers, and biologists for its evolution into being large enough to incubate an embryo and small enough to emerge from a bird’s body and not roll away once laid. The egg is structurally sound enough to support the weight of the chick and has been called the “perfect shape.” Researchers at the University of Kent, the Environmental Treatment Research Institute and Vita-Market Ltd have discovered a universal mathematical formula that can describe any bird egg that exists in nature, a feat that had never been successful until now.

The universal equation that describes the shape of an egg

Four geometric figures were used to analyze all egg shapes: sphere, ellipsoid, ovoid and pyriform (conical or pyriform), with a mathematical formula for the pyriform yet to be derived. To correct for this problem, the researchers introduced an additional function into the ovoid formula, developing a mathematical model to fit an entirely new geometric shape characterized as the last stage in the evolution of the sphere-ellipsoid, applicable to any egg geometry.

This new universal mathematical formula for egg shape is based on four parameters: length, maximum width, vertical axis displacement, and diameter at one-quarter of the egg’s length. The discovery represents a significant step in understanding not only the shape, but also how and why it evolved, making biological and technological applications possible. For example, this new equation can be applied to the engineering construction of thin-walled egg-shaped vessels, which are expected to be stronger than typical spherical ones.

Describing the egg using a mathematical formula simplifies work in the fields of biological systematics, optimization of technological parameters, incubation and poultry selection. But it can also be useful for designing engineering systems and cutting-edge technologies as well as in architecture to identify how much load an ovoid structure can support with minimal material consumption. “Biological evolutionary processes such as egg formation need to be studied mathematically as a basis for research in evolutionary biology,” said Darren Griffin, professor of genetics at the University of Kent and one of the authors of the research. The new “universal formula can be applied to fundamental disciplines, particularly the food and poultry industries, and will serve as an impetus for further investigations inspired by the egg as an object of research,” the scholar explained.

In Israel, archaeologists found a 1,000-year-old egg that they accidentally broke.

Stefania Bernardini