# A Universal Equation for the Shape of an Egg

Egg shapes have long fascinated the interest of mathematicians, biologists and engineers who are interested in how they work from an analytical perspective. Throughout evolution, the shape has been highly regarded because it is large enough to incubate an embryo while also being small enough to exit the body efficiently, stable enough to bear weight, and serves as the beginning of life for so many different kinds of species. The egg has been dubbed the "ideal shape" because of its shape.

### Analysis of an egg

All egg shapes were analysed using four geometric figures: the sphere, the ellipsoid, the ovoid, and the pyriform (conical or pear-shaped), the latter of which lacked a mathematical formula. The sphere, the ellipsoid, the ovoid, and the pyriform (conical or pear-shaped).

A mathematical model that fits a completely novel geometric shape, dubbed "the final stage of the sphere-ellipsoid evolution," was developed in order to address this problem. This mathematical model is applicable to any egg geometry and was developed by researchers by adding an additional function to the ovoid formula.

### Parameters that determine shape of an egg

Four parameters determine the shape of an egg, according to this new universal mathematical formula. These parameters are: egg length; maximum breadth; vertical axis shift; and egg diameter at one-quarter of the egg's length.

In addition to advancing our understanding of not only the egg shape, but also how and why it evolved, this long-awaited universal formula opens the door to a plethora of biological and technological applications.

Mathematics has already found applications in a variety of fields, including mechanical engineering, agriculture, food research, biosciences, aeronautics, and architecture, to name a couple. As an illustration, this formula can be used in the engineering design of thin-walled egg-shaped vessels, which should be stronger than typical spherical vessels because of their thin walls.

This new formula represents a significant advancement with a wide range of applications, including but not limited to those listed below:

1. A biological object that has been described in scientifically accurate detail. Because an egg can now be described mathematically, work in the fields of biological systematics, technological parameter optimization, egg incubation, and poultry selection will be significantly simplified. This will benefit everyone.
2. Determination of the physical characteristics of a biological object in an accurate and straightforward manner The external properties of an egg are critical for researchers and engineers who are developing technologies for incubating, processing, storing, and sorting eggs, among other things. An easy-to-understand identification procedure that makes use of the egg volume, surface area, radius of curvature, and other indicators to describe the egg's contours is required, and this formula fulfils that need.
3. The potential of bioinspired engineering in the future. The egg is a naturally occurring biological system that has been studied in order to develop engineering systems and cutting-edge technologies for use in the future. It is common to see the egg-shaped geometric figure in architecture, such as on the roof of London City Hall and the Gherkin, and construction because it is capable of withstanding heavy loads while consuming little material. This formula can be applied to egg-shaped geometric figures with relative ease.

Darren Griffin, a professor of genetics at the University of Kent and the study's principal investigator, made the following statement about the findings: "The mathematical descriptions of biological evolutionary processes such as egg formation must be investigated further, as demonstrated by this formula, in order to serve as a foundation for evolutionary biology research in general. With this universal formula, researchers can apply it across fundamental disciplines, particularly in the food and poultry industries. It will also serve as a springboard for further research into the egg as a research object in the future."

"This mathematical equation demonstrates our appreciation and understanding of a certain philosophical harmony between mathematics and biology," Dr Michael Romanov said in a statement.

Former University of Kent visiting researcher Dr Valeriy Narushin shared his thoughts on the subject: "The application of this formula across industries, from art to technology, architecture to agriculture, is something we are looking forward to seeing. This scientific breakthrough demonstrates the critical importance of cross-disciplinary collaboration in research projects."

The Annals of the New York Academy of Sciences publishes an article titled "Egg and math: establishing a universal formula for egg shape" that explores the relationship between eggs and mathematics.