# The shape of a perfect egg, defined by a universal formula

The shape of an egg has been demonstrated throughout evolution to be one of the greatest characteristics for the embryonic development of egg-laying species. The form is ideal for the process of incubation, and its size is appropriate in relation to the body of animals for birth. Furthermore, eggs are well-designed to protect the fragile embryo away from the extremes of its immediate environment.

From an analytical standpoint, the egg, as one of the most traditional food items, has long piqued the interest of mathematicians, engineers, and biologists. To date, the shape of a bird’s egg has eluded a generally applicable mathematical definition as a key parameter in oomorphology. All egg forms may be analyzed using four geometric figures: the sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have unambiguous mathematical definitions, each derived from the preceding statement, but a formula for the pyriform profile has yet to be developed.

To address this issue, researchers added an extra function to the ovoid formula, creating a mathematical model to suit a completely unique geometric shape defined as the last step in the evolution of the sphere-ellipsoid, which is applicable to any egg geometry. This universal formula is based on four parameters: egg length, maximum breadth, shift of the vertical axis, and the diameter at one-quarter of the egg length.

This mathematical equation underlines our understanding and appreciation of a certain philosophical harmony between mathematics and biology, and from those two a way towards further comprehension of our universe, understood neatly in the shape of an egg.’

Dr Michael Romanov, Visiting Researcher at the University of Kent

Mathematical descriptions of all fundamental egg forms have previously been used in food science, mechanical engineering, agriculture, biosciences, architecture, and aeronautics. This formula, for example, can be used in the engineering design of thin-walled egg-shaped containers that must be stronger than ordinary spherical ones.

This new formula represents a significant advance with several applications, including competent scientific description of a biological object, accurate and simple determination of the physical characteristics of a biological object, and future biology-inspired engineering.