The shape of the humble and ubiquitous egg has long puzzled scientists, mathematicians and engineers because of the perfection of its design.
It is large enough to incubate an embryo, small enough to exit the body in the most efficient way, not roll away once laid, is structurally sound enough to bear weight and be the beginning of life for 10,500 species that have survived since the dinosaurs.
Now researchers in the UK have discovered the universal mathematical formula that can describe any bird’s egg existing in nature, a feat which they say has been unsuccessful until this point.
Previous analysis of all egg shapes has focused on four geometric figures: sphere, ellipsoid, ovoid, and pyriform (more commonly known as conical). But until now a mathematical formula for the pyriform has not been developed.
Mathematical model applies to any egg geometry
To rectify this, the researcher team introduced an additional function into the ovoid formula and have developed a mathematical model that is applicable to any egg geometry.
The research team is from the University of Kent, the Research Institute for Environment Treatment and Vita-Market Ltd.
Their new universal mathematical formula for the egg shape 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 long sought-for universal formula is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications possible,” they say in a media statement.
Used in fields like engineering and architecture
The mathematics surrounding eggs shapes is already used in fields such as food research, mechanical engineering, agriculture, biosciences, architecture and aeronautics.
As an example, this new formula can be applied to engineering construction of thin-walled vessels that are shaped like an egg. According to the researchers, these vessels would be stronger than typical spherical ones.
In architecture, egg-shaped geometry is already used in designs such as the roof of the London City Hall and the famous Gherkin skyscraper in London’s financial district. These designs can bear great loads using a minimum amount of material.
“We look forward to seeing the application of this formula across industries – from art to technology, architecture to agriculture. This breakthrough reveals why such collaborative research from separate disciplines is essential,” said Dr Valeriy Narushin, former visiting researcher at the University of Kent.