Math World Egg-static About New Egg-shape Equation

By: Jesslyn Shields  | 

egg sizes
The long sought after universal formula for egg shape is a big step in understanding how and why the shapes evolved, which will make important technological and biological applications possible. Philipp Schulze/picture alliance/Getty Images

Birds lay eggs, but not all of them are built the same. A chicken, for instance, lays elliptical eggs, while King penguin eggs are teardrop shaped. And while not all eggs are created equal, they all have a similar job: to be big enough to incubate a baby bird while small enough to efficiently pass out of a mama bird's body. Not only that, but they also have to be able to bear the weight of a parent's body, and under no circumstances should their shape allow them to roll. Birds have perfected all this, as did their dinosaur ancestors before them.

Not that it was easy — or easy to understand. Scientists, engineers and mathematicians have long puzzled over eggs. There are four general shapes an egg can be: sphere, ellipsoid, ovoid and what's known as pyriform, or pear-shaped. While the shapes of the first three have been described by mathematicians with equations, the geometry of the fourth, conical shape has had egg experts scratching their heads for years.


Research published in August 2021 in Annals of the New York Academy of Sciences has cracked the case of a mathematical formula that can describe the shape of every bird egg. Unlike previous formulas, this one covers pyriform, or "pear-shaped" eggs, which are laid by penguins and wading birds.

The research team at the University of Kent added a function to the formula for the ovoid egg shape to create a universal formula that can describe any egg you might stumble upon. The measurements needed for the formula are the egg length, maximum breadth, shift of the vertical axis and the diameter at one quarter of the egg length. Here is the basic formula:

egg sizes
The formula covers pyriform, or "pear-shaped" eggs, such as those from penguins and wading birds.
Kent School of Biosciences/HowStuffWorks

The quest for this formula might not seem to have much in the way of practical application, but it can help scientists understand more about how eggs evolved. It will also be helpful to engineers trying to emulate the elegant, thin-walled strength of an egg in other, human-made structures. And that's not all.

"We look forward to seeing the application of this formula across industries, from art to technology, architecture to agriculture," study co-author Valeriy Narushin said in a press release. "This breakthrough reveals why such collaborative research from separate disciplines is essential."