Finally, an elusive equation defining all forms of bird eggs has been discovered.

The pear-shaped egg casing was the most difficult to crack.

Scientists have been attempting to solve a mathematical puzzle for years: is there an equation that correctly describes each and every bird egg? Variable shell forms make things more difficult. However, it turns out that the solution is straightforward.

Researchers explain in an upcoming edition of the Annals of the New York Academy of Sciences that a formula employing just four readily measurable parameters can compute the shape of every bird egg, be it round as a ping-pong ball, a smooshed spherical, oblong, or a curvy pear.  The eggs-perts had been stumped by that last form.

They were tethered to an equation that couldn't represent pyriform, or conical, eggs adequately.Researchers previously devised an algorithm that took into consideration spherical brown hawk owl eggs (SN: 6/22/17), elliptical emu eggs (SN: 10/31/18), ovoid osprey eggs, and other eggs of comparable form. The pear-shaped eggs of birds like great snipes and King penguins, however, did not follow this pattern.  

The length of the egg, its maximum width, its diameter at the point where its pointed end finishes, and the location of its maximum diameter in respect to the midpoint of its length are all required inputs for the new formula. The universal equation was created by adding one more function and putting the last diameter variable into existing egg math.

According to Darren Griffin, a geneticist at the University of Kent in England, who worked on the project with Kent biologist Michael Romanov and Valeriy Narushin, an agricultural engineer formerly at Kent, the discovery might have real-world ramifications. Knowing how to compute the shape of an egg, for example, might help designers construct better cushioned or form-fitting egg cartons, reducing grocery store waste and the frustrating experience of bringing a carton of eggs home, lifting the top, and finding your eggs smashed. Before leaving the store, “we're all required to check in the box,” but Griffin thinks it's easy to forget.

The equation might be useful in conservation efforts as well. "One of the considerations when restoring a bird species would be 'How likely are the eggs to break? Griffin adds. Knowing the math of an egg might help researchers determine which portions of the egg are more prone to breaking, which could then assist them choose where and how best to place them in certain ecosystems to help boost the population in those places.  According to Mark Hauber, an ornithologist at the University of Illinois at Urbana-Champaign, the formula's simplicity "makes this method practicable for field investigations" and might even allow researchers to obtain data from digital images.

The equation might be useful in conservation efforts as well. "One of the considerations when restoring a bird species would be 'How likely are the eggs to break?'" Griffin adds. Knowing the math of an egg might help researchers determine which portions of the egg are more prone to breaking, which could then assist them choose where and how best to place them in certain ecosystems to help boost the population in those places.  According to Mark Hauber, an ornithologist at the University of Illinois at Urbana-Champaign, the formula's simplicity "makes this method practicable for field investigations" and might even allow researchers to obtain data from digital images.

The universal formula is the first step in "solving such a puzzle." They're now working on a new set of egg challenges, such as finding a universal formula for calculating the volume and surface area of diverse eggs and delving into "mathematical shell mysteries," such as why shell thickness varies by species.

CITATIONS

V.G. Narushin, M.N. Romanov and D.K. Griffin. Egg and math: introducing a universal formula for egg shape. Annals of the New York Academy of Sciences, 2021. doi.org: 10.1111/nyas.14680.