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Math: Finally a universal equation to describe the shape of an egg!

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Maria Gill
Maria Gill
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Teams of scientists from the University of Kent in England and the Environmental Remediation Research Institute in Ukraine have come up with a solution to this puzzle. They published the results of their work in the journal Annals of the New York Academy of Sciences, edited by New York Academy of Sciences.

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It’s not just a simple question about shape

The seemingly simplified shape of the egg is one of nature’s most unique and amazing shapes. It has intrigued the scientific world for a very long time. An equation was actually developed a few years ago, but it relates only to the spherical, oval and elliptical eggs of very specific species such as the eagle or the brown owl. Unfortunately, this equation does not apply to pear-shaped (pear-shaped) eggs like those of king or sniper penguins.

This is why a team of mathematicians at the University of Kent attempted to write a universal equation to describe the properties and behavior of all eggs.

With good reason, the role of the egg is crucial to the evolution and evolution of the species: it forms an envelope capable of allowing the perfect development of the embryo, it must withstand the constraints to which it is exposed during egg-laying, it must not roll during expulsion and it must withstand the weight of the bird incubating it.

This scientific discovery goes beyond a simple study of the mathematical laws that govern the oval shape of the egg. It will make it possible to understand the evolution of birds, a direct descendant of also egg-laying dinosaurs, but also to predict the behavior of increasingly common oval architecture by developing more efficient enclosures to protect them.broken chicken eggs.

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4D mathematical equation

It’s a multidisciplinary team, consisting of a mathematician, a biologist and an engineer, that tackled this seemingly insurmountable puzzle not so long ago.

All spheres, ellipticals, and ovals contain a mathematical equation. In fact, the mathematical equation for an ellipse is derived from knowing it from an ellipse which is itself a derivative of a sphere.

In order to come up with the “winning formula”, the scientists used the basic dimensions of an egg – its length, maximum width, and diameter as a quarter of its length. They also introduced an additional function, the offset of its vertical axis. By incorporating these values, which are easy to measure using traditional measuring tools, they succeeded in creating an equation that allows calculating the shape of all bird eggs, whether they are round like those of the Ural owl. , oval like that of the song slaw or pear-shaped like the thick-beaked Murre, a bird that nests along the coasts of the Arctic islands.

This new mathematical formula actually corresponds to the evolution of Transformation of Fritz Hogelschwer. Applicable to all types of eggs.

Applications in biology and architecture

This new mathematical equation finds applications in many disciplines. In the field of biology, it is now possible to improve some processes such as incubation, selection or even storage of eggs, just by incorporating easily measurable values ​​such as volume, area, radius or curvature of eggs. an egg.

But the most amazing applications of this mathematical formula are in architecture. Some ovals are used in architecture in the design of some buildings, especially those that are subjected to strong mechanical stresses due to the wind in particular. Many well-known buildings display this type of architecture, such as the 45-meter-high London City Hall and the nacelles of the London Eye (London Eye) also called the Millennium Wheel, a Ferris wheel in the British capital built in 1999.

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The new global equation applied to all whites should make it possible to improve the architecture of oval-shaped buildings that “grow” around the world by allowing them, among other things, to withstand more loads and stresses while using less materials.

In their study published in Annals of the New York Academy of SciencesMichael Romanov adds:This mathematical equation underscores our understanding and appreciation of a certain philosophical harmony between mathematics and biology. It paves the way for a deeper understanding of our universe, which here manifests precisely in the form of an egg.»

This study also highlights the astonishing value of pooling knowledge in different scientific disciplines. Who would have thought that biology and architecture would intersect around an egg?


Valery J. Narushin, Michael N. Romanoff, Darren K. Griffin, “Eggs and Mathematics: Introducing a Universal Formula for the Shape of Eggs,” Annals of the New York Academy of Sciences, August 23, 2021, Available here.

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