“There are a lot of hypotheses, but no conclusive explanation or theory,” says Stoddard, who’s an evolutionary biologist based at Princeton University. “It was a good puzzle.”

To solve it, Stoddard teamed up with L. Mahadevan, a biophysicist at Harvard University who has studied “how leaves ripple, how tendrils coil, and how the brain folds, among other things.” He realized that all eggs could be described according to two simple characteristics—how asymmetric they are, and how elliptical they are. Measure these traits, and you can plot every bird egg on a simple graph. They did that for the eggs of 1,400 bird species, whose measurements Stoddard extracted from almost 50,000 photos. It was the resulting graph that revealed the left-field nature of chicken eggs.

As well as measuring eggs, the team also collected a huge amount of data for their 1,400 bird species, including body mass, clutch number, diet, nest location, how quickly they grow, the climate in which they live, and more. Some of these factors can explain egg size—bigger birds with smaller clutches tend to have longer eggs—but to the team’s surprise, none of these factors explained egg shape. This meant that many of the existing hypotheses for egg shape don’t actually hold up when you study a lot of eggs. Cliff-nesting birds, for example, don’t have pointier-than-average eggs.

In fact, only one factor correlated well with egg shape: a bird’s flying ability. You can quantify that by measuring a bird’s wing. The wingtips of the most accomplished aeronauts are longer relative to their hand bones. And as Stoddard’s team found, these good fliers are also more likely to have asymmetric and elliptical eggs. “I was truly surprised by that,” she says.

You can see that pattern across the birds in general, and you can even see it within closely related groups. Hummingbirds are great fliers, but their closest relatives—the swifts—are even better, and while hummingbird eggs are symmetrical, swift eggs are pointed, more like pine nuts than Tic Tacs. Owls tend to have spherical eggs, but the better fliers among them, like barn owls, have more elliptical ones than their relatives.

Penguins are exceptions that prove the rule. They may be flightless but they swim by essentially flying underwater, so their eggs are pointed rather than symmetric; they were probably influenced by the same evolutionary forces that create asymmetric eggs in strong airborne fliers.

Those forces are not obvious, but they’re related to the way eggs are built. It begins when an unfertilized egg cell is added to a globule of yolk, and sent down a bird’s oviduct—a long canal that Stoddard describes as “a stretchy tube like a sock or pantyhose.” On its travels, it is fertilized by sperm, surrounded by white, and coated in two membranes. The membranes are pumped with fluid like a balloon being inflated, and finally surrounded by a shell. Counter-intuitively, it’s not the shell that matters most, but the membranes. If you dissolve the shell in acid, the naked egg will still retain its original shape.