A universal formula for avian egg shape

The bird’s oomorphology has far escaped mathematical formulation universally applicable. All bird egg shapes can be laid in four basic geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical/pear-shaped). The first three have a clear mathematical definition, each derived from expression of the previous, but a formula for the pyriform profile has yet to be inferred. To rectify this, we introduced an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere—ellipsoid—Hügelschäffer’s ovoid transformation applicable to any avian egg shape geometry. Required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical description is invariably a significant step in understanding not only the egg shape itself, but how and why it evolved, thus making widespread biological and technological applications theoretically possible.