Their formula incorporates features of four geometric shapes: the sphere, ellipsoid, ovoid and pyriform (conical or pear-shaped). The last of these, the least well-known, is given in two dimensions by the following parametric curve: t → (cos2t, cos3 t × sin t ) for t* ∈ [0, π].
This modelling problem is more important than it might seem, because an egg's shape—varying notably from one species to another—affects the embryo's survival (the shape affects the egg's structural strength) and thus helps us investigate this evolutionary question mathematically.
The model has many practical applications in avian biology (parasite detection, in ovo sex identification, improved hatching rates…), and it also revives theoretical questions about the mathematical nature of the universe.
