What is an oval, officially and overall? Old and new mathematical descriptions

Deriving from the Latin “ovum” (egg), the oval is a commonly used term, but does not have the status of a standard geometric figure like a circle or ellipse. Consequently, the oval lacks both a mathematical descriptive basis to attribute a set of key geometric parameters and an elegant formula to describe its contours. Herein, we consider the basis for deriving the formula of an oval for typical egg profiles. Specifically, these are round, ellipsoid, classic oval, pyriform (conical) and biconical shapes. To do this, we adhered to four basic postulates: (i) the ability to describe all possible egg shapes; (ii) a minimum set of measurable geometric parameters; (iii) the application of some universal indices (ratios of key geometric dimensions) to describe mathematical models; (iv) conformity with the “Main Axiom of the Mathematical Formula of the Bird’s Egg.” Additionally, we sought to comply with the principles of mathematical elegance. Following these theoretical assumptions and practical verification, we obtained a mathematically supported, elegant formula for this well-known but non-standardized geometric figure. The derived oval geometry equation will find use in applied problems of biology, construction, engineering and school curricula, alongside the classical figures of the circle and ellipse.