ovoide

Ovoide is a term used to describe something egg-shaped or resembling an egg in silhouette. The word derives from the Latin ovum, through various languages, and is commonly applied in everyday language as well as in technical contexts to denote a rounded, elongated form with a tapering ends.

In geometry, an ovoid (also encountered as ovoide in some languages) refers to a strictly convex solid whose boundary is smooth and has positive Gaussian curvature at every point. In this sense, an ovoid generalizes the idea of an ellipsoid while not requiring the perfect symmetry of a true ellipsoid. Egg-shaped solids that are not exact ellipsoids fall under this broad geometric intuition, and the term highlights their convex, closed, and smoothly curved nature.

In finite and projective geometry, an ovoid has a more specific meaning. In the projective space PG(3,q), an ovoid is a set of q^2+1 points with no three collinear, and it can be realized as the point set of an elliptic quadric Q^−(3,q). Ovoids in this sense play a role in the study of incidence structures and related combinatorial objects, such as generalized quadrangles.

Beyond formal contexts, ovoide-like shapes appear in biology, geology, architecture, and product design to describe objects that are distinctly egg-shaped, balancing elongated form with rounded ends. See also: oval, ellipsoid.