saddleshaped

Saddleshaped is an adjective describing an object or surface that resembles a saddle, curving upward in one direction and downward in an orthogonal direction. In differential geometry, saddleshaped surfaces have negative Gaussian curvature at all points, meaning they are locally saddle-like rather than dome- or bowl-shaped.

A canonical mathematical example is the hyperbolic paraboloid, given by z = x^2 − y^2, which curves upward along the x-axis and downward along the y-axis. In multivariable calculus, the term is also used to describe a saddle point, a critical point where the function has a minimum along one direction and a maximum along another, so it is not a local extremum.

In applied disciplines, saddleshaped forms are used in architecture and structural design because they can distribute loads efficiently and create aesthetically distinctive shells or roofs. Saddleshaped domes or shells appear in modern architecture and are studied for their stiffness characteristics in engineering contexts.

In anatomy and dentistry, saddleshaped describes surfaces that resemble a saddle, such as articulating surfaces in saddle joints, for example the carpometacarpal joint of the thumb, where opposing surfaces are reciprocally curved to permit a wide range of motion.

The term is primarily descriptive and cross-disciplinary; more precise terminology is often preferred in specialized fields (for example, saddle surface in geometry or saddle joint in anatomy). Saddleshaped curvature is contrasted with spherical or cylindrical curvatures.