Hyperboloid

All screws of a given pitch belonging to a system of the third order are the generators of a certain hyperboloid. There is... a different hyperboloid for each pitch. ...all these hyperboloids are concentric.

— Hyperboloid

[F]or the hyperboloid of one sheet and the hyperbolic paraboloid the curvature is negative at every point.

— Hyperboloid

Upon the hyperboloid of one sheet, and likewise upon the hyperbolic paraboloid, the two lines of striction coincide.

— Hyperboloid

[F]or the bare hyperboloid, both real and Lambertian sources are in the same plane. This is a limitation in certain applications; however, we can manipulate these positions with lenses to place the sources at more convenient locations. ...this is an ideal concentrator. ...we have postulated an ideal lens while the hyperboloid is an ideal concentrator, albeit operating on a virtual source. The design considerations readily follow from the geometry of the hyperbola.

— Hyperboloid