a conic section is a conic section of the same type (ellipse, parabola,...) one gets: Any plane section of an elliptic cone is a conic section. Obviously, any right circular cone contains circles. This is also true, but less obvious, in the general case (see circular section). The intersection of an elliptic cone with a concentric sphere is a spherical conic. Projective geometry In projective geometry, a cylinder is simply a cone whose apex is at infinity. Intuitively, if one keeps the base fixed and takes the limit as the apex goes to infinity, one obtains a cylinder, the angle of the side increasing as arctan, in the limit forming a right angle. This is useful in the definition of degenerate conics, which require considering the cylindrical conics. According to G. B. Halsted, a cone is generated similarly to a Steiner conic only with a projectivity and axial pencils (not in perspective) rather than the projective ranges used for the Steiner conic: "If two copunctual non-costraight axial pencils are projective but not perspective, the meets of correlated planes form a 'conic surface of the second order', or 'cone'." Generalizations The definition of a cone may be extended to higher dimensions; see convex cone. In this case, one says that a convex set C in the real vector space Rn is a cone (with apex at the origin) if for every vector x in C and every nonnegative real number a, the vector ax is in C. In this context, the analogues of circular cones are not usually special; in fact one is often interested in polyhedral cones. An even more general concept is the topological cone, which is defined in arbitrary topological spaces. See also Bicone Cone (linear algebra) Cylinder (geometry) Democritus Generalized conic Hyperboloid List of shapes Pyrometric cone Quadric Rotation of axes Ruled surface Translation of axes Notes References External links An interactive Spinning Cone from Maths Is Fun Paper model cone Lateral surface area of an oblique cone Cut a Cone An interactive demonstration of the intersection of a cone with a plane Elementary shapes Surfaces