cone,
n. 1. also called nappe. a. a solid with a plane base bounded by a closed curve every point of which is joined to a fixed point (the vertex) lying outside the plane of the base. A conical surface is swept out by a line segment,
such as VA above, with one end, V, fixed at the vertex and the other, A, tracing the curve. If no qualification is stated, the base is usually understood to be circular or elliptical; in the figure it is the plane ellipse ABCD. The volume of a circular cone is (1/3)πr2h, where r is the radius of the base and h is the perpendicular height of the cone. A right circular cone has its vertex perpendicularly above or below the center of the a circular base. See also frustum.
b. either of the infinite solids swept out by the infinite lines of which these segments are part. Two cones are thus generated, of which one has ABCD as a cross-section, and the other is a reflection of the first in the vertex V. 2. the infinite solid bounded by the locus of a line passing through a fixed point (the vertex) as it sweeps out a plane closed curve; this constructs two cones in the preceding sense, joined at the vertex. 3. in a vector space, a translate of any set that is closed under positive multiplication. Often a cone is required to contain the origin, and to be convex.
b. either of the infinite solids swept out by the infinite lines of which these segments are part. Two cones are thus generated, of which one has ABCD as a cross-section, and the other is a reflection of the first in the vertex V. 2. the infinite solid bounded by the locus of a line passing through a fixed point (the vertex) as it sweeps out a plane closed curve; this constructs two cones in the preceding sense, joined at the vertex. 3. in a vector space, a translate of any set that is closed under positive multiplication. Often a cone is required to contain the origin, and to be convex.