cone (math)

cone or conical surface, in mathematics, surface generated by a moving line (the generator) that passes through a given fixed point (the vertex) and continually intersects a given fixed curve (the directrix). The generator creates two conical surfaces—one above and one below the vertex—called nappes. If the directing curve is a conic section (e.g., a circle or ellipse) the cone is called a quadric cone. The most common type of cone is the right circular cone, a quadric cone in which the directrix is a circle and the line drawn from the vertex to the center of the circle is perpendicular to the circle. The generator of a cone in any of its positions is called an element. The solid bounded by a conical surface and a plane (the base) whose intersection with the conical surface is a closed curve is also called a cone. The altitude of a cone is the perpendicular distance from its vertex to its base. The lateral area is the area of its conical surface. The volume is equal to one third the product of the altitude and the area of the base. The frustum of a cone is the portion of the cone between the base and a plane parallel to the base of the cone cutting the cone in two parts.

cone / kōn/ • n. 1. a solid or hollow object that tapers from a circular or roughly circular base to a point. ∎  Math. a surface or solid figure generated by the straight lines that pass from a circle or other closed curve to a single point (the vertex) not in the same plane as the curve. A cone with the vertex perpendicularly over the center of a circular base is a right circular cone. ∎  (also traffic cone) a plastic cone-shaped object that is used to separate off or close sections of a road. ∎  an edible wafer container shaped like a cone in which ice cream is served. ∎  a conical mountain or peak, esp. one of volcanic origin. ∎  (also pyrometric cone) a ceramic pyramid that melts at a known temperature and is used to indicate the temperature of a kiln. 2. the dry fruit of a conifer, typically tapering to a rounded end and formed of a tight array of overlapping scales on a central axis that separate to release the seeds. ∎  a flower resembling a pine cone, esp. that of the hop plant. 3. Anat. a light-sensitive cell of one of the two types present in the retina of the eye, responding mainly to bright light and responsible for sharpness of vision and color perception. Compare with rod (sense 5).

con·ic / ˈkänik/ chiefly Math. • adj. of or like a cone. • n. short for conic section. See also conics.