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cone, in mathematics
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.
(mathematics). (1) A cone, or conical surface, is the locus of lines (generators) in space that join all the points of a curve (directrix) to a given point (vertex) in space. If the directrix is a line, then the cone reduces to a plane. If the directrix is a curve
of the second degree not lying in the same plane as the vertex, then we obtain a quadric conical surface (see Figure 1, where the directrix is an ellipse). The simplest surface of this type is a circular, or right circular, cone, whose directrix is a circle and whose vertex can be orthogonally projected to the center of the circle.
(2) In elementary geometry, a circular cone is a geometric solid bounded by the surface of a circular cone and the plane containing the directing circle (Figure 2). Its volume is equal to πr2h/3, and its lateral area to πrl If a cone is cut by a second plane parallel to the first, a frustum of the cone (Figure 3) is obtained, whose volume is equal to π(R2 + r2 + Rr)h/3 and whose lateral area is π(R + r)l.