Cone

Article By:

Frame, J. Sutherland Formerly, Department of Mathematics, Michigan State University, East Lansing, Michigan.

Last reviewed:January 2020

DOI:https://doi.org/10.1036/1097-8542.156200

The solid of revolution obtained by revolving a right triangle about one of its shorter sides is called a cone, or more precisely a right circular cone (see illustration). More generally, the term cone is used in solid geometry to describe a solid bounded by a plane and a portion of one nappe of a conical surface. In analytic geometry, however, the term cone refers not to a solid but to a conical surface. This is a surface generated by a straight line which moves so that it always intersects a given plane curve, called the directrix, and passes through a point, called the vertex, not in the plane of the directrix. The generating line in each of its positions is called an element of the cone. The vertex divides the surface into two parts, called nappes, that are congruent to each other in the extended sense (under rotation and reflection combined) but may not be superposable by a rigid motion in three-dimensional space.

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