Symmetry

The property of symmetry describes certain physical phenomena, geometric shapes, and mathematical equations that remain unchanged despite changes in orientation or other properties. This illustration shows three geometric shapes and indicates the manner in which they are symmetrical. The top two figures remain unchanged as they revolve around a central point, while the lower triangle can rotate 180 degrees about a central line without changing.

Cone (geometry)

Cone (geometry), in geometry, surface generated by a straight line that moves along a closed curve while always passing through a fixed point. The straight line is called the generatrix, the fixed point is called the vertex, and the closed curve is called the directrix. If the generatrix is of infinite length, it generates two conical surfaces on opposite sides of the vertex. If the directrix of the cone is a circle, the cone is usually referred to as a circular cone.

Mathematicians study oblique cones (in which the axis is not perpendicular to the plane of the base) and various noncircular cones (in which the base is in the form of an ellipse or some other closed curve). The surface that is commonly called a cone, however, is the right circular cone.

Definition of a Cone

A cone is defined as the surface swept out by a straight line, called the generatrix, as it travels all the way around a closed curve, called the directrix, while remaining in contact with a fixed point, called the vertex. An infinitely long generatrix forms two cones, point to point.