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.