Definition:Cone (Geometry)

Definition
A cone is a three-dimensional geometric figure which consists of the set of all straight lines joining the perimeter of a plane figure $ABC$ to a point $P$ not in the plane of the figure:


 * Cone.png

Base
The plane figure $ABC$ is called the base of the cone.

Apex
The point $P$ is known as the apex of the cone.

Height

 * HeightOfCone.png

Let a perpendicular $AE$ be dropped from the apex of a cone to the plane containing its base.

The length $h$ of the line $AC$ is the height of the cone.

Right Circular Cone
When a cone is under discussion, it usually means a right circular cone.

A right circular cone is a cone:
 * whose base is a circle;
 * A line perpendicular to the base through its center passes through the apex of the cone:


 * RightCircularCone.png

Axis
The perpendicular through the center of the base through the apex is called the axis of the cone.

Double Napped Cone
A double napped cone is one where the lines joining the apex to the perimeter of the base extend indefinitely in either dimension:


 * DoubleNappedCone.png

Comment
Hence the colloquial phrase "base over apex" as the description of a particularly flamboyant personal tumble.