Definition:Cone (Geometry)
This page is about Cone in the context of Geometry. For other uses, see Cone.
Definition
A cone is a three-dimensional geometric figure which consists of the set of all straight lines joining the boundary of a plane figure $PQR$ to a point $A$ not in the same plane of $PQR$:
Parts of Cone
Base
The plane figure $PQR$ is called the base of the cone.
Apex
In the above diagram, the point $A$ is known as the apex of the cone.
Directrix
Let $K$ be a cone.
Let $B$ be the base of $K$.
The boundary of $B$ is known as the directrix of $K$.
Generatrix
Let $K$ be a cone.
Let $A$ be the apex of $K$.
Let $B$ be the base of $K$.
Then a line joining the apex of $K$ to its directrix is a generatrix of $K$.
Lateral Surface
Let $K$ be a cone.
The curved area of $K$ is known as the lateral surface of $K$.
Axis
Let $K$ be a cone whose base has a center of symmetry $C$.
Let $\LL$ be the straight line from the apex of $K$ to $C$.
Then $\LL$ is known as the axis of $K$.
Altitude
Let a perpendicular $AE$ be dropped from the apex of a cone to the plane containing its base.
The line segment $AE$ is an altitude of the cone.
Height
Let a perpendicular $AE$ be dropped from the apex of a cone to the plane containing its base.
The length $h$ of the line $AE$ is the height of the cone.
Classification
Cones are classified according to the shape of the base, for example:
Circular Cone
A circular cone is a cone which has a base whose shape is a circle.
Elliptical Cone
An elliptical cone is a cone which has a base whose shape is an ellipse.
Right Cone
A right cone is a cone which has an axis which is perpendicular to its base.
Oblique Cone
An oblique cone is a cone whose apex does not intersect a perpendicular through the center of its base.
Right Circular Cone
A right circular cone is a cone:
- whose base is a circle
- in which there is a line perpendicular to the base through its center which passes through the apex of the cone:
- which is made by having a right-angled triangle turning along one of the sides that form the right angle.
Double Napped Cone
A double napped cone is a cone where the lines joining the apex to the circumference of the base extend indefinitely in either dimension:
Also see
- Results about cones can be found here.
Linguistic Note
The adjectival form of cone is conical.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cone
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cone
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- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): cone