Cone - Other Mathematical Meanings

Other Mathematical Meanings

In mathematical usage, the word "cone" is used also for an 'infinite cone', the union of a set of half-lines that start at a common apex point and go through a base. Observe that an infinite cone is not bounded by its base and extends to infinity. A 'doubly infinite cone', or 'double cone', is the union of a set of straight lines that pass through a common apex point and go through a base, therefore double infinite cones extend symmetrically on both sides of the apex.

The boundary of an infinite or doubly infinite cone is a conical surface, and the intersection of a plane with this surface is a conic section. For infinite cones, the word axis again usually refers to the axis of rotational symmetry (if any). Either half of a double cone on one side of the apex is called a 'nappe'.

Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.

Also, an oblique shaped cone is known as a circular based pyramid due to the inwardly converging hypos towards the apex point.