In mathematics, a cone is the quadric surface generated when a line is rotated around a fixed point (called the apex), at a fixed angle from another line (called the axis), both lines passing through that fixed point. It also can be described as the locus of all the points belonging to all the lines that pass through a given point, and that intersect at that point at a fixed angle to the axis line.
A cone is represented in Cartesian coordinates by the equation
- ax² + by² + cz² = 0.
A cone with its apex cut off by a plane parallel to its base is called a conical frustum.
In botany, the term cone refers to a roughly conical (that is, "cone-shaped" as defined above) structure characterized by scales or bracts arranged around a central axis, usually in conifers and cycads.