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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.

Lower half of a mathematical cone

A cone is represented in Cartesian coordinates by the equation

ax² + by² + cz² = 0.

The shape called cone in more colloquial usage is half of a mathematical cone, being divided at the apex; or else more than half if it is removed at some distance from the apex (i.e., a frustum - see below). Common cone-shaped objects are an ice cream cone (with the point down), plastic traffic cones on roads for temporarily guiding traffic (with the point up), and pine cones (see botanical definition below).

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.

In vertebrate anatomy, a cone is a type of light-sensitive cell found along with rods in the retina of the eye.