Hohlkegel

Hohlkegel, German for "hollow cone," refers to a geometric shape. It is the surface formed by lines passing through a fixed point, the apex, and intersecting a fixed circle, the directrix, which does not contain the apex. Imagine a cone with its interior removed, leaving only the curved outer surface. This surface extends infinitely in both directions from the apex.

The mathematical description of a hohlkegel is often given in terms of its apex, axis, and angle. The axis is a line that passes through the apex and the center of the directrix circle. The angle, known as the semi-vertical angle, is the angle between the axis and any of the generating lines. A hohlkegel can be visualized as two cones joined at their apexes, forming a double cone.

In applications, the term can refer to a physical object shaped like a hollow cone. For example, in optics, a hohlkegel can be used to direct or shape light. In engineering, it might be part of a nozzle or a funnel. The term is primarily used in geometric and mathematical contexts, though its visual representation is common in everyday objects. The surface itself is a fundamental shape in conic sections, from which parabolas, ellipses, and hyperbolas can be derived.