Nappes

Definition

Nappes are the two separate sheets or surfaces that constitute a double cone. Each nappe extends infinitely in opposite directions from the vertex of the cone.

5 Must Know Facts For Your Next Test

1. Nappes are essential when studying conic sections as they determine the type of conic section formed by intersecting a plane with a double cone.
2. The upper and lower nappes refer to the two halves of the double cone, divided by its vertex.
3. When a plane intersects one nappe parallel to its base, the resulting conic section is a parabola.
4. If a plane intersects both nappes but not through the vertex, it forms a hyperbola.
5. A circle or an ellipse is formed when a plane intersects only one nappe at an angle less than that made by the generator lines of the cone.

Related terms

Conic Sections:

Curves obtained by intersecting a plane with a double cone; includes ellipses, parabolas, and hyperbolas.

Double Cone: A geometric shape consisting of two right circular cones placed apex to apex.

Vertex:

The point where the two nappes of a double cone meet.