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➗calculus ii review

Nappes

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

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.

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