Intersection of Plane and Hyperboloid of 2 Sheets

Intersection of Plane and Hyperboloid of 2 Sheets
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2019-02-03 09:35
This example demonstrates the intersection curve formed between a plane and a hyperboloid of two sheets. Key mathematical concepts include hyperboloids, planes, quadratic surfaces, and their intersection properties. The construction utilizes GeoGebra's Rotate and IntersectPath commands to visualize the intersection curve by rotating the plane and calculating intersection points. Suitable for high school and above students studying spatial geometry and quadratic surfaces.

GeoGebra Commands & Parameters

  1. Rotate(Translate[Rotate[Plane[(0, 0, 0), (0, 1, 0), (1, 0, 0)], b, xAxis], Vector[(0, 0, d)]], c, zAxis) → e
  2. IntersectPath(e, a) → f