3D Cone-Slice Intersection Demo

3D Cone-Slice Intersection Demo
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2015-10-14 02:27
This example demonstrates the 3D geometric shapes formed by the intersection of a cone and a plane, including ellipses, hyperbolas, and parabolas. It involves core mathematical concepts such as cone sections, ellipses, hyperbolas, parabolas, 3D vectors, centroids, linear equations, and logarithmic functions. The construction uses GeoGebra commands like InfiniteCone, Line, Plane, and IntersectPath. Suitable for high school students and math enthusiasts learning spatial geometry and properties of conic sections.

GeoGebra Commands & Parameters

  1. InfiniteCone((0, 0, 0), (0, 0, 1), α) → a
  2. Line((0, 0, 0), (0, sin(β), cos(β))) → c
  3. Line(A, c) → e
  4. Line(A, (1, 0, h)) → b
  5. Plane(b, e) → d
  6. IntersectPath(d, a) → f