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Intersection of Two Cones Demo

Intersection of Two Cones Demo
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2018-08-16 00:21
VectorSolid GeometryParametric EquationGeometric Construction
This example demonstrates the intersection shape of two cones in 3D space. Key math concepts include solid geometry, intersection calculation, and parametric equations. GeoGebra commands/objects used in construction are Vector, Length, Cone, CurveCartesian, and Textfield. Suitable for high school and university students learning solid geometry, spatial geometric bodies, and their intersection properties, as well as basic geometry teaching.

GeoGebra Commands & Parameters

  1. Vector(Point[{((1 + r^(2)) * cos((2 * θ))), ((1 + r^(2)) * sin((2 * θ)))}]) → w
  2. Vector(Point[{(-(1 + R^(2))), 0}]) → v
  3. Length(Vector[v + w]) → A
  4. Cone(Point[{0, 0, H}], Point[{0, 0, 0}], (H * R)) → d, e, f
  5. Cone(Point[{0, 0, (-H)}], Point[{0, 0, 0}], (H * R)) → g, h_1, i
  6. Cone(Point[{s, t - (h * sin(θ)), u - (h * cos(θ))}], Point[{s, t, u}], (h * r)) → q, q_2, q_3
  7. Cone(Point[{s, t + (h * sin(θ)), u + (h * cos(θ))}], Point[{s, t, u}], (h * r)) → l_3, l_2, l_3
  8. CurveCartesian(ξ_d(η), (η * cos(ω)) - (ζ_d(η) * sin(ω)), (sin(ω) * η) + (cos(ω) * ζ_d(η)), η, (-η_{def}), η_{def}) → γ_d
  9. CurveCartesian(ξ_u(η), (η * cos(ω)) - (ζ_u(η) * sin(ω)), (sin(ω) * η) + (cos(ω) * ζ_u(η)), η, (-η_{def}), η_{def}) → γ_u
  10. Textfield(s) → Eingabefeld1
  11. Textfield(t) → Eingabefeld2
  12. Textfield(u) → Eingabefeld3
  13. Textfield(θ) → Eingabefeld4
  14. Textfield(η_{def}) → Eingabefeld5
  15. Textfield(R) → Eingabefeld6
  16. Textfield(r) → Eingabefeld7