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Cones and Planes

Cones and Planes
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2016-12-03 04:34
Coordinate GeometrySolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the geometric shapes formed by the intersection of a cone and a plane. Key mathematical concepts include solid geometry, specifically cones and planes. Using GeoGebra commands such as InfiniteCone, Plane, and IntersectPath, dynamic graphics of the intersection can be constructed. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. InfiniteCone((0, 0, 0), zAxis, α) → a
  2. Axes(a) → d, e, f
  3. Rotate(f, (-α), yAxis) → f'_1
  4. Point(f'_1) → A
  5. Rotate(f, α, yAxis) → f'
  6. Point(f') → B
  7. Plane(A, B_1, B) → b
  8. IntersectPath(b, a) → c
  9. Axes(c) → i, j
  10. AngularBisector(f', i) → b2, b1
  11. Center(a) → O
  12. Vector(O, B) → vOB
  13. Angle(Vector[A, B], Vector[A, O]) → β
  14. Vector(O, A) → vOA
  15. Rotate(vOA, β / 2, A, k) → vOA'
  16. Angle(Vector[B, A], Vector[O, B]) → α1
  17. Rotate(vOB, α1 / 2, B, k) → vOB'
  18. Ray(B, B') → g
  19. Intersect(f, b1) → G
  20. OrthogonalLine(G, i, k) → h
  21. Intersect(i, h) → H
  22. Circle(G, H, k) → p
  23. Sphere(G, H) → l
  24. Ray(A, A') → m
  25. Intersect(f, b2) → L
  26. OrthogonalLine(L, i, k) → n
  27. Intersect(i, n) → M
  28. Circle(L, M, k) → s
  29. Point(c) → P
  30. Line(O, P) → a_1
  31. Segment(M, P) → b_1
  32. Segment(P, H) → e_1
  33. Sphere(L, M) → l'
  34. OrthogonalLine(L, f'_1, k) → q
  35. OrthogonalLine(G, f'_1, k) → r
  36. Intersect(f'_1, r) → C
  37. Intersect(q, f'_1) → D
  38. Circle(f, C) → t
  39. Circle(f, D) → c_1
  40. Line(O, P) → d_1
  41. Intersect(d_1, c_1) → E,
  42. Intersect(d_1, t) → F,
  43. Segment(P, F) → f_1
  44. Segment(E, P) → g_1
  45. Segment(O, E) → h_1