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平面间夹角概念验证

平面间夹角概念验证
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2020-05-01 19:30
向量立体几何几何作图
①本范例演示了两个平面之间夹角的计算与可视化；②涉及的核心数学概念包括平面方程、向量点积、角度计算；③作图要点：使用Point, Polygon, Circle, Intersect, Segment, Vector, OrthogonalPlane, Translate, Angle等GeoGebra命令构建平面与向量，通过计算向量点积与模长求夹角；④适合高中立体几何教学或自学，帮助理解空间几何关系。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, D) → poly1, d, a, b
  4. Polygon(A, C, B) → poly2, b_1, a_1, c
  5. Circle(A, 6, zAxis) → e
  6. Circle(B, 6, zAxis) → f
  7. Circle(A, 6, xAxis) → g
  8. Circle(B, 6, xAxis) → h
  9. Intersect(e, g) → E, F, ,
  10. Intersect(f, h) → G, H, ,
  11. Segment(F, H) → i
  12. Point(i) → I
  13. Vector(F, I) → u
  14. Point(c) → J
  15. OrthogonalPlane(J, c) → j
  16. Intersect(b_1, j) → K
  17. Intersect(b, j) → L
  18. Segment(K, J) → k
  19. Segment(J, L) → l
  20. Polygon(A, J, L) → poly3, l_1, a_2, j_1
  21. Polygon(A, J, K) → poly4, k_1, a_3, j_2
  22. Polygon(J, K, C, B) → poly5, j_3, k_2, c_1, b_2
  23. Polygon(J, L, D, B) → poly6, j_4, l_2, d_1, b_3
  24. Intersect(a_1, j) → M
  25. Intersect(a, j) → N
  26. Segment(M, J) → m
  27. Segment(J, N) → n
  28. Polygon(C, M, J, A) → poly7, c_2, m_1, j_5, a_4
  29. Polygon(M, B, J) → poly8, j_6, m_2, b_4
  30. Polygon(A, J, N, D) → poly9, a_5, j_7, n_1, d_2
  31. Polygon(N, J, B) → poly10, b_5, n_2, j_8
  32. Translate(poly5, u) → poly5'
  33. Translate(poly6, u) → poly6'
  34. Translate(poly8, u) → poly8'
  35. Translate(poly10, u) → poly10'
  36. Angle(D, A, C) → α
  37. Angle(K, J, L) → β
  38. Angle(C, B, D) → γ
  39. Angle(K, J, A) → δ
  40. Angle(L, J, A) → ε
  41. Angle(M, J, N) → ζ
  42. Angle(M, J, A) → η
  43. Angle(N, J, A) → θ
  44. Angle(M, J, L) → ι
  45. Angle(K, J, N) → κ
  46. Segment(K, J) → s