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五点球体

五点球体
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2019-06-15 04:44
三角函数解析几何立体几何几何作图
①本范例演示了五点球体的几何构造与性质；②涉及的核心数学概念包括球体、三角函数、中值、分数、勾股定理、椭圆；③作图要点提炼自构造摘要，使用了Intersect（相交）、Point（点）、Sphere（球体）、PointIn（点在...内）、Midpoint（中点）、CircleArc（圆弧）、Segment（线段）、OrthogonalPlane（正交平面）、OrthogonalLine（正交线）等GeoGebra命令/对象；④适合高中及以上学段，用于立体几何与解析几何的教学与探索。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → A
  2. Point(zAxis) → B
  3. Sphere(A, B) → a
  4. PointIn(a) → C
  5. PointIn(a) → E
  6. PointIn(a) → F
  7. PointIn(a) → D
  8. Midpoint(B, F) → G
  9. Midpoint(B, D) → H
  10. Midpoint(B, C) → I
  11. Midpoint(B, E) → J
  12. Midpoint(C, D) → K
  13. Midpoint(C, E) → L
  14. Midpoint(C, F) → M
  15. Midpoint(D, E) → N
  16. Midpoint(D, F) → O
  17. CircleArc(A, B, C) → c
  18. CircleArc(A, B, D) → d
  19. CircleArc(A, B, E) → e
  20. CircleArc(A, B, F) → f
  21. CircleArc(A, C, D) → g
  22. CircleArc(A, C, E) → h
  23. CircleArc(A, C, F) → k
  24. CircleArc(A, D, E) → p
  25. CircleArc(A, D, F) → q
  26. CircleArc(A, E, F) → r
  27. Point(c) → P
  28. Point(d) → Q
  29. Point(e) → R
  30. Point(f) → S
  31. Point(g) → T
  32. Point(h) → U
  33. Point(k) → V
  34. Point(p) → W
  35. Point(q) → Z
  36. Point(r) → A_1
  37. Segment(B, D) → i
  38. Segment(B, F) → j
  39. Segment(B, E) → l
  40. Segment(B, C) → m
  41. Segment(C, D) → n
  42. Segment(C, E) → s
  43. Segment(C, F) → t
  44. Segment(D, E) → b
  45. Segment(D, F) → f_1
  46. Segment(F, E) → g_1
  47. OrthogonalPlane(P, m) → p_1
  48. OrthogonalPlane(Q, i) → q_1
  49. OrthogonalPlane(R, l) → r_1
  50. OrthogonalPlane(S, j) → p_2
  51. OrthogonalPlane(T, n) → q_2
  52. OrthogonalPlane(U, s) → r_2
  53. OrthogonalPlane(V, t) → p_3
  54. OrthogonalPlane(W, b) → q_3
  55. OrthogonalPlane(Z, f_1) → r_3
  56. OrthogonalPlane(A_1, g_1) → p_4
  57. OrthogonalLine(A, p_1) → h_1
  58. Circle(h_1, P) → c_1
  59. OrthogonalLine(A, q_1) → i_1
  60. Circle(i_1, Q) → d_1
  61. OrthogonalLine(A, r_1) → j_1
  62. Circle(j_1, R) → e_1
  63. OrthogonalLine(A, p_2) → k_1
  64. Circle(k_1, S) → s_1
  65. OrthogonalLine(A, q_2) → l_1
  66. Circle(l_1, T) → t_1
  67. OrthogonalLine(A, r_2) → m_1
  68. OrthogonalLine(A, p_3) → n_1
  69. Circle(n_1, V) → e_2
  70. OrthogonalLine(A, q_3) → a_1
  71. Circle(a_1, W) → f_2
  72. OrthogonalLine(A, r_3) → b_1
  73. Circle(b_1, Z) → g_2
  74. OrthogonalLine(A, r_2) → h_2
  75. Circle(h_2, U) → k_2
  76. OrthogonalLine(A, p_4) → i_2
  77. Circle(i_2, A_1) → s_2