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2017-03-05 06:22
圆三角函数几何作图
该范例演示了单位圆上的几何均值。涉及的核心数学概念包括圆、几何均值和单位圆。通过使用GeoGebra命令如Point、Ray、OrthogonalLine等，构造了动态的几何图形。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(y = 0) → A
  2. Ray(A, B) → f
  3. Point(f) → C
  4. OrthogonalLine(C, p) → q
  5. Ray(C, F) → i
  6. Point(i) → G
  7. Ray(G, H) → j
  8. Point(j) → I
  9. Segment(I, G) → k
  10. Circle(I, G) → c
  11. Ray(C, D) → h
  12. Intersect(l, h) → E
  13. Ray(E, J) → m
  14. Intersect(c, m, 1) → K
  15. Ray(K, I) → n
  16. Intersect(n, y = 0) → L
  17. Circle(L, K) → d
  18. Intersect(d, y = 0) → M, N
  19. Segment(K, N) → r
  20. Intersect(c, r, 2) → O
  21. Line(O, G) → s
  22. Intersect(q, s) → P
  23. Segment(K, P) → q_1
  24. Segment(K, P) → t
  25. Segment(P, O) → a
  26. Dilate(N, If[0 < b ≤ 1, 1 - b, 0], O) → N'
  27. Segment(N, N') → e
  28. Dilate(O, If[1 < b ≤ 2, 2 - b, 0], K) → O'
  29. Segment(O, O') → f_1
  30. Dilate(K, If[2 < b ≤ 3, 3 - b, 0], C) → K'
  31. Angle(K, C, A) → α
  32. Segment(K, K') → g_1
  33. Dilate(O, If[3 < b ≤ 4, 4 - b, 0], G) → O'_1
  34. Segment(O, O'_1) → h_1
  35. Dilate(G, If[4 < b ≤ 5, 5 - b, 0], P) → G'
  36. Dilate(C, If[4 < b ≤ 5, 5 - b, 0], P) → C'
  37. Segment(G, G') → i_1
  38. Segment(C, C') → j_1
  39. Segment(M, N) → k_1
  40. Circle(G, g_1 + j_1) → c_1
  41. Segment(M, G) → l_1
  42. Segment(G, Q) → m_1
  43. Segment(Q, N) → n_1
  44. Dilate(M, If[5 < b ≤ 6, 6 - b, 0], G) → M'
  45. Segment(M, M') → p_1
  46. Rotate(K, If[6 < b ≤ 7, ((-(b - 6)) * π / 2), ((-π)) / 2], P) → K'_1
  47. Rotate(P, If[6 < b ≤ 7, ((-(b - 6)) * π / 2), ((-π)) / 2], P) → P'
  48. Segment(K'_1, P') → r_1
  49. Dilate(P, If[7 < b ≤ 8, 8 - b, 0], G) → P'_1
  50. Vector(P, P'_1) → u
  51. Translate(K'_1, u) → R
  52. Translate(P', u) → P''
  53. Segment(R, P'') → s_1
  54. Midpoint(M, Q) → S
  55. Rotate(Q, If[8 < b ≤ 9, ((-(b - 8)) * π), (-π)], S) → Q'
  56. CircleArc(S, Q', Q) → d_1
  57. OrthogonalLine(G, n_1) → t_1
  58. Intersect(d_1, t_1) → T,
  59. Angle(T, G, S) → β
  60. Dilate(T, If[10 < b ≤ 11, 11 - b, 0], G) → T'
  61. Segment(T, T') → a_1
  62. Dilate(K, If[11 < b ≤ 12, 12 - b, 0], G) → K'_2
  63. Segment(K, K'_2) → b_1
  64. Angle(T, G, K) → γ
  65. Rotate(K, If[13 < b ≤ 14, ((-(b - 13)) * γ), (-γ)], G) → K'_3
  66. Rotate(K'_2, If[13 < b ≤ 14, ((-(b - 13)) * γ), (-γ)], G) → U
  67. Segment(K'_3, U) → f_2
  68. Segment(S, Q') → g_2
  69. Segment(M, N) → h_2
  70. CircleArc(S, M, Q) → e_1
  71. CircleSector(S, Q', Q) → c_2