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动态几何图形演示 by Tim Brzezinski (13)

动态几何图形演示 by Tim Brzezinski (13)
几何画板及绘图内容加载中，请稍等……
2017-12-26 14:33
三角函数解析几何复数几何作图
①本范例动态演示复数与几何变换的关联，通过图形变化直观展示数学原理；②涉及核心概念包括复数、线性方程、三角函数、几何变换等；③作图要点运用了多边形、线段、圆、交点、中点、线、缩放、旋转等GeoGebra命令；④适合高中及以上数学学习者和教师用于教学演示与探索。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Segment(D, A) → f
  3. Segment(A, B) → g
  4. Segment(B, C) → h
  5. Segment(C, D) → i
  6. Circle(D, f / 3) → e
  7. Intersect(e, f, 1) → E
  8. Circle(E, f / 3) → k
  9. Intersect(k, f) → F, G
  10. Circle(A, g / 3) → p
  11. Intersect(p, g) → H,
  12. Midpoint(H, B) → I
  13. Circle(B, h / 3) → q
  14. Intersect(q, h) → J,
  15. Midpoint(J, C) → K
  16. Circle(C, i / 3) → r
  17. Intersect(r, i) → L,
  18. Midpoint(L, D) → M
  19. Line(E, K) → j
  20. Line(G, J) → l
  21. Line(H, M) → m
  22. Line(I, L) → n
  23. Intersect(j, m) → N
  24. Intersect(l, m) → O
  25. Intersect(n, j) → P
  26. Intersect(l, q1) → Q, R, Intersect(l, q1)_1, Intersect(l, q1)_2
  27. Intersect(n, l) → S
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], H) → A'
  29. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], E) → D'
  30. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], R) → B'
  31. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], L) → C'
  32. Segment(C, C') → s
  33. Segment(D, D') → t
  34. Segment(A, A') → f_1
  35. Segment(B, B') → g_1
  36. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], J) → B'_1
  37. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], J) → B''
  38. Segment(B'_1, B'') → h_1
  39. Rotate(C, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], L) → C'_1
  40. Rotate(C', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], L) → C''
  41. Segment(C'_1, C'') → s'
  42. Rotate(D, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], E) → D'_1
  43. Rotate(D', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], E) → D''
  44. Segment(D'_1, D'') → t'
  45. Rotate(A, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → A'_1
  46. Rotate(A', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → A''
  47. Segment(A'_1, A'') → i_1
  48. Rotate(C'_1, If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], M) → T
  49. Rotate(C'', If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], M) → C'''
  50. Segment(T, C''') → s''
  51. Rotate(D'_1, If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], G) → U
  52. Rotate(D'', If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], G) → D'''
  53. Segment(U, D''') → t''
  54. Rotate(A'_1, If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], I) → V
  55. Rotate(A'', If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], I) → A'''
  56. Segment(V, A''') → j_1
  57. Rotate(B'_1, If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], K) → W
  58. Rotate(B'', If[2 < o ≤ 3, ((-(o - 2)) * π), (-π)], K) → B'''
  59. Segment(W, B''') → k_1
  60. Dilate(E, If[4 < o ≤ 5, 5 - o, 0], N) → E'
  61. Dilate(M, If[4 < o ≤ 5, 5 - o, 0], N) → M'
  62. Dilate(G, If[4 < o ≤ 5, 5 - o, 0], O) → G'
  63. Dilate(L, If[4 < o ≤ 5, 5 - o, 0], P) → L'
  64. Segment(E, E') → l_1
  65. Segment(G, G') → m_1
  66. Segment(M, M') → n_1
  67. Segment(L, L') → p_1
  68. Dilate(N, If[5 < o ≤ 6, 6 - o, 0], P) → N'
  69. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], S) → O'
  70. Dilate(N, If[5 < o ≤ 6, 6 - o, 0], O) → N'_1
  71. Dilate(P, If[5 < o ≤ 6, 6 - o, 0], S) → P'
  72. Segment(N, N'_1) → q_1
  73. Segment(N, N') → r_1
  74. Segment(P, P') → s_1
  75. Segment(O, O') → t_1
  76. Dilate(P, If[6 < o ≤ 7, 7 - o, 0], K) → P'_1
  77. Dilate(S, If[6 < o ≤ 7, 7 - o, 0], J) → S'
  78. Dilate(O, If[6 < o ≤ 7, 7 - o, 0], H) → O'_1
  79. Dilate(S, If[6 < o ≤ 7, 7 - o, 0], I) → S'_1
  80. Segment(P, P'_1) → a_1
  81. Segment(S, S') → b_1
  82. Segment(S, S'_1) → c_1
  83. Segment(O, O'_1) → d_1
  84. Rotate(E, If[8 < o ≤ 9, ((o - 8) * π), π], N) → E'_1
  85. Rotate(E', If[8 < o ≤ 9, ((o - 8) * π), π], N) → E''
  86. Segment(E'_1, E'') → e_1
  87. Rotate(E'_1, If[9 < o ≤ 10, ((o - 9) * π), π], P) → Z
  88. Rotate(E'', If[9 < o ≤ 10, ((o - 9) * π), π], P) → E'''
  89. Segment(Z, E''') → f_2
  90. Rotate(G, If[10 < o ≤ 11, ((o - 10) * π), π], O) → G'_1
  91. Rotate(G', If[10 < o ≤ 11, ((o - 10) * π), π], O) → G''
  92. Segment(G'_1, G'') → g_2
  93. Rotate(G'_1, If[11 < o ≤ 12, ((o - 11) * π), π], S) → A_1
  94. Rotate(G'', If[11 < o ≤ 12, ((o - 11) * π), π], S) → G'''
  95. Segment(A_1, G''') → h_2
  96. Rotate(M, If[12 < o ≤ 13, ((o - 12) * π), π], N) → M'_1
  97. Rotate(M', If[12 < o ≤ 13, ((o - 12) * π), π], N) → M''
  98. Segment(M'_1, M'') → i_2
  99. Rotate(M'_1, If[13 < o ≤ 14, ((o - 13) * π), π], O) → B_1
  100. Rotate(M'', If[13 < o ≤ 14, ((o - 13) * π), π], O) → M'''
  101. Segment(B_1, M''') → j_2
  102. Rotate(L, If[14 < o ≤ 15, ((o - 14) * π), π], P) → L'_1
  103. Rotate(L', If[14 < o ≤ 15, ((o - 14) * π), π], P) → L''
  104. Segment(L'_1, L'') → k_2
  105. Rotate(L'_1, If[15 < o ≤ 16, ((o - 15) * π), π], S) → C_1
  106. Rotate(L'', If[15 < o ≤ 16, ((o - 15) * π), π], S) → L'''
  107. Segment(C_1, L''') → l_2