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动态几何图形演示 by Tim Brzezinski (11)

动态几何图形演示 by Tim Brzezinski (11)
几何画板及绘图内容加载中，请稍等……
2018-03-29 01:09
多边形向量三角函数解析几何几何作图
这个范例动态演示了由 Antonio Gutierrez 提出的几何问题，通过可视化展示了三角函数、组合数学和解析几何的应用。范例利用了 Rotate（旋转）、Angle（角度）、Ray（射线）、Segment（线段）、Point（点）、Min（最小值）、Circle（圆）、Intersect（交点）、CircleSector（圆扇形）、Line（直线）、Dilate（缩放）、Vector（向量）、Polygon（多边形）、LineBisector（角平分线）等 GeoGebra 命令和对象，适合高中及以上学生学习和理解复杂几何构造。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Ray(B, A') → f
  4. Segment(B, A) → g
  5. Point(f) → C
  6. Angle(B, C, A) → β
  7. Rotate(B, γ, C) → B'
  8. Angle(B, C, B') → δ
  9. Ray(C, B') → h
  10. Point(h) → D
  11. Ray(D, A) → i
  12. Segment(A, B) → j
  13. Segment(B, C) → k
  14. Segment(C, D) → l
  15. Segment(D, A) → m
  16. Min({j, k, l, m}) → b
  17. Ray(A, B) → n
  18. Ray(B, C) → p
  19. Circle(B, (0.25 * b)) → c
  20. Intersect(c, n, 2) → E
  21. Intersect(c, p, 1) → F
  22. Circle(C, (0.25 * b)) → d
  23. Circle(D, (0.25 * b)) → e
  24. Circle(A, (0.25 * b)) → q
  25. Intersect(d, h, 1) → G
  26. Intersect(d, p, 2) → H
  27. Intersect(e, i, 1) → I
  28. Intersect(e, h, 2) → J
  29. Intersect(q, n, 1) → K
  30. Intersect(q, i, 2) → L
  31. CircleSector(B, F, E) → r
  32. CircleSector(C, G, H) → s
  33. CircleSector(D, I, J) → t
  34. CircleSector(A, K, L) → c_1
  35. Angle(C, D, A) → ε
  36. Line(B, A) → f_1
  37. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'_1
  38. Vector(A, A'_1) → v
  39. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], C) → B'_1
  40. Vector(B, B'_1) → w
  41. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], D) → C'
  42. Vector(C, C') → u_1
  43. Polygon(B, A, D, C) → poly1, b_1, a_1, d_2, c_2
  44. Circle(B, 10) → h_1
  45. Circle(A, 5) → k_1
  46. Circle(C, 5) → p_1
  47. Circle(D, 5) → q_1
  48. Intersect(h_1, n) → M, N
  49. Intersect(p_1, p) → O, P
  50. Intersect(q_1, h) → Q, R
  51. Intersect(k_1, i) → S, T
  52. Rotate(C, (π - α) / 2, B) → C'_1
  53. Angle(C, B, C'_1) → ζ
  54. Rotate(P, ((-(π - δ))) / 2, C) → P'
  55. Angle(P, C, P') → η
  56. Rotate(A, (π - ε) / 2, D) → A'_2
  57. Angle(A, D, A'_2) → θ_1
  58. Angle(B, A, T) → θ
  59. Rotate(T, (-((π - θ) / 2)), A) → T'
  60. Line(B, C'_1) → j_1
  61. Line(C, P') → l_1
  62. Line(D, A'_2) → m_1
  63. Intersect(j_1, l_1) → V
  64. Intersect(l_1, m_1) → W
  65. Rotate(B, θ / 2, A) → B'_2
  66. Angle(B, A, B'_2) → ι
  67. Ray(A, B'_2) → i_1
  68. Intersect(j_1, i_1) → U
  69. LineBisector(V, U) → n_1
  70. Line(A, U) → r_1
  71. Intersect(m_1, r_1) → Z
  72. Circle(U, V, W) → s_1
  73. LineBisector(V, W) → t_1
  74. LineBisector(Z, W) → f_2
  75. Intersect(t_1, f_2) → A_1
  76. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], V) → B'_3
  77. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], W) → C'_2
  78. Dilate(D, If[0 < u ≤ 1, 1 - u, 0], Z) → D'
  79. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], U) → A'_3
  80. Segment(B, B'_3) → g_1
  81. Segment(C, C'_2) → d_1
  82. Segment(D, D') → e_1
  83. Segment(A, A'_3) → g_2
  84. Rotate(F, If[1 < u ≤ 2, ((u - 1) * ζ), ζ], B) → F'
  85. Rotate(G, If[1 < u ≤ 2, ((u - 1) * (π - δ) / 2), (π - δ) / 2], C) → G'
  86. Rotate(I, If[1 < u ≤ 2, ((u - 1) * θ_1), θ_1], D) → I'
  87. Rotate(K, If[1 < u ≤ 2, ((u - 1) * θ / 2), θ / 2], A) → K'
  88. CircleSector(B, F, F') → e_2
  89. CircleSector(C, G, G') → h_2
  90. CircleSector(D, I, I') → k_2
  91. CircleSector(A, K, K') → p_2
  92. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], V) → C'_3
  93. Dilate(D, If[2 < u ≤ 3, 3 - u, 0], W) → D'_1
  94. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], Z) → A'_4
  95. Dilate(B, If[2 < u ≤ 3, 3 - u, 0], U) → B'_4
  96. Segment(C, C'_3) → i_2
  97. Segment(D, D'_1) → j_2
  98. Segment(A, A'_4) → l_2
  99. Segment(B, B'_4) → m_2
  100. Rotate(e_2, If[3 < u ≤ 4, ((u - 3) * ζ), ζ], B) → q_2
  101. Rotate(h_2, If[3 < u ≤ 4, ((u - 3) * (π - δ) / 2), (π - δ) / 2], C) → r_2
  102. Rotate(k_2, If[3 < u ≤ 4, ((u - 3) * θ_1), θ_1], D) → s_2
  103. Rotate(p_2, If[3 < u ≤ 4, ((u - 3) * θ / 2), θ / 2], A) → t_2
  104. Dilate(A_1, If[5 < u ≤ 6, 6 - u, 0], V) → A'_5
  105. Circle(A_1, A'_5) → c_3