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等边三角形与矩形面积问题动态演示

等边三角形与矩形面积问题动态演示
几何画板及绘图内容加载中，请稍等……
2016-12-15 04:11
测试改名0多边形几何作图
①本范例演示等边三角形内接于矩形的动态图形与面积计算问题；②涉及核心数学概念包括面积计算、解析几何、几何变换；③构造过程中运用了Line（线）、Segment（线段）、Circle（圆）、Intersect（交点）、Rotate（旋转）、Polygon（多边形）等GeoGebra命令与对象；④适合高中数学教学与几何作图学习，可用于理解特殊图形的面积关系与变换性质。

GeoGebra 命令及参数

  1. Line(A, B) → i
  2. Segment(A, B) → l
  3. OrthogonalLine(B, i) → f
  4. Circle(B, l / 2) → d
  5. Intersect(d, f, 2) → C
  6. OrthogonalLine(A, l) → q
  7. Circle(B, 1) → c
  8. Intersect(c, f, 2) → D
  9. Ray(B, D) → g
  10. Rotate(B, α, A) → B'
  11. Angle(B, A, B') → β
  12. Ray(A, B') → h
  13. Intersect(g, h) → E
  14. Polygon(A, E, 3) → poly1, m, n, p, F
  15. Polygon(E, B, A) → poly3, a_1, e, b
  16. OrthogonalLine(F, q) → r
  17. Intersect(q, r) → G
  18. Intersect(r, g) → H
  19. Polygon(A, F, G) → poly2, g_1, a, f_1
  20. Polygon(E, H, F) → poly4, f_2, e_1, h_1
  21. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], E) → A'
  22. Segment(A, A') → s
  23. Dilate(E, If[1 < o ≤ 2, 2 - o, 0], F) → E'
  24. Rotate(A, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A'_1
  25. Rotate(A', If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A''
  26. Segment(A'_1, A'') → s'
  27. Rotate(A'_1, If[2 < o ≤ 3, ((o - 2) * π / 3), π / 3], F) → I
  28. Rotate(A'', If[2 < o ≤ 3, ((o - 2) * π / 3), π / 3], F) → A'''
  29. Segment(I, A''') → s''
  30. Angle(A, G, H) → γ
  31. Angle(G, H, B) → δ
  32. Angle(H, B, A) → ε
  33. Segment(G, F) → t
  34. Segment(G, A) → i_1
  35. Segment(F, H) → j_1
  36. Segment(H, B) → k_1
  37. Segment(B, A) → l_1
  38. Circle(A, (0.2 * l_1)) → c_1
  39. Intersect(c_1, l_1) → J,
  40. Intersect(c_1, s) → K,
  41. CircleSector(A, J, K) → d_1
  42. Segment(B, E) → m_1
  43. Segment(B, A) → n_1
  44. Segment(H, E) → p_1
  45. OrthogonalLine(G, s') → r_1
  46. OrthogonalLine(B, s) → s_1
  47. Intersect(r_1, s') → L
  48. OrthogonalLine(H, s'') → q_1
  49. Intersect(q_1, s'') → M
  50. Intersect(s_1, s) → N
  51. Dilate(G, If[4 < o ≤ 5, 5 - o, 0], L) → G'
  52. Segment(G, L) → t_1
  53. Circle(H, t_1) → c_2
  54. Segment(H, M) → b_1
  55. Intersect(c_2, b_1) → O, U
  56. Segment(G, G') → g_2
  57. Dilate(B, If[5 < o ≤ 6, 6 - o, 0], N) → B'_1
  58. Segment(B, B'_1) → h_2
  59. Dilate(H, If[6 < o ≤ 7, 7 - o, 0], O) → H'
  60. Segment(H, H') → i_2
  61. Dilate(O, If[7 < o ≤ 8, 8 - o, 0], M) → O'
  62. Segment(O, O') → j_2
  63. Line(O, g_2) → k_2
  64. Point(k_2) → P
  65. Angle(H, O, P) → ζ
  66. Dilate(L, If[8 < o ≤ 9, 9 - o, 0], O) → L'
  67. Vector(L, L') → u
  68. Translate(G, u) → G'_1
  69. Translate(G', u) → G''
  70. Segment(G'_1, G'') → l_2
  71. Rotate(G'_1, If[9 < o ≤ 10, (((-(o - 9)) * 2) * π / 3), (-2 * π / 3)], O) → Q
  72. Rotate(G'', If[9 < o ≤ 10, (((-(o - 9)) * 2) * π / 3), (-2 * π / 3)], O) → G'''
  73. Segment(Q, G''') → m_2
  74. Line(M, h_2) → n_2
  75. Point(n_2) → R
  76. Angle(H, M, R) → η
  77. Dilate(N, If[10 < o ≤ 11, 11 - o, 0], M) → N'
  78. Vector(N, N') → v
  79. Translate(B, v) → B'_2
  80. Dilate(B, If[10 < o ≤ 11, 11 - o, 0], M) → B'_3
  81. Vector(B, B'_3) → w
  82. Translate(B, w) → B'_4
  83. Translate(B'_1, w) → S
  84. Segment(B'_4, S) → p_2
  85. Rotate(B'_4, If[11 < o ≤ 12, ((-(o - 11)) * π / 3), ((-π)) / 3], M) → T
  86. Rotate(S, If[11 < o ≤ 12, ((-(o - 11)) * π / 3), ((-π)) / 3], M) → S'
  87. Segment(T, S') → q_2
  88. Angle(G, L, A) → θ
  89. Angle(A, N, B) → ι
  90. Angle(H, M, A'') → κ