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动态演示几何问题

动态演示几何问题
几何画板及绘图内容加载中，请稍等……
2017-04-23 09:01
向量三角函数解析几何参数方程几何作图
①这个范例动态演示了Antonio Gutierrez在Twitter上提出的一个几何问题，涉及对数、随机变量、等腰三角形、参数曲线和实数的可视化；②核心数学概念包括对数运算、随机变量分布、等腰三角形的性质、参数曲线的绘制以及实数轴上的表示；③作图要点提炼自GeoGebra命令：Rotate（旋转）、Ray（射线）、Point（点）、Polygon（多边形）、Line（直线）、Intersect（交点）、Segment（线段）、Midpoint（中点）、Angle（角度）、Min（最小值）、Circle（圆）、CircleSector（圆扇形）、Dilate（缩放）、Vector（向量）、Translate（平移）、OrthogonalLine（垂线）；④适合高中及以上数学学习者，用于理解复杂几何问题的动态变化过程和核心概念应用。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Ray(B, A') → g
  3. Point(g) → C
  4. Polygon(B, C, 4) → poly2, n, p, q, r, F, G
  5. Line(A, G) → h_3
  6. Polygon(C, A, 4) → poly1, j, k, l, m, D, E
  7. Line(B, D) → j_2
  8. Intersect(h_3, j_2) → D_1
  9. Rotate(A, If[0 < u ≤ 1, (u * π / 2), π / 2], C) → A'_1
  10. Rotate(C, If[0 < u ≤ 1, (u * π / 2), π / 2], C) → C'
  11. Segment(C', A'_1) → i'
  12. Midpoint(i') → V
  13. Angle(A, B, A') → α
  14. Segment(A, B) → f
  15. Segment(B, C) → h
  16. Segment(C, A) → i
  17. Angle(poly2) → β, γ, δ, ε
  18. Angle(poly1) → ζ, η, θ, ι
  19. Segment(C, E) → s
  20. Segment(E, D) → t
  21. Segment(D, A) → b
  22. Segment(B, G) → c
  23. Segment(G, F) → d
  24. Segment(F, C) → e
  25. Min(i, h) → o
  26. Circle(E, (0.15 * o)) → c_1
  27. Polygon(B, A, C) → poly3, c_2, b_1, a_1
  28. Intersect(c_1, s, 1) → H
  29. Intersect(c_1, t, 1) → I
  30. Line(B, E) → f_1
  31. Line(A, F) → g_1
  32. Line(G, D) → h_1
  33. Circle(A, (0.15 * o)) → d_1
  34. Intersect(d_1, b, 1) → K
  35. Intersect(d_1, i, 1) → L
  36. CircleSector(A, K, L) → e_1
  37. Rotate(B, If[0 < u ≤ 1, (u * π / 2), π / 2], B) → B'
  38. Rotate(C, If[0 < u ≤ 1, (u * π / 2), π / 2], B) → C'_1
  39. Segment(B', C'_1) → h'
  40. Rotate(B', If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], G) → B''
  41. Rotate(C'_1, If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], G) → M
  42. Segment(B'', M) → h''
  43. Rotate(C', If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], E) → C''
  44. Rotate(A'_1, If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], E) → N
  45. Segment(C'', N) → i''
  46. Rotate(C'', If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], D) → C'''
  47. Rotate(N, If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], D) → N'
  48. Segment(C''', N') → i'''
  49. Rotate(B'', If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], F) → B'''
  50. Rotate(M, If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], F) → M'
  51. Segment(B''', M') → h'''
  52. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], D) → A'_2
  53. Vector(A, A'_2) → v
  54. Translate(e_1, v) → k_1
  55. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], C) → A'_3
  56. Vector(A, A'_3) → w
  57. Translate(e_1, w) → p_1
  58. Line(C, A) → i_1
  59. Point(i_1) → O
  60. Angle(O, C, F) → κ
  61. Rotate(p_1, If[4.5 < u ≤ 5.5, ((u - 4.5) * (π / 2 + κ)), π / 2 + κ], C) → q_1
  62. Rotate(k_1, If[4.5 < u ≤ 5.5, ((u - 4.5) * π / 2), π / 2], D) → r_1
  63. Dilate(D, If[5.5 < u ≤ 6.5, 6.5 - u, 0], E) → D'
  64. Dilate(C, If[5.5 < u ≤ 6.5, 6.5 - u, 0], F) → C'_2
  65. Vector(C, C'_2) → u_1
  66. Vector(D, D') → v_1
  67. Translate(r_1, v_1) → s_1
  68. Translate(q_1, u_1) → t_1
  69. Rotate(s_1, If[6.5 < u ≤ 7.5, ((u - 6.5) * π / 2), π / 2], E) → d_2
  70. Rotate(t_1, If[6.5 < u ≤ 7.5, ((u - 6.5) * π / 2), π / 2], F) → e_2
  71. Dilate(F, If[7.5 < u ≤ 8.5, 8.5 - u, 0], G) → F'
  72. Dilate(E, If[7.5 < u ≤ 8.5, 8.5 - u, 0], V) → E'
  73. Vector(E, E') → w_1
  74. Vector(F, F') → j_1
  75. Translate(d_2, w_1) → f_2
  76. Translate(e_2, j_1) → g_2
  77. Rotate(g_2, If[8.5 < u ≤ 9.5, ((u - 8.5) * π / 2), π / 2], G) → h_2
  78. Circle(G, 2) → p_2
  79. Circle(D, 2) → q_2
  80. Circle(F, 2) → r_2
  81. Intersect(r_2, g_1, 2) → P
  82. Intersect(p_2, h_1, 1) → Q
  83. Intersect(d_1, g_1, 1) → R
  84. Intersect(q_2, h_1, 2) → S
  85. Circle(B, 2) → s_2
  86. Intersect(s_2, f_1, 1) → T
  87. Intersect(c_1, f_1, 2) → U
  88. Rotate(f_2, If[8.5 < u ≤ 9.5, ((u - 8.5) * π / 2), π / 2], V) → k_2
  89. Dilate(V, If[9.5 < u ≤ 10.5, 10.5 - u, 0], C) → V'
  90. Vector(V, V') → u_2
  91. Translate(k_2, u_2) → t_2
  92. Dilate(B, If[11 < u ≤ 12, 12 - u, 0], D) → B'_1
  93. Segment(B, B'_1) → m_2
  94. Dilate(A, If[12 < u ≤ 13, 13 - u, 0], D_1) → A'_4
  95. Segment(A, A'_4) → n_2
  96. Dilate(D_1, If[13 < u ≤ 14, 14 - u, 0], G) → J'
  97. Line(G, n_2) → g_3
  98. Point(g_3) → A_1
  99. Angle(F, G, A_1) → λ
  100. Circle(B, (0.15 * o)) → r_3
  101. Intersect(r_3, f, 1) → B_1
  102. Intersect(r_3, h, 1) → C_1
  103. CircleSector(B, B_1, C_1) → s_3
  104. Line(C, D_1) → i_3
  105. Line(B, A) → j_3
  106. Intersect(j_3, i_3) → E_1
  107. Segment(D_1, J') → a_2
  108. Dilate(C, If[14 < u ≤ 15, 15 - u, 0], D_1) → C'_3
  109. Segment(C, C'_3) → m_1
  110. Dilate(D_1, If[15 < u ≤ 16, 16 - u, 0], E_1) → J
  111. Segment(D_1, J) → n_1
  112. OrthogonalLine(C, j_3) → i_2
  113. Intersect(j_3, i_2) → W
  114. Dilate(A, If[16 < u ≤ 17, 17 - u, 0], W) → A'_5
  115. Vector(A, A'_5) → l_1
  116. Translate(e_1, l_1) → c_3
  117. Line(A, m_1) → l_2
  118. Point(j_3) → Z
  119. Angle(Z, A, D) → μ
  120. Rotate(c_3, If[16 < u ≤ 17, ((-(u - 16)) * μ), (-μ)], W) → d_3