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动态四边形与内切圆演示

动态四边形与内切圆演示
几何画板及绘图内容加载中，请稍等……
2017-09-09 23:41
圆多边形概率统计几何作图滑块动画
①本范例动态演示四边形与内切圆的关系，通过调整参数观察图形变化；②涉及核心概念：平行四边形、正方形、内切圆、分段函数、随机实验、直方图、等腰三角形；③作图要点：运用了Polygon（多边形）、Segment（线段）、Rotate（旋转）、Angle（角度）、Ray（射线）、Intersect（交点）、Line（直线）、Mirror（镜像）、Dilate（缩放）、Vector（向量）、Translate（平移）、Point（点）等命令；④适合高中数学教学，用于理解几何变换与统计概率的结合。

GeoGebra 命令及参数

  1. Polygon(B, B_2, 4) → poly1, f, g, h, i, C, B_1
  2. Polygon(C, C_2, 4) → poly2, j, k, l, m, D, C_1
  3. Polygon(A_2, B, 4) → poly3, n, p, q, r, A_1, A
  4. Segment(A, D) → s
  5. Rotate(D, π / 4, A) → D'
  6. Angle(D, A, D') → α
  7. Rotate(A, (-(π / 4)), D) → A'
  8. Angle(A', D, A) → β
  9. Ray(A, D') → t
  10. Ray(D, A') → a
  11. Intersect(t, a) → D_2
  12. Line(A, D) → b
  13. Mirror(D_2, b) → D_1
  14. Polygon(D_2, A, 4) → poly4, c, d, e, f_1, F, G
  15. Segment(A_1, D_2) → g_1
  16. Segment(D_2, C_1) → h_1
  17. Segment(C_1, B_2) → i_1
  18. Segment(B_2, A_1) → j_1
  19. Segment(B_1, A_2) → k_1
  20. Segment(A_2, D_1) → l_1
  21. Segment(D_1, C_2) → m_1
  22. Segment(C_2, B_1) → n_1
  23. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], B_2) → B'
  24. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], A_2) → B'_1
  25. Segment(B, B') → p_1
  26. Segment(B, B'_1) → q_1
  27. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B_2) → B'_2
  28. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B_2) → B''
  29. Segment(B'_2, B'') → r_1
  30. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B) → B'_3
  31. Rotate(B'_1, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B) → E
  32. Segment(B'_3, E) → s_1
  33. Rotate(B'_2, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], C) → H
  34. Rotate(B'', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], C) → B'''
  35. Segment(H, B''') → t_1
  36. Rotate(B'_3, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], A_1) → I
  37. Rotate(E, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], A_1) → E'
  38. Segment(I, E') → a_1
  39. Rotate(H, If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], B_1) → H'
  40. Rotate(B''', If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], B_1) → J
  41. Segment(H', J) → b_1
  42. Rotate(I, If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], A) → I'
  43. Rotate(E', If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], A) → E''
  44. Segment(I', E'') → c_1
  45. Angle(C, B_2, B) → γ
  46. Angle(B_1, C, B_2) → ε
  47. Angle(B, B_1, C) → δ
  48. Angle(A_1, B, A_2) → ζ
  49. Angle(A, A_1, B) → η
  50. Angle(A_2, A, A_1) → θ
  51. Dilate(C_2, If[5 < o ≤ 6, 6 - o, 0], C) → K
  52. Segment(C_2, K) → d_1
  53. Rotate(C_2, If[6 < o ≤ 7, ((o - 6) * π / 2), π / 2], C) → L
  54. Rotate(K, If[6 < o ≤ 7, ((o - 6) * π / 2), π / 2], C) → K'
  55. Segment(L, K') → e_1
  56. Rotate(L, If[7 < o ≤ 8, ((o - 7) * π / 2), π / 2], C_1) → L'
  57. Rotate(K', If[7 < o ≤ 8, ((o - 7) * π / 2), π / 2], C_1) → K''
  58. Segment(L', K'') → f_2
  59. Rotate(L', If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], D) → L''
  60. Rotate(K'', If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], D) → K'''
  61. Segment(L'', K''') → g_2
  62. Angle(C_2, C, C_1) → ι
  63. Angle(C, C_1, D) → κ
  64. Angle(C_1, D, C_2) → λ
  65. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], D_2) → A'_1
  66. Segment(A, A'_1) → h_2
  67. Rotate(A, If[10 < o ≤ 11, ((-(o - 10)) * π / 2), ((-π)) / 2], A) → A'_3
  68. Rotate(A'_1, If[10 < o ≤ 11, ((-(o - 10)) * π / 2), ((-π)) / 2], A) → M
  69. Segment(A'_3, M) → i_2
  70. Angle(D_1, A, D_2) → μ
  71. Dilate(A, If[11 < o ≤ 12, 12 - o, 0], D_1) → A'_2
  72. Vector(A, A'_2) → u
  73. Translate(A, u) → A'_4
  74. Translate(A'_1, u) → N
  75. Segment(A'_4, N) → j_2
  76. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], D_2) → A'_5
  77. Vector(A, A'_5) → v
  78. Translate(A'_3, v) → O
  79. Translate(M, v) → M'
  80. Segment(O, M') → k_2
  81. Dilate(A_1, If[15 < o ≤ 16, 16 - o, 0], D_2) → P
  82. Segment(A_1, P) → l_2
  83. Dilate(D_2, If[16 < o ≤ 17, 17 - o, 0], C_1) → Q
  84. Segment(D_2, Q) → m_2
  85. Dilate(D_2, If[17 < o ≤ 18, 18 - o, 0], C_1) → R
  86. Vector(D_2, R) → w
  87. Translate(A_1, w) → S
  88. Translate(P, w) → P'
  89. Segment(S, P') → n_2
  90. Dilate(D_2, If[18 < o ≤ 19, 19 - o, 0], A_1) → T
  91. Vector(D_2, T) → u_1
  92. Translate(D_2, u_1) → U
  93. Translate(Q, u_1) → Q'
  94. Segment(U, Q') → p_2
  95. Polygon(A_1, D_2, C_1, B_2) → poly5, a_2, d_2, c_2, b_2
  96. Dilate(B_1, If[19 < o ≤ 20, 20 - o, 0], A_2) → V
  97. Segment(B_1, V) → q_2
  98. Dilate(D_1, If[19 < o ≤ 20, 20 - o, 0], A_2) → W
  99. Segment(D_1, W) → r_2
  100. Dilate(A_2, If[20 < o ≤ 21, 21 - o, 0], B_1) → Z
  101. Vector(A_2, Z) → v_1
  102. Translate(D_1, v_1) → E_1
  103. Translate(W, v_1) → W'
  104. Segment(E_1, W') → s_2
  105. Dilate(B_1, If[21 < o ≤ 22, 22 - o, 0], C_2) → F_1
  106. Vector(B_1, F_1) → w_1
  107. Translate(B_1, w_1) → G_1
  108. Translate(V, w_1) → V'
  109. Segment(G_1, V') → t_2
  110. Polygon(C_2, D_1, A_2, B_1) → poly6, c_3, d_3, a_3, b_3
  111. Line(B_2, r_2) → e_2
  112. Point(e_2) → H_1
  113. Dilate(A_2, If[23 < o ≤ 24, 24 - o, 0], B_2) → I_1
  114. Vector(A_2, I_1) → u_2
  115. Translate(C_2, u_2) → J_1
  116. Translate(D_1, u_2) → K_1
  117. Translate(A_2, u_2) → L_1
  118. Translate(B_1, u_2) → M_1
  119. Polygon(J_1, K_1, L_1, M_1) → poly6', j_3, k_3, l_3, m_3
  120. Rotate(J_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → P_1
  121. Rotate(K_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → Q_1
  122. Rotate(L_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → R_1
  123. Rotate(M_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → S_1
  124. Polygon(P_1, Q_1, R_1, S_1) → poly6'', p_3, q_3, r_3, s_3