积极 AI Logo 积极 AI

动画37：多边形与圆的综合几何变换演示

动画37：多边形与圆的综合几何变换演示
几何画板及绘图内容加载中，请稍等……
2016-06-17 02:35
圆多边形角变换滑块动画
①本范例通过动态动画展示了一个包含多边形、圆、角、线段及多种几何变换的复合图形，直观呈现了图形元素之间的位置关系与运动规律。②核心数学概念涵盖角度、四边形、三角形、多边形、圆、向量、平移、旋转、镜像（对称）、缩放（位似）以及最优化问题、方程、统计和算术运算等，体现了多领域几何知识的综合应用。③作图要点：从构造摘要可见，使用了Ray、Point、Circle、Intersect、Segment、Angle、CircleSector、Vector、Translate、Dilate、If、Line、Polygon、Rotate、Mirror、Midpoint、CircleArc等GeoGebra命令，涉及大量对象如P、B、A、h_1、R、j_1、a、g、I_1、H、l_1、H_1、C、k_1、k、Z、b、M、N、D_1、E_1、e、f、D、E、γ、ε、ζ、h、J、K、L、q、t、u、c_1、v、j、q'、l，通过条件判断（If）和动态滑块实现动画效果。④适合中学高年级至大学低年级学生用于几何变换、动态几何和数学建模的探究学习，也可作为教师制作交互式几何课件的参考范例。

GeoGebra 命令及参数

  1. Ray(P, A) → h_1
  2. Point(h_1) → R
  3. Ray(A, R) → j_1
  4. Ray(A, B) → a
  5. Circle(A, 1.5) → g
  6. Intersect(g, j_1) → I_1,
  7. Intersect(g, a, 1) → H
  8. Segment(P, A) → l_1
  9. Intersect(g, l_1, 1) → H_1
  10. Segment(P, C) → k_1
  11. Circle(C, 1.5) → k
  12. Intersect(k, k_1) → Z,
  13. Ray(B, C) → b
  14. Intersect(k, b) → M, N
  15. Point(a) → D_1
  16. Point(b) → E_1
  17. Ray(B, D_1) → e
  18. Ray(C, E_1) → f
  19. Point(e) → D
  20. Point(f) → E
  21. Angle(A, C, B) → γ
  22. Angle(D, B, C) → ε
  23. Angle(E, C, A) → ζ
  24. Circle(B, 1.5) → h
  25. Intersect(h, b, 1) → J
  26. Intersect(h, a, 1) → K
  27. Intersect(h, a, 2) → L
  28. CircleSector(B, J, K) → q
  29. CircleSector(B, L, J) → t
  30. Vector(B, C) → u
  31. CircleSector(A, I_1, H) → c_1
  32. Vector(A, C) → v
  33. Translate(q, u) → q'
  34. Segment(B, C) → l
  35. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  36. Vector(B, C') → w
  37. Translate(q, w) → q'_1
  38. Dilate(A, If[1 < j ≤ 2, 2 - j, 0], C) → C'_1
  39. Vector(A, C'_1) → m
  40. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  41. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  42. Vector(B, C'_2) → u_1
  43. Vector(A, A') → v_1
  44. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  45. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  46. Ray(C, P) → g_1
  47. Point(g_1) → Q
  48. Ray(P, Q) → i_1
  49. Point(i_1) → S
  50. Point(j_1) → T
  51. Circle(P, 1.5) → p_1
  52. Intersect(p_1, l_1) → U,
  53. Intersect(p_1, i_1) → V,
  54. Intersect(p_1, k_1) → W,
  55. CircleSector(P, U, W) → q_1
  56. Intersect(k, b, 2) → A_1
  57. Line(P, b) → b_1
  58. Intersect(p_1, b_1) → C_1, G_1
  59. Angle(B, A, P) → α
  60. Vector(P, C) → i
  61. Dilate(P, If[2 < j ≤ 3, 3 - j, 0], C) → P'
  62. Vector(P, P') → w_1
  63. Translate(q_1, w_1) → r_1
  64. CircleSector(C, N, Z) → s
  65. CircleSector(P, V, U) → t_1
  66. Dilate(P, If[2 < n ≤ 3, 3 - n, 0], C) → P'_1
  67. Vector(P, P'_1) → m_1
  68. If(2 < n ≤ 3, Translate[t_1, m_1], Translate[t_1, w_1]) → e_2
  69. Angle(H, A, I_1) → δ
  70. Angle(V, P, U) → η
  71. Angle(U, P, W) → θ
  72. Polygon(A, B, C, P) → poly1, a_2, b_2, c_2, p_2
  73. Segment(A, C) → n_1
  74. Intersect(g, n_1) → F,
  75. Intersect(k, n_1) → G,
  76. Line(P, n_1) → c
  77. Line(B, n_1) → d
  78. CircleSector(C, Z, G) → d_1
  79. CircleSector(C, G, M) → s_1
  80. CircleSector(A, H, F) → d_2
  81. If(0 < j ≤ 1, Dilate[C, 1 - j, B]) → I
  82. If(1 < j ≤ 2, Dilate[A, 2 - j, P]) → O
  83. If(1 < j ≤ 2, Dilate[C, 2 - j, P]) → B_1
  84. Vector(C, I) → r
  85. Vector(A, O) → u_2
  86. Translate(s_1, r) → h_2
  87. Rotate(d_2, 180°, A) → k_2
  88. Vector(A, B) → v_2
  89. Vector(C, B) → w_2
  90. Translate(s_1, w_2) → s_2
  91. Mirror(s_2, B) → t_2
  92. Vector(A, P) → i_2
  93. Vector(C, P) → j_2
  94. CircleSector(A, F, H_1) → f_2
  95. Translate(f_2, i_2) → d_3
  96. Vector(C, B_1) → l_2
  97. Translate(d_1, j_2) → f_3
  98. Mirror(f_3, P) → g_3
  99. Translate(f_2, u_2) → h_3
  100. Translate(d_1, l_2) → k_3
  101. Segment(A, B) → m_2
  102. Polygon(A, B, C) → poly2, c_4, a_3, b_3
  103. Polygon(A, C, P) → poly3, p_4, a_4, c_5
  104. Midpoint(m_2) → M_4
  105. Midpoint(l) → J_1
  106. Midpoint(k_1) → M_2
  107. Midpoint(l_1) → M_3
  108. Segment(J, C) → n_2
  109. Segment(J_1, C) → i_3
  110. Rotate(J_1, If[0 < j ≤ 1, (((-j) * 180))°, -180°], J_1) → M_1
  111. Rotate(C, If[0 < j ≤ 1, (((-j) * 180))°, -180°], J_1) → C'_3
  112. Segment(M_1, C'_3) → j_3
  113. Rotate(s_1, If[0 < j ≤ 1, (((-j) * 180))°, -180°], J_1) → r_3
  114. Segment(J_1, B) → r_2
  115. Rotate(d_2, If[0 < j ≤ 1, ((j * 180))°, 180°], M_4) → p
  116. Rotate(A, If[0 < j ≤ 1, ((j * 180))°, 180°], M_4) → A'_1
  117. Segment(M_4, A'_1) → g_2
  118. Rotate(C, If[1 < j ≤ 2, (((j - 1) * 180))°, 180°], M_2) → C'_4
  119. Segment(M_2, C'_4) → q_2
  120. Rotate(d_1, If[1 < j ≤ 2, (((j - 1) * 180))°, 180°], M_2) → c_3
  121. Rotate(A, If[1 < j ≤ 2, (((-(j - 1)) * 180))°, 180°], M_3) → A'_2
  122. Segment(M_3, A'_2) → e_3
  123. Rotate(f_2, If[1 < j ≤ 2, (((-(j - 1)) * 180))°, 180°], M_3) → p_3
  124. CircleArc(C, G, M) → q_3
  125. CircleArc(A, H, F) → s_3
  126. CircleArc(C, Z, G) → t_3
  127. CircleArc(A, F, H_1) → d_4
  128. Segment(M_2, C) → l_3
  129. Segment(M_2, P) → m_3
  130. Segment(P, M_3) → n_3
  131. Segment(M_3, A) → b_4
  132. Segment(A, M_4) → e_4
  133. Segment(M_4, B) → f_4