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等腰三角形与菱形的单位圆平移动画

等腰三角形与菱形的单位圆平移动画
几何画板及绘图内容加载中，请稍等……
2017-05-17 22:37
测试改名0圆变换几何作图滑块动画
该范例展示了一个基于单位圆的动态几何动画，通过旋转、平移和缩放等变换，在圆内构造等腰三角形、四边形及菱形等图形，并观察它们随参数变化而运动的过程。核心数学概念包括等腰三角形的性质、菱形的判定、单位圆上的角度关系、向量的平移与缩放，以及几何变换的复合。作图要点使用了GeoGebra的Rotate（旋转）、Angle（角度）、Ray（射线）、Point（点）、Circle（圆）、Intersect（交点）、Segment（线段）、Line（直线）、LineBisector（中垂线）、CircleSector（扇形）、Dilate（缩放）、Vector（向量）、Translate（平移）、Midpoint（中点）、Polygon（多边形）等命令，涉及大量辅助对象如B_1、C、A'、α、f、g等。适合高中或大学低年级学生用于理解几何变换与动态构造，也可作为教师演示动画辅助教学。

GeoGebra 命令及参数

  1. Rotate(B_1, 45°, C) → A'
  2. Angle(B_1, C, A') → α
  3. Ray(C, A') → f
  4. Ray(C, B_1) → g
  5. Rotate(A', 45°, C) → A''
  6. Angle(A', C, A'') → β
  7. Ray(C, A'') → h
  8. Point(f) → A
  9. Circle(C, A) → c
  10. Intersect(c, h, 1) → D
  11. Segment(A, D) → i
  12. Line(A, g) → j
  13. Intersect(j, h) → E
  14. LineBisector(A, E) → k
  15. Intersect(k, g) → B
  16. Segment(A, B) → l
  17. Segment(B, E) → m
  18. Circle(C, m / 2) → d
  19. Intersect(d, h, 1) → F
  20. Segment(B, F) → n
  21. Segment(A, C) → p
  22. Segment(C, B) → q
  23. Line(C, F) → r
  24. Circle(C, 1) → e
  25. Intersect(e, r, 1) → G
  26. Ray(C, G) → s
  27. Circle(E, (0.3 * Distance[E, D])) → t
  28. Intersect(t, j, 2) → H
  29. Intersect(t, h, 2) → I
  30. CircleSector(E, H, I) → c_1
  31. Segment(A, E) → a
  32. Segment(D, C) → b
  33. Rotate(c_1, If[0 < o ≤ 1, ((-o) * π / 2), ((-π)) / 2], E) → d_1
  34. Dilate(E, If[1.5 < o ≤ 2.5, 2.5 - o, 0], C) → E'
  35. Vector(E, E') → u
  36. Translate(d_1, u) → e_1
  37. Circle(C, Radius[t]) → f_1
  38. Intersect(f_1, p, 1) → J
  39. Intersect(f_1, q) → K,
  40. Dilate(C, If[2.5 < o ≤ 3.5, 3.5 - o, 0], A) → C'
  41. Rotate(D, If[2.5 < o ≤ 3.5, ((-(o - 2.5)) * π / 4), ((-π)) / 4], C) → D'
  42. Rotate(C, If[2.5 < o ≤ 3.5, ((-(o - 2.5)) * π / 4), ((-π)) / 4], C) → C'_1
  43. Segment(D', C'_1) → b'
  44. Intersect(f_1, b) → L,
  45. CircleSector(C, J, L) → g_1
  46. Rotate(g_1, If[4 < o ≤ 5, ((-(o - 4)) * π / 4), ((-π)) / 4], C) → h_1
  47. Segment(C, F) → i_1
  48. Segment(F, E) → j_1
  49. Segment(E, D) → k_1
  50. Dilate(C, If[5 < o ≤ 6, 6 - o, 0], F) → C'_2
  51. Segment(C, C'_2) → l_1
  52. Midpoint(B, E) → M
  53. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], M) → B'
  54. Segment(B, B') → m_1
  55. Dilate(M, If[7 < o ≤ 8, 8 - o, 0], E) → M'
  56. Segment(M, M') → n_1
  57. Line(M, j_1) → p_1
  58. Point(p_1) → N
  59. Angle(N, M, B) → γ
  60. Dilate(F, If[8 < o ≤ 9, 9 - o, 0], M) → F'
  61. Vector(F, F') → v
  62. Translate(C, v) → C'_3
  63. Translate(C'_2, v) → O
  64. Segment(C'_3, O) → q_1
  65. Rotate(C'_3, If[9 < o ≤ 10, ((-(o - 9)) * (π - γ)), (-(π - γ))], M) → P
  66. Rotate(O, If[9 < o ≤ 10, ((-(o - 9)) * (π - γ)), (-(π - γ))], M) → O'
  67. Segment(P, O') → r_1
  68. Rotate(P, If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], M) → P'
  69. Rotate(O', If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], M) → O''
  70. Segment(P', O'') → s_1
  71. Angle(A, B, E) → δ
  72. Rotate(P, If[11 < o ≤ 12, ((-(o - 11)) * δ), (-δ)], B) → P'_1
  73. Rotate(O', If[11 < o ≤ 12, ((-(o - 11)) * δ), (-δ)], B) → O''_1
  74. Segment(P'_1, O''_1) → t_1
  75. Rotate(P', If[11 < o ≤ 12, ((-(o - 11)) * δ), (-δ)], B) → P''
  76. Rotate(O'', If[11 < o ≤ 12, ((-(o - 11)) * δ), (-δ)], B) → O'''
  77. Segment(P'', O''') → a_1
  78. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], D) → A'_1
  79. Segment(B, D) → f_2
  80. Circle(B, f_2 / 3) → c_2
  81. Intersect(c_2, f_2, 1) → Q
  82. Circle(Q, f_2 / 3) → d_2
  83. Intersect(d_2, f_2, 2) → R
  84. Dilate(B, If[13 < o ≤ 14, 14 - o, 0], Q) → B'_1
  85. Dilate(Q, If[14 < o ≤ 15, 15 - o, 0], R) → B'_2
  86. Dilate(R, If[15 < o ≤ 16, 16 - o, 0], D) → R'
  87. Segment(B, B'_1) → g_2
  88. Segment(Q, B'_2) → h_2
  89. Segment(R, R') → i_2
  90. Angle(D, B, C) → ε
  91. Rotate(C, If[16 < o ≤ 17, ((-(o - 16)) * ε), (-ε)], B) → C'_4
  92. Rotate(B, If[16 < o ≤ 17, ((-(o - 16)) * ε), (-ε)], B) → B'_3
  93. Segment(C'_4, B'_3) → q'
  94. Rotate(C'_4, If[17 < o ≤ 18, ((o - 17) * π), π], Q) → S
  95. Rotate(B'_3, If[17 < o ≤ 18, ((o - 17) * π), π], Q) → T
  96. Segment(S, T) → q''
  97. Rotate(S, If[18 < o ≤ 19, ((o - 18) * π), π], R) → S'
  98. Rotate(T, If[18 < o ≤ 19, ((o - 18) * π), π], R) → T'
  99. Segment(S', T') → q'''
  100. Segment(B, F) → j_2
  101. Circle(B, q / 2) → e_2
  102. Intersect(e_2, j_2, 1) → U
  103. Circle(U, q / 2) → k_2
  104. Intersect(k_2, j_2, 2) → V
  105. Dilate(B, If[19 < o ≤ 20, 20 - o, 0], U) → B'_4
  106. Dilate(U, If[20 < o ≤ 21, 21 - o, 0], V) → U'
  107. Dilate(V, If[21 < o ≤ 22, 22 - o, 0], F) → V'
  108. Dilate(F, If[19 < o ≤ 20, 20 - o, 0], V) → F'_1
  109. Dilate(V, If[20 < o ≤ 21, 21 - o, 0], U) → V'_1
  110. Dilate(U, If[21 < o ≤ 22, 22 - o, 0], B) → U'_1
  111. Segment(F, F'_1) → l_2
  112. Segment(V, V'_1) → m_2
  113. Segment(U, U'_1) → n_2
  114. Angle(F, B, C) → ζ
  115. Rotate(F, If[22 < o ≤ 23, ((o - 22) * π), π], V) → F'_2
  116. Rotate(F'_1, If[22 < o ≤ 23, ((o - 22) * π), π], V) → W
  117. Segment(F'_2, W) → p_2
  118. Rotate(F'_2, If[23 < o ≤ 24, ((o - 23) * π), π], U) → Z
  119. Rotate(W, If[23 < o ≤ 24, ((o - 23) * π), π], U) → W'
  120. Segment(Z, W') → q_2
  121. Rotate(Z, If[24 < o ≤ 25, ((o - 24) * ζ), ζ], B) → Z'
  122. Rotate(W', If[24 < o ≤ 25, ((o - 24) * ζ), ζ], B) → W''
  123. Segment(Z', W'') → r_2
  124. Rotate(Z', If[25 < o ≤ 26, ((o - 25) * π), π], Z') → Z''
  125. Rotate(W'', If[25 < o ≤ 26, ((o - 25) * π), π], Z') → W'''
  126. Segment(Z'', W''') → s_2
  127. Polygon(A, D, C, B) → poly1, a_2, d_3, c_3, b_2
  128. Segment(A, D) → b_1