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动态几何作图演示

动态几何作图演示
几何画板及绘图内容加载中，请稍等……
2018-01-15 09:47
圆函数三角函数解析几何几何作图
这个范例动态演示了涉及几何平均数、单位圆、勾股定理和函数图像的几何问题。通过旋转、相交、缩放等操作，直观展示几何关系。构造过程中运用了 Rotate, Ray, Line, Point, Intersect, Segment, Dilate, Angle, Circle, CircleSector, Vector, Translate, Polygon, Midpoint, CircleArc, Semicircle, OrthogonalLine, Distance 等命令和对象。适合高中数学教学，用于理解复杂几何概念和函数图像的关联。

GeoGebra 命令及参数

  1. Rotate(D, a°, A) → B'
  2. Ray(A, B') → g
  3. Line(D, g) → h
  4. Point(g) → B
  5. Ray(A, D) → f
  6. Line(B, f) → i
  7. Intersect(h, i) → C
  8. Line(A, C) → t_1
  9. Line(C, D) → i_3
  10. Segment(A, D) → b_2
  11. Point(b_2) → E
  12. Line(B, E) → j_3
  13. Intersect(j_3, t_1) → F
  14. Dilate(F, If[7 < o ≤ 8, 8 - o, 0], E) → O'
  15. Segment(F, O') → r_1
  16. Intersect(i_3, j_3) → G
  17. Segment(E, G) → g_2
  18. Segment(B, C) → g_3
  19. Segment(A, B) → f_3
  20. Angle(D, A, B') → α
  21. Segment(B, C) → j
  22. Segment(A, D) → k
  23. Segment(D, C) → l
  24. Segment(A, B) → m
  25. Min(m, k) → b
  26. Circle(B, (0.2 * b)) → d
  27. Circle(A, (0.2 * b)) → e
  28. Circle(D, (0.2 * b)) → p
  29. Circle(C, (0.2 * b)) → c
  30. Intersect(e, k, 1) → E_1
  31. Intersect(e, m, 1) → F_1
  32. Intersect(p, k, 1) → G_1
  33. Intersect(p, l, 1) → H
  34. Intersect(d, g, 2) → I
  35. Ray(B, I) → q
  36. Intersect(c, h, 2) → J
  37. Ray(C, J) → r
  38. Intersect(c, i, 2) → K
  39. Ray(C, K) → s
  40. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  41. Segment(A, A') → t
  42. Rotate(E_1, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  43. CircleSector(A, E_1, E') → c_1
  44. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], B) → A'_1
  45. Vector(A, A'_1) → u
  46. Translate(c_1, u) → d_1
  47. Segment(A, A'_1) → f_1
  48. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], C) → C'
  49. Vector(B, C') → v
  50. Translate(d_1, v) → e_1
  51. Segment(B, C') → g_1
  52. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], D) → D'
  53. Segment(C, D') → h_1
  54. Polygon(A, D, C, B) → poly1, a_1, b_1, d_2, c_2
  55. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], B) → A'_2
  56. Vector(A, A'_2) → w
  57. Translate(A, w) → A'_3
  58. Translate(A', w) → A''
  59. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], D) → A'_4
  60. Vector(A, A'_4) → u_1
  61. Translate(A, u_1) → A'_5
  62. Translate(A'_1, u_1) → L
  63. Rotate(C, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → D'_2
  64. Rotate(D', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → D''
  65. Rotate(B, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → C'_2
  66. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → C''
  67. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → A'_7
  68. Rotate(A'_1, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → M
  69. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A'_8
  70. Rotate(A', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A''_1
  71. Rotate(C, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → D'_3
  72. Rotate(D', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → D''_1
  73. Rotate(B, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → C'_3
  74. Rotate(C', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → C''_1
  75. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → A'_9
  76. Rotate(A'_1, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → N
  77. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → A'_{10}
  78. Rotate(A', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → A''_2
  79. Line(A, C) → s_2
  80. Midpoint(A, C) → Q
  81. Rotate(A, If[16 < o ≤ 17, ((o - 16) * π), π], Q) → A'_{11}
  82. Line(A, C) → h_3
  83. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_6
  84. Segment(A, A'_6) → i_1
  85. Circle(G, r_1) → k_1
  86. Segment(F, E) → j_1
  87. Intersect(k_1, j_3, 2) → P
  88. Circle(P, 1) → p_1
  89. Intersect(p_1, j_3, 2) → R
  90. Segment(G, P) → l_1
  91. Ray(P, R) → m_1
  92. Intersect(k_1, i_3) → U, V
  93. Ray(G, V) → n_1
  94. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], F) → C'_1
  95. Segment(B, C'_1) → q_1
  96. Dilate(E, If[8 < o ≤ 9, 9 - o, 0], G) → S'
  97. Dilate(D, If[8 < o ≤ 9, 9 - o, 0], G) → B'_1
  98. Segment(D, B'_1) → s_1
  99. Segment(E, S') → f_2
  100. Rotate(E, If[10 < o ≤ 11, ((o - 10) * π), π], G) → S'_1
  101. Rotate(S', If[10 < o ≤ 11, ((o - 10) * π), π], G) → S''
  102. Rotate(P, If[11 < o ≤ 13, ((o - 11) * π / 2), π], Midpoint[F, P]) → P'
  103. Midpoint(F, P) → W
  104. CircleArc(W, P, P') → e_2
  105. Semicircle(F, P) → k_2
  106. OrthogonalLine(E, m_1) → i_2
  107. Distance(B, F) → distanceCO
  108. OrthogonalLine(G, m_1) → j_2
  109. Intersect(k_2, j_2) → A_1,
  110. Distance(A_1, G) → distanceA1T
  111. Distance(A_1, G) → distanceA1G
  112. Distance(B, F) → distanceBF
  113. Rotate(F, If[10 < o ≤ 11, ((o - 10) * π), π], Midpoint[F, P]) → F'
  114. Rotate(O', If[10 < o ≤ 11, ((o - 10) * π), π], Midpoint[F, P]) → O''
  115. Segment(F', O'') → h_2
  116. Angle(A_1, G, F) → β
  117. Dilate(G, If[13 < o ≤ 14, 14 - o, 0], A_1) → G'
  118. Segment(G, G') → l_2
  119. Angle(B, F, A) → γ
  120. Rotate(B, If[14 < o ≤ 15, ((o - 14) * γ / 2), γ / 2], F) → B'_2
  121. Rotate(C'_1, If[14 < o ≤ 15, ((o - 14) * γ / 2), γ / 2], F) → O
  122. Segment(B'_2, O) → m_2
  123. Dilate(F, If[15 < o ≤ 16, 16 - o, 0], G) → F'_1
  124. Vector(F, F'_1) → v_1
  125. Translate(B'_2, v_1) → S
  126. Translate(O, v_1) → O'_1
  127. Segment(S, O'_1) → n_2
  128. Rotate(S, If[16 < o ≤ 17, ((-(o - 16)) * (γ / 2 + π / 2)), (-(γ / 2 + π / 2))], G) → S'_2
  129. Rotate(O'_1, If[16 < o ≤ 17, ((-(o - 16)) * (γ / 2 + π / 2)), (-(γ / 2 + π / 2))], G) → T
  130. Segment(S'_2, T) → p_2