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旋转与缩放演示

旋转与缩放演示
几何画板及绘图内容加载中，请稍等……
2020-01-29 18:42
圆三角函数几何作图
①本范例演示了一个图形在旋转过程中同时进行缩放的动态效果；②涉及的核心数学概念包括旋转、缩放、圆、三角函数等；③作图要点提炼自构造摘要，使用了Mirror（镜像）、Segment（线段）、CircleSector（扇形）、Circle（圆）、Rotate（旋转）、Dilate（缩放）、Vector（向量）、Translate（平移）等GeoGebra命令和对象；④适合高中阶段学习几何变换、函数图像和动态几何的师生使用。

GeoGebra 命令及参数

  1. Mirror(U, f) → U'
  2. Mirror(V, f) → V'
  3. Mirror(T, f) → T'
  4. Mirror(S, f) → S'
  5. Mirror(R, f) → R'
  6. Mirror(Q, f) → Q'
  7. Mirror(P, f) → P'
  8. Segment(A, P) → g
  9. Segment(A, Q) → h
  10. Segment(R, A) → i
  11. Segment(S, A) → j
  12. Segment(A, T) → k
  13. Segment(U, A) → l
  14. Segment(A, V) → m
  15. Segment(C, A) → n
  16. Segment(A, D) → p
  17. Segment(A, E) → q
  18. Segment(A, F) → r
  19. Segment(A, G) → s
  20. Segment(A, V') → t
  21. Segment(U', A) → a
  22. Segment(A, T') → b
  23. Segment(S', A) → d
  24. Segment(A, R') → e
  25. Segment(Q', A) → f_1
  26. Segment(A, P') → g_1
  27. Segment(B, A) → h_1
  28. CircleSector(A, P, Q) → c_1
  29. CircleSector(A, Q, R) → d_1
  30. CircleSector(A, U', T') → e_1
  31. CircleSector(A, D, E) → k_1
  32. Segment(H, A) → i_1
  33. Segment(A, I) → j_1
  34. Segment(J, A) → l_1
  35. CircleSector(A, H, I) → p_1
  36. CircleSector(A, I, J) → q_1
  37. Segment(A, O) → m_1
  38. CircleSector(A, V, C) → r_1
  39. Circle(A, 5.019) → c
  40. Rotate(S, (-(D7°)), A) → S'_1
  41. Rotate(A, (-(D7°)), A) → A'
  42. Segment(S'_1, A') → j'
  43. Rotate(d_1, (-(D7°)), A) → s_1
  44. Rotate(e_1, (-(D7°)), A) → c_2
  45. Rotate(q_1, (-(D7°)), A) → d_2
  46. Rotate(k_1, (-(D7°)), A) → e_2
  47. Rotate(r_1, (-(D7°)), A) → f_2
  48. Rotate(A, (-(D7°)), A) → A'_1
  49. Rotate(P, (-(D7°)), A) → P'_1
  50. Segment(A'_1, P'_1) → g'
  51. Rotate(A, (-(D7°)), A) → A'_2
  52. Rotate(Q, (-(D7°)), A) → Q'_1
  53. Segment(A'_2, Q'_1) → h'
  54. Rotate(R, (-(D7°)), A) → R'_1
  55. Rotate(A, (-(D7°)), A) → A'_3
  56. Segment(R'_1, A'_3) → i'
  57. Rotate(A, (-(D7°)), A) → A'_4
  58. Rotate(T, (-(D7°)), A) → T'_1
  59. Segment(A'_4, T'_1) → k'
  60. Rotate(U, (-(D7°)), A) → U'_1
  61. Rotate(A, (-(D7°)), A) → A'_5
  62. Segment(U'_1, A'_5) → l'
  63. Rotate(A, (-(D7°)), A) → A'_6
  64. Rotate(V, (-(D7°)), A) → V'_1
  65. Segment(A'_6, V'_1) → m'
  66. Rotate(C, (-(D7°)), A) → C'
  67. Rotate(A, (-(D7°)), A) → A'_7
  68. Segment(C', A'_7) → n'
  69. Rotate(A, (-(D7°)), A) → A'_8
  70. Rotate(D, (-(D7°)), A) → D'
  71. Segment(A'_8, D') → p'
  72. Rotate(A, (-(D7°)), A) → A'_9
  73. Rotate(E, (-(D7°)), A) → E'
  74. Segment(A'_9, E') → q'
  75. Rotate(A, (-(D7°)), A) → A'_{10}
  76. Rotate(F, (-(D7°)), A) → F'
  77. Segment(A'_{10}, F') → r'
  78. Rotate(A, (-(D7°)), A) → A'_{11}
  79. Rotate(V', (-(D7°)), A) → V''
  80. Segment(A'_{11}, V'') → t'
  81. Rotate(U', (-(D7°)), A) → U''
  82. Rotate(A, (-(D7°)), A) → A'_{12}
  83. Segment(U'', A'_{12}) → a'
  84. Rotate(A, (-(D7°)), A) → A'_{13}
  85. Rotate(T', (-(D7°)), A) → T''
  86. Segment(A'_{13}, T'') → b'
  87. Rotate(S', (-(D7°)), A) → S''
  88. Rotate(A, (-(D7°)), A) → A'_{14}
  89. Segment(S'', A'_{14}) → d'
  90. Rotate(A, (-(D7°)), A) → A'_{15}
  91. Rotate(R', (-(D7°)), A) → R''
  92. Segment(A'_{15}, R'') → e'
  93. Rotate(Q', (-(D7°)), A) → Q''
  94. Rotate(A, (-(D7°)), A) → A'_{16}
  95. Segment(Q'', A'_{16}) → n_1
  96. Rotate(A, (-(D7°)), A) → A'_{17}
  97. Rotate(P', (-(D7°)), A) → P''
  98. Segment(A'_{17}, P'') → a_1
  99. Rotate(B, (-(D7°)), A) → B'
  100. Rotate(A, (-(D7°)), A) → A'_{18}
  101. Segment(B', A'_{18}) → b_1
  102. Rotate(H, (-(D7°)), A) → H'
  103. Rotate(A, (-(D7°)), A) → A'_{19}
  104. Segment(H', A'_{19}) → h_2
  105. Rotate(A, (-(D7°)), A) → A'_{20}
  106. Rotate(I, (-(D7°)), A) → I'
  107. Segment(A'_{20}, I') → i_2
  108. Rotate(J, (-(D7°)), A) → J'
  109. Rotate(A, (-(D7°)), A) → A'_{21}
  110. Segment(J', A'_{21}) → j_2
  111. Rotate(A, (-(D7°)), A) → A'_{22}
  112. Rotate(O, (-(D7°)), A) → O'
  113. Segment(A'_{22}, O') → k_2
  114. Rotate(c_1, (-(D7°)), A) → t_1
  115. Rotate(L, (-(D7°)), A) → L'
  116. Circle(W, 3) → g_2
  117. Segment(Z, W) → l_2
  118. Rotate(Z, D7°, W) → Z'
  119. Rotate(W, D7°, W) → W'
  120. Segment(Z', W') → m_2
  121. Rotate(Z, (-(((2 * D7))°)), W) → Z'_1
  122. Rotate(W, (-(((2 * D7))°)), W) → W'_1
  123. Segment(Z'_1, W'_1) → n_2
  124. Dilate(Z, D7, W) → Z'_2
  125. Dilate(W, D7, W) → W'_2
  126. Dilate(W'_2, D7 / 100, W) → B_1
  127. Circle(W, Z') → r_2
  128. Dilate(g_2, D7 / 200, W) → p_2
  129. Dilate(g_2, D7 / 190, W) → q_2
  130. Dilate(r_2, (30 * 1 / D7), W) → s_2
  131. Vector((0, 0), (11, 0)) → v
  132. Translate(s_2, v) → t_2
  133. Dilate(t_2, 2, A) → c_3
  134. Dilate(t_2, 3, A) → d_3
  135. Dilate(t_2, 4, A) → e_3
  136. Dilate(t_2, 5, A) → f_3
  137. Dilate(t_2, 6, A) → g_3
  138. Dilate(t_2, 7, A) → h_3
  139. Dilate(t_2, 8, A) → k_3
  140. Dilate(t_2, 9, A) → p_3

AI 绘图提示语参考

画一个动态旋转和缩小的图形，展示形状在旋转的同时进行缩放的效果。图形包含多个圆、扇形和线段，通过镜像、旋转和缩放等变换生成。首先创建一个中心点，然后围绕该点绘制多个圆和扇形，再通过镜像和旋转操作生成对称图形，最后将所有元素组合成一个动态变化的整体，体现几何变换和三角函数的原理。
以上提示语为根据原始绘图命令整理而来，仅供参考。