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矩形中的矩形

矩形中的矩形
几何画板及绘图内容加载中，请稍等……
2020-05-12 23:59
几何作图
①本范例演示在一个大矩形内绘制多个小矩形，并计算它们的面积与占比；②涉及的核心数学概念包括面积计算、百分比、统计特征、自然数与算术运算；③作图要点——从下方『构造摘要』提炼用到了 Point（点）、Dilate（缩放）、Polygon（多边形）、Textfield（文本框）等 GeoGebra 命令/对象；④适合初中及以上学生学习几何图形的面积、比例关系，以及数学可视化。

GeoGebra 命令及参数

  1. Point(Circle[A, m1]) → B
  2. Dilate(Rotate[B, 90°, A], n1 / m1, A) → C
  3. Polygon(A, B, B + C - A, C) → q1, a, b, f, c
  4. Point(Circle[A_1, m1]) → B_1
  5. Dilate(Rotate[B_1, 90°, A_1], n1 / m1, A_1) → C_1
  6. Polygon(A_1, B_1, B_1 + C_1 - A_1, C_1) → q1_1, a_1, b_1, f_1, c_1
  7. Polygon(D, D + (m2, 0), D + (m2, n2), D + (0, n2)) → q2, d, g, h, i
  8. Point(Circle[A_2, m1]) → B_2
  9. Dilate(Rotate[B_2, 90°, A_2], n1 / m1, A_2) → C_2
  10. Polygon(A_2, B_2, B_2 + C_2 - A_2, C_2) → q1_2, a_2, b_2, f_2, c_2
  11. Point(Circle[A_3, m1]) → B_3
  12. Dilate(Rotate[B_3, 90°, A_3], n1 / m1, A_3) → C_3
  13. Polygon(A_3, B_3, B_3 + C_3 - A_3, C_3) → q1_3, a_3, b_3, f_3, c_3
  14. Point(Circle[A_4, m1]) → B_4
  15. Dilate(Rotate[B_4, 90°, A_4], n1 / m1, A_4) → C_4
  16. Polygon(A_4, B_4, B_4 + C_4 - A_4, C_4) → q1_4, a_4, b_4, f_4, c_4
  17. Point(Circle[A_5, m1]) → B_5
  18. Dilate(Rotate[B_5, 90°, A_5], n1 / m1, A_5) → C_5
  19. Polygon(A_5, B_5, B_5 + C_5 - A_5, C_5) → q1_5, a_5, b_5, f_5, c_5
  20. Point(Circle[A_6, m1]) → B_6
  21. Dilate(Rotate[B_6, 90°, A_6], n1 / m1, A_6) → C_6
  22. Polygon(A_6, B_6, B_6 + C_6 - A_6, C_6) → q1_6, a_6, b_6, f_6, c_6
  23. Point(Circle[A_7, m1]) → B_7
  24. Dilate(Rotate[B_7, 90°, A_7], n1 / m1, A_7) → C_7
  25. Polygon(A_7, B_7, B_7 + C_7 - A_7, C_7) → q1_7, a_7, b_7, f_7, c_7
  26. Point(Circle[A_8, m1]) → B_8
  27. Dilate(Rotate[B_8, 90°, A_8], n1 / m1, A_8) → C_8
  28. Polygon(A_8, B_8, B_8 + C_8 - A_8, C_8) → q1_8, a_8, b_8, f_8, c_8
  29. Point(Circle[A_9, m1]) → B_9
  30. Dilate(Rotate[B_9, 90°, A_9], n1 / m1, A_9) → C_9
  31. Polygon(A_9, B_9, B_9 + C_9 - A_9, C_9) → q1_9, a_9, b_9, f_9, c_9
  32. Point(Circle[A_{10}, m1]) → B_{10}
  33. Dilate(Rotate[B_{10}, 90°, A_{10}], n1 / m1, A_{10}) → C_{10}
  34. Polygon(A_{10}, B_{10}, B_{10} + C_{10} - A_{10}, C_{10}) → q1_{10}, a_{10}, b_{10}, f_{10}, c_{10}
  35. Point(Circle[A_{11}, m1]) → B_{11}
  36. Dilate(Rotate[B_{11}, 90°, A_{11}], n1 / m1, A_{11}) → C_{11}
  37. Polygon(A_{11}, B_{11}, B_{11} + C_{11} - A_{11}, C_{11}) → q1_{11}, a_{11}, b_{11}, f_{11}, c_{11}
  38. Point(Circle[A_{12}, m1]) → B_{12}
  39. Dilate(Rotate[B_{12}, 90°, A_{12}], n1 / m1, A_{12}) → C_{12}
  40. Polygon(A_{12}, B_{12}, B_{12} + C_{12} - A_{12}, C_{12}) → q1_{12}, a_{12}, b_{12}, f_{12}, c_{12}
  41. Point(Circle[A_{13}, m1]) → B_{13}
  42. Dilate(Rotate[B_{13}, 90°, A_{13}], n1 / m1, A_{13}) → C_{13}
  43. Polygon(A_{13}, B_{13}, B_{13} + C_{13} - A_{13}, C_{13}) → q1_{13}, a_{13}, b_{13}, f_{13}, c_{13}
  44. Point(Circle[A_{14}, m1]) → B_{14}
  45. Dilate(Rotate[B_{14}, 90°, A_{14}], n1 / m1, A_{14}) → C_{14}
  46. Polygon(A_{14}, B_{14}, B_{14} + C_{14} - A_{14}, C_{14}) → q1_{14}, a_{14}, b_{14}, f_{14}, c_{14}
  47. Point(Circle[A_{15}, m1]) → B_{15}
  48. Dilate(Rotate[B_{15}, 90°, A_{15}], n1 / m1, A_{15}) → C_{15}
  49. Polygon(A_{15}, B_{15}, B_{15} + C_{15} - A_{15}, C_{15}) → q1_{15}, a_{15}, b_{15}, f_{15}, c_{15}
  50. Point(Circle[A_{16}, m1]) → B_{16}
  51. Dilate(Rotate[B_{16}, 90°, A_{16}], n1 / m1, A_{16}) → C_{16}
  52. Polygon(A_{16}, B_{16}, B_{16} + C_{16} - A_{16}, C_{16}) → q1_{16}, a_{16}, b_{16}, f_{16}, c_{16}
  53. Point(Circle[A_{17}, m1]) → B_{17}
  54. Dilate(Rotate[B_{17}, 90°, A_{17}], n1 / m1, A_{17}) → C_{17}
  55. Polygon(A_{17}, B_{17}, B_{17} + C_{17} - A_{17}, C_{17}) → q1_{17}, a_{17}, b_{17}, f_{17}, c_{17}
  56. Textfield(m1) → InputBox1
  57. Textfield(n1) → InputBox2
  58. Textfield(m2) → InputBox3
  59. Textfield(n2) → InputBox4
  60. Point(Circle[A_{18}, m1]) → B_{18}
  61. Dilate(Rotate[B_{18}, 90°, A_{18}], n1 / m1, A_{18}) → C_{18}
  62. Polygon(A_{18}, B_{18}, B_{18} + C_{18} - A_{18}, C_{18}) → q1_{18}, a_{18}, b_{18}, f_{18}, c_{18}
  63. Textfield(m1) → InputBox1_1
  64. Textfield(n1) → InputBox2_1
  65. Point(Circle[A_{19}, m1]) → B_{19}
  66. Dilate(Rotate[B_{19}, 90°, A_{19}], n1 / m1, A_{19}) → C_{19}
  67. Polygon(A_{19}, B_{19}, B_{19} + C_{19} - A_{19}, C_{19}) → q1_{19}, a_{19}, b_{19}, f_{19}, c_{19}
  68. Textfield(m1) → InputBox1_2
  69. Textfield(n1) → InputBox2_2
  70. Point(Circle[A_{20}, m1]) → B_{20}
  71. Dilate(Rotate[B_{20}, 90°, A_{20}], n1 / m1, A_{20}) → C_{20}
  72. Polygon(A_{20}, B_{20}, B_{20} + C_{20} - A_{20}, C_{20}) → q1_{20}, a_{20}, b_{20}, f_{20}, c_{20}
  73. Textfield(m1) → InputBox1_3
  74. Textfield(n1) → InputBox2_3
  75. Point(Circle[A_{21}, m1]) → B_{21}
  76. Dilate(Rotate[B_{21}, 90°, A_{21}], n1 / m1, A_{21}) → C_{21}
  77. Polygon(A_{21}, B_{21}, B_{21} + C_{21} - A_{21}, C_{21}) → q1_{21}, a_{21}, b_{21}, f_{21}, c_{21}
  78. Textfield(m1) → InputBox1_4
  79. Textfield(n1) → InputBox2_4
  80. Point(Circle[A_{22}, m1]) → B_{22}
  81. Dilate(Rotate[B_{22}, 90°, A_{22}], n1 / m1, A_{22}) → C_{22}
  82. Polygon(A_{22}, B_{22}, B_{22} + C_{22} - A_{22}, C_{22}) → q1_{22}, a_{22}, b_{22}, f_{22}, c_{22}
  83. Textfield(m1) → InputBox1_5
  84. Textfield(n1) → InputBox2_5
  85. Point(Circle[A_{23}, m1]) → B_{23}
  86. Dilate(Rotate[B_{23}, 90°, A_{23}], n1 / m1, A_{23}) → C_{23}
  87. Polygon(A_{23}, B_{23}, B_{23} + C_{23} - A_{23}, C_{23}) → q1_{23}, a_{23}, b_{23}, f_{23}, c_{23}
  88. Textfield(m1) → InputBox1_6
  89. Textfield(n1) → InputBox2_6

AI 绘图提示语参考

画一个大矩形，并在其内部绘制多个小矩形，每个小矩形通过旋转和缩放得到，展示它们之间的面积和百分比关系，构造顺序从小到大依次绘制多个小矩形，最后展示大矩形和所有小矩形的组合。
以上提示语为根据原始绘图命令整理而来，仅供参考。