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Rectangles within a Rectangle

Rectangles within a Rectangle
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2020-05-12 23:59
Geometric Construction
This example demonstrates drawing multiple smaller rectangles within a larger rectangle, calculating their areas, and understanding percentage relationships. Key math concepts include area calculation, percentages, statistical characteristics, natural numbers, and arithmetic. It uses GeoGebra commands like Point, Dilate, Polygon, and Textfield for construction. Suitable for middle school students and above to explore geometric area, proportions, and mathematical visualization.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a large rectangle and multiple smaller rectangles inside it, each obtained by rotating and scaling, showing their areas and percentage relationships, construct in order from small to large, finally display the combination of the large rectangle and all smaller rectangles.
The prompt above was compiled from the original drawing commands and is for reference only.