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Garden Problem

Garden Problem
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2018-11-29 00:39
PolygonVectorTrigonometryInequality
This example dynamically demonstrates the construction of a complex geometric figure, involving core math concepts like trigonometry, vector operations, polygon creation, and inequality analysis. Key GeoGebra commands and objects used include Polygon, Vector, Translate, and If, as summarized. Suitable for high school and above learners to understand geometric constructions and parametric modeling.

GeoGebra Commands & Parameters

  1. Polygon(E, F, 4) → poly1, f, g, h, i, G, H
  2. Vector(E, H) → u
  3. Vector(E, F) → v
  4. Translate(poly1, v) → poly2
  5. Translate(poly2, v) → poly3
  6. Translate(poly3, v) → poly4
  7. Translate(poly4, v) → poly5
  8. Translate(poly1, u) → poly6
  9. Translate(poly6, u) → poly11
  10. Translate(poly6, v) → poly7
  11. Translate(poly7, v) → poly8
  12. Translate(poly8, v) → poly9
  13. Translate(poly9, v) → poly10
  14. Translate(poly11, v) → poly12
  15. Translate(poly12, v) → poly13
  16. Translate(poly13, v) → poly14
  17. Translate(poly14, v) → poly15
  18. Translate(poly11, u) → poly16
  19. Translate(poly16, v) → poly17
  20. Translate(poly17, v) → poly18
  21. Translate(fl1_1, u) → fl1_6
  22. Translate(fl1_6, u) → fl1_{11}
  23. Translate(fl1_{11}, u) → fl1_{16}
  24. Translate(fl1_{16}, u) → fl1_{21}
  25. Translate(fl1_1, v) → fl1_2
  26. Translate(fl1_2, v) → fl1_3
  27. Translate(poly18, v) → poly19
  28. Translate(poly19, v) → poly20
  29. Translate(fl1_{21}, v) → fl1_{22}
  30. Translate(poly16, u) → poly21
  31. Translate(poly21, v) → poly22
  32. Translate(fl2_1, v) → fl2_2
  33. Translate(fl2_2, v) → fl2_3
  34. Translate(fl2_3, v) → fl2_4
  35. Translate(fl2_4, v) → fl2_5
  36. Translate(poly22, v) → poly23
  37. Translate(poly23, v) → poly24
  38. Translate(poly24, v) → poly25
  39. Translate(fl1_3, v) → fl1_4
  40. Translate(fl1_4, v) → fl1_5
  41. Translate(fl1_6, v) → fl1_7
  42. Translate(fl1_6, Vector[(2 * v)]) → fl1_8
  43. Translate(fl1_6, Vector[(3 * v)]) → fl1_9
  44. Translate(fl1_6, Vector[(4 * v)]) → fl1_{10}
  45. Translate(fl2_1, u) → fl2_6
  46. Translate(fl2_6, v) → fl2_7
  47. Translate(fl2_6, Vector[(2 * v)]) → fl2_8
  48. Translate(fl2_6, Vector[(3 * v)]) → fl2_9
  49. Translate(fl2_6, Vector[(4 * v)]) → fl2_{10}
  50. If(n_1 ≟ 0 ∨ n_2 ≟ 0 ∨ n_3 ≟ 0 ∨ n_4 ≟ 0 ∨ n_5 ≟ 0 ∨ n_6 ≟ 0 ∨ n_7 ≟ 0 ∨ n_8 ≟ 0 ∨ n_9 ≟ 0 ∨ n_{10} ≟ 0 ∨ n_{11} ≟ 0 ∨ n_{12} ≟ 0 ∨ n_{13} ≟ 0 ∨ n_{14} ≟ 0 ∨ n_{15} ≟ 0 ∨ n_{16} ≟ 0 ∨ n_{17} ≟ 0 ∨ n_{18} ≟ 0 ∨ n_{19} ≟ 0 ∨ n_{20} ≟ 0 ∨ n_{21} ≟ 0 ∨ n_{22} ≟ 0 ∨ n_{23} ≟ 0 ∨ n_{24} ≟ 0 ∨ n_{25} ≟ 0, 0, 1) → alln
  51. Translate(fl1_{11}, v) → fl1_{12}
  52. Translate(fl1_{11}, Vector[(2 * v)]) → fl1_{13}
  53. Translate(fl1_{11}, Vector[(3 * v)]) → fl1_{14}
  54. Translate(fl1_{11}, Vector[(4 * v)]) → fl1_{15}
  55. Translate(fl1_{16}, v) → fl1_{17}
  56. Translate(fl1_{16}, Vector[(2 * v)]) → fl1_{18}
  57. Translate(fl1_{16}, Vector[(3 * v)]) → fl1_{19}
  58. Translate(fl1_{16}, Vector[(4 * v)]) → fl1_{20}
  59. Translate(fl1_{22}, v) → fl1_{23}
  60. Translate(fl1_{22}, Vector[(2 * v)]) → fl1_{24}
  61. Translate(fl1_{22}, Vector[(3 * v)]) → fl1_{25}
  62. Translate(fl2_6, u) → fl2_{11}
  63. Translate(fl2_{11}, v) → fl2_{12}
  64. Translate(fl2_{11}, Vector[(2 * v)]) → fl2_{13}
  65. Translate(fl2_{11}, Vector[(3 * v)]) → fl2_{14}
  66. Translate(fl2_{11}, Vector[(4 * v)]) → fl2_{15}
  67. Translate(fl2_{11}, u) → fl2_{16}
  68. Translate(fl2_{16}, v) → fl2_{17}
  69. Translate(fl2_{16}, Vector[(2 * v)]) → fl2_{18}
  70. Translate(fl2_{16}, Vector[(3 * v)]) → fl2_{19}
  71. Translate(fl2_{16}, Vector[(4 * v)]) → fl2_{20}
  72. Translate(fl2_{16}, u) → fl2_{21}
  73. Translate(fl2_{21}, v) → fl2_{22}
  74. Translate(fl2_{21}, Vector[(2 * v)]) → fl2_{23}
  75. Translate(fl2_{21}, Vector[(3 * v)]) → fl2_{24}
  76. Translate(fl2_{21}, Vector[(4 * v)]) → fl2_{25}

AI Drawing Prompt Reference

Draw a complex geometric figure with multiple polygons and vectors. Start by creating a quadrilateral, then generate a series of new polygons by translating the previous polygon using vector u and v. Next, create some line segments and generate more line segments through translation operations, forming a complex geometric structure.
The prompt above was compiled from the original drawing commands and is for reference only.