正六边形三边形密铺

正六边形三边形密铺
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2022-12-02 06:28
①本范例演示了正六边形以三边形方式进行的正则密铺图形;②涉及的核心数学概念包括多边形构造、向量运算、几何变换等;③作图要点提炼自构造摘要,使用了Point、Polygon、Vector、Translate等GeoGebra命令与对象;④适合高中数学教学,用于展示平面图形的密铺特性与变换规律。

GeoGebra 命令及参数

  1. Point(xAxis) → B
  2. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  3. Polygon(D, C, 6) → poly2, l, J, m, n, p, q, r, G, H, I
  4. Polygon(I, H, 6) → poly3, s, N, t, a, b, c, d, K, L, M
  5. Point(xAxis) → O
  6. Vector(B, O) → u
  7. Translate(poly1, u) → poly1'
  8. Point(yAxis) → P
  9. Vector(A, P) → v
  10. Translate(poly2, v) → poly2'
  11. Translate(poly2, u) → poly2'_{1}
  12. Translate(poly1', u) → poly1''
  13. Translate(poly2', u) → poly2''
  14. Translate(poly3, u) → poly3'
  15. Translate(poly1', v) → poly1''_{1}
  16. Translate(poly1'', v) → poly1'''
  17. Translate(poly1, v) → poly1'_{1}
  18. Translate(poly2', v) → poly2''_{1}
  19. Translate(poly2'_{1}, u) → poly4
  20. Translate(poly2'', u) → poly2'''
  21. Translate(poly2''_{1}, u) → poly5
  22. Translate(poly5, u) → poly5'
  23. Translate(poly1''', u) → poly6
  24. Translate(poly1'', u) → poly1'''_{1}
  25. Translate(poly4, u) → poly4'
  26. Translate(poly3', u) → poly3''
  27. Translate(poly2''', u) → poly7
  28. Translate(poly1'''_{1}, u) → poly8
  29. Translate(poly6, u) → poly6'
  30. Translate(poly1'_{1}, v) → poly9
  31. Translate(poly2''_{1}, v) → poly10
  32. Translate(poly1''_{1}, v) → poly11
  33. Translate(poly1''', v) → poly12
  34. Translate(poly5, v) → poly5'_{1}
  35. Translate(poly9, v) → poly9'
  36. Translate(poly10, v) → poly10'
  37. Translate(poly11, v) → poly11'
  38. Translate(poly5'_{1}, v) → poly13
  39. Translate(poly12, v) → poly12'
  40. Translate(poly5', v) → poly5''
  41. Translate(poly6, v) → poly6'_{1}
  42. Translate(poly7, v) → poly7'
  43. Translate(poly7', v) → poly7''
  44. Translate(poly6'_{1}, v) → poly14
  45. Translate(poly5'', v) → poly5'''
  46. Translate(poly6', v) → poly6''
  47. Translate(poly7'', v) → poly7'''
  48. Translate(poly6'', v) → poly6'''
  49. Translate(poly6''', v) → poly15
  50. Translate(poly9', v) → poly9''
  51. Translate(poly10', v) → poly10''
  52. Translate(poly11', v) → poly11''
  53. Translate(poly13, v) → poly13'
  54. Translate(poly12', v) → poly12''
  55. Translate(poly5''', v) → poly16
  56. Translate(poly14, v) → poly14'
  57. Translate(poly7''', v) → poly17
  58. Translate(poly4', u) → poly4''
  59. Translate(poly7, u) → poly7'_{1}
  60. Translate(poly6', u) → poly6''_{1}
  61. Translate(poly7', u) → poly7''_{1}
  62. Translate(poly6'', u) → poly6'''_{1}
  63. Translate(poly7''_{1}, v) → poly18
  64. Translate(poly18, v) → poly18'
  65. Translate(poly6'''_{1}, v) → poly19
  66. Translate(poly19, v) → poly19'
  67. Translate(poly18', v) → poly18''
  68. Translate(poly8, u) → poly8'
  69. Translate(poly9'', v) → poly9'''
  70. Translate(poly11'', v) → poly11'''
  71. Translate(poly12'', v) → poly12'''
  72. Translate(poly14', v) → poly14''
  73. Translate(poly15, v) → poly15'
  74. Translate(poly19', v) → poly19''
  75. Translate(poly7'_{1}, u) → poly20
  76. Translate(poly7''_{1}, u) → poly21
  77. Translate(poly18, u) → poly18'_{1}
  78. Translate(poly4'', u) → poly4'''
  79. Translate(poly18'_{1}, v) → poly22
  80. Translate(poly22, v) → poly22'
  81. Translate(poly8', u) → poly8''
  82. Translate(poly8'', v) → poly8'''
  83. Translate(poly8''', v) → poly23
  84. Translate(poly23, v) → poly23'
  85. Translate(poly23', v) → poly23''
  86. Translate(poly23'', v) → poly23'''
  87. Translate(poly3'', u) → poly3'''
  88. Translate(poly3''', u) → poly24

AI 绘图提示语参考

画一个正则平铺{6,3}的六边形网格:先在平面上取两条参考轴确定基准点A,并以A和另一点B为起点构造一个以6边为边数的正六边形。再用六边形的对应顶点关系构造相邻的第二、第三个六边形,使它们在同一平面上连成带状布局。然后在两组平移方向上定义平移向量:一组由B指向参考轴上的O,另一组由A指向参考轴上的P。按这两个向量对第1、2、3个六边形进行重复平移,形成多行多列的规则六边形镶嵌,并让各平移后的六边形与原图保持边对边贴合。
以上提示语为根据原始绘图命令整理而来,仅供参考。