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数学与服装：约卡德花式提花机

数学与服装：约卡德花式提花机
几何画板及绘图内容加载中，请稍等……
2020-02-23 16:51
向量数列解析几何几何作图
①本范例演示约卡德花式提花机中的图案生成与变换过程；②涉及的核心数学概念包括平移、向量、周长、比例、反射、角度等；③作图要点：使用了If、Random、Sequence、Vector等GeoGebra命令，以及A1至A25、B1至B15等对象进行图案的随机生成与变换；④适合高中阶段学生学习向量、变换及算法思想，也可用于设计类课程中展示数学在艺术中的应用。

GeoGebra 命令及参数

  1. If(true, Polygon[C6, C6 + (1, 0), C6 + (0, -1)]) → D6
  2. If(true, Polygon[C7, C7 + (1, 0), C7 + (0, -1)]) → D7
  3. If(true, Polygon[C8, C8 + (1, 0), C8 + (0, -1)]) → D8
  4. If(true, Polygon[C9, C9 + (1, 0), C9 + (0, -1)]) → D9
  5. If(true, Polygon[C11, C11 + (1, 0), C11 + (0, -1)]) → D11
  6. If(true, Polygon[C12, C12 + (1, 0), C12 + (0, -1)]) → D12
  7. If(true, Polygon[C13, C13 + (1, 0), C13 + (0, -1)]) → D13
  8. If(true, Polygon[C14, C14 + (1, 0), C14 + (0, -1)]) → D14
  9. If(true, Polygon[C16, C16 + (1, 0), C16 + (0, -1)]) → D16
  10. If(true, Polygon[C17, C17 + (1, 0), C17 + (0, -1)]) → D17
  11. If(true, Polygon[C18, C18 + (1, 0), C18 + (0, -1)]) → D18
  12. If(true, Polygon[C19, C19 + (1, 0), C19 + (0, -1)]) → D19
  13. If(true, Polygon[C21, C21 + (1, 0), C21 + (0, -1)]) → D21
  14. If(true, Polygon[C22, C22 + (1, 0), C22 + (0, -1)]) → D22
  15. If(true, Polygon[C23, C23 + (1, 0), C23 + (0, -1)]) → D23
  16. If(true, Polygon[C24, C24 + (1, 0), C24 + (0, -1)]) → D24
  17. Random(1, 4) → n
  18. Sequence({Segment[(i, 0), (i, 4)], Segment[(0, i), (4, i)]}, i, 0, 4) → liste1
  19. If(true, Polygon[C7, C7 + (0, -1), C7 + (-1, -1)]) → D26
  20. If(true, Polygon[C8, C8 + (0, -1), C8 + (-1, -1)]) → D27
  21. If(true, Polygon[C9, C9 + (0, -1), C9 + (-1, -1)]) → D28
  22. If(true, Polygon[C10, C10 + (0, -1), C10 + (-1, -1)]) → D29
  23. If(true, Polygon[C12, C12 + (0, -1), C12 + (-1, -1)]) → D31
  24. If(true, Polygon[C13, C13 + (0, -1), C13 + (-1, -1)]) → D32
  25. If(true, Polygon[C14, C14 + (0, -1), C14 + (-1, -1)]) → D33
  26. If(true, Polygon[C15, C15 + (0, -1), C15 + (-1, -1)]) → D34
  27. If(true, Polygon[C17, C17 + (0, -1), C17 + (-1, -1)]) → D36
  28. If(true, Polygon[C18, C18 + (0, -1), C18 + (-1, -1)]) → D37
  29. If(true, Polygon[C19, C19 + (0, -1), C19 + (-1, -1)]) → D38
  30. If(true, Polygon[C20, C20 + (0, -1), C20 + (-1, -1)]) → D39
  31. If(true, Polygon[C22, C22 + (0, -1), C22 + (-1, -1)]) → D41
  32. If(true, Polygon[C23, C23 + (0, -1), C23 + (-1, -1)]) → D42
  33. If(true, Polygon[C24, C24 + (0, -1), C24 + (-1, -1)]) → D43
  34. If(true, Polygon[C25, C25 + (0, -1), C25 + (-1, -1)]) → D44
  35. Vector(O, O + (4, 0)) → u
  36. Vector(O, O + (0, 4)) → v
  37. Sequence(Sequence[Translate[liste1, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → l1
  38. Sequence(Sequence[Translate[D6, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L6
  39. Sequence(Sequence[Translate[D7, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L7
  40. Sequence(Sequence[Translate[D8, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L8
  41. Sequence(Sequence[Translate[D9, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L9
  42. Sequence(Sequence[Translate[D11, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L11
  43. Sequence(Sequence[Translate[D12, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L12
  44. Sequence(Sequence[Translate[D13, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L13
  45. Sequence(Sequence[Translate[D14, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L14
  46. Sequence(Sequence[Translate[D16, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L16
  47. Sequence(Sequence[Translate[D17, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L17
  48. Sequence(Sequence[Translate[D18, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L18
  49. Sequence(Sequence[Translate[D19, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L19
  50. Sequence(Sequence[Translate[D21, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L21
  51. Sequence(Sequence[Translate[D22, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L22
  52. Sequence(Sequence[Translate[D23, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L23
  53. Sequence(Sequence[Translate[D24, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L24
  54. Sequence(Sequence[Translate[D26, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L26
  55. Sequence(Sequence[Translate[D27, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L27
  56. Sequence(Sequence[Translate[D28, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L28
  57. Sequence(Sequence[Translate[D29, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L29
  58. Sequence(Sequence[Translate[D31, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L31
  59. Sequence(Sequence[Translate[D32, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L32
  60. Sequence(Sequence[Translate[D33, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L33
  61. Sequence(Sequence[Translate[D34, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L34
  62. Sequence(Sequence[Translate[D36, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L36
  63. Sequence(Sequence[Translate[D37, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L37
  64. Sequence(Sequence[Translate[D38, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L38
  65. Sequence(Sequence[Translate[D39, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L39
  66. Sequence(Sequence[Translate[D41, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L41
  67. Sequence(Sequence[Translate[D42, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L42
  68. Sequence(Sequence[Translate[D43, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L43
  69. Sequence(Sequence[Translate[D44, Vector[(s * u) + (t * v)]], s, 0, p], t, 0, q) → L44

AI 绘图提示语参考

绘制一个由4×4网格构成的方形图案区域，每个网格单元内随机填充两种方向的小三角形或小方块，形成类似提花织机的纹理。整体图案通过水平和垂直方向的平移重复排列，构成更大的对称阵列。图形包含基础网格线、随机生成的单元图案，以及用于平移的水平和垂直向量，展示几何变换与重复规律。
以上提示语为根据原始绘图命令整理而来，仅供参考。