积极 AI Logo 积极 AI

几何变换与音乐数学

几何变换与音乐数学
几何画板及绘图内容加载中，请稍等……
2023-03-11 03:44
向量数列解析几何变换几何作图
所属专题 Música y Matemáticas
①本范例通过动态演示几何变换，展示图形的对称性与变换规律；②涉及核心数学概念包括几何变换、对称性、向量、数列、解析几何；③作图要点运用了Polygon（多边形）、Midpoint（中点）、Mirror（镜像）、Vector（向量）、Sequence（数列）等GeoGebra命令与对象；④适合高中及以上数学学习，用于理解几何变换与数学应用。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → c1, a, b, c, d
  2. Midpoint(c) → E
  3. Mirror(A, E) → A'
  4. Mirror(B, E) → B'
  5. Mirror(C, E) → C'
  6. Mirror(D, E) → D'
  7. Vector(B, D) → u
  8. Vector(A, C) → v
  9. Sequence(Sequence[Polygon[Translate[A, Vector[(k * u) + (s * v)]], Translate[B, Vector[(k * u) + (s * v)]], Translate[C, Vector[(k * u) + (s * v)]], Translate[D, Vector[(k * u) + (s * v)]]], k, -20, 20], s, -20, 20) → m1, {{5.468000000000075, 5.468000000000075, 5.468000000000302, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.46799999999962, 5.467999999999847, 5.468000000000075, 5.468000000000302, 5.468000000000075, 5.467999999999847, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.467999999999847, 5.4679999999993925, 5.468000000000075, 5.467999999999847, 5.46799999999962, 5.467999999999847, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.4679999999997335, 5.46799999999962, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.467999999999989}, {5.468000000000075, 5.4679999999997335, 5.468000000000302, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.4679999999993925, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.468000000000302, 5.467999999999847, 5.46799999999962, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.46799999999962, 5.467999999999847, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999904, 5.467999999999847, 5.468000000000131, 5.467999999999904, 5.468000000000032, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.467999999999989}, {5.467999999999961, 5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999847, 5.46799999999962, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000302, 5.468000000000075, 5.467999999999847, 5.467999999999847, 5.468000000000302, 5.467999999999847, 5.468000000000302, 5.468000000000075, 5.468000000000075, 5.4679999999997335, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000131, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000046, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999961}, {5.468000000000188, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000188, 5.4679999999997335, 5.467999999999847, 5.468000000000188, 5.4679999999997335, 5.46799999999962, 5.46799999999962, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.46799999999962, 5.468000000000075, 5.468000000000302, 5.468000000000075, 5.468000000000302, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000188, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999904, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000032, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.467999999999961}, {5.467999999999904, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.467999999999847, 5.468000000000075, 5.468000000000302, 5.467999999999961, 5.468000000000188, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000245, 5.468000000000018, 5.468000000000018, 5.4679999999999325, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.468000000000032, 5.468000000000018, 5.467999999999961, 5.468000000000018}, {5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.468000000000075, 5.468000000000188, 5.468000000000188, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999989, 5.468000000000018, 5.468000000000032, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.468000000000018}, {5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000131, 5.468000000000018, 5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.468000000000018, 5.468000000000032, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999904, 5.467999999999961}, {5.468000000000032, 5.468000000000018, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999989, 5.4679999999999325, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.468000000000018, 5.468000000000032, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.467999999999961}, {5.468000000000018, 5.468000000000032, 5.468000000000018, 5.468000000000103, 5.468000000000046, 5.468000000000018, 5.468000000000075, 5.468000000000018, 5.467999999999904, 5.467999999999961, 5.468000000000131, 5.467999999999847, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000188, 5.467999999999904, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.467999999999989, 5.468000000000075, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961}, {5.4680000000000195, 5.467999999999996, 5.4680000000000035, 5.468000000000032, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.46799999999979, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999904, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.4679999999999325, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000188, 5.467999999999961}, {5.467999999999989, 5.468000000000046, 5.4680000000000355, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.468000000000075, 5.468000000000046, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999904, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999904, 5.467999999999904, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.467999999999904, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000046, 5.468000000000018, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999975, 5.468000000000046, 5.467999999999904, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.467999999999961}, {5.468000000000018, 5.467999999999989, 5.468000000000018, 5.468000000000014, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.468000000000075, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000046, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.467999999999847, 5.467999999999961, 5.468000000000075}, {5.468000000000018, 5.468000000000018, 5.468000000000103, 5.468000000000032, 5.468000000000018, 5.468000000000017, 5.4680000000000035, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.467999999999904, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999989, 5.468000000000018, 5.468000000000075, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.468000000000018, 5.467999999999996, 5.467999999999982, 5.467999999999989, 5.4680000000000035, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999961}, {5.467999999999904, 5.467999999999904, 5.467999999999961, 5.467999999999989, 5.468000000000046, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.468000000000046, 5.467999999999989, 5.468000000000046, 5.4679999999999325, 5.468000000000046, 5.468000000000046, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.467999999999975, 5.4680000000000035, 5.467999999999996, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.467999999999847, 5.4679999999997335, 5.468000000000188, 5.467999999999961}, {5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999982, 5.468, 5.467999999999989, 5.4680000000000035, 5.467999999999996, 5.468000000000018, 5.4679999999999325, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.468000000000032, 5.467999999999982, 5.468000000000011, 5.4680000000000035, 5.468000000000011, 5.468000000000032, 5.468000000000046, 5.468000000000018, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999847}, {5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.4679999999999325, 5.467999999999961, 5.467999999999989, 5.4680000000000035, 5.468000000000014, 5.468000000000007, 5.468000000000011, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.468000000000032, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.468000000000046, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.468000000000018, 5.468000000000011, 5.4680000000000035, 5.4680000000000035, 5.467999999999996, 5.4680000000000035, 5.468000000000046, 5.468000000000046, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999847}, {5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.4680000000000035, 5.4679999999999955, 5.467999999999996, 5.467999999999989, 5.467999999999996, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.468000000000011, 5.468000000000011, 5.4680000000000035, 5.467999999999996, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999847, 5.468000000000131, 5.468000000000188, 5.468000000000075, 5.468000000000075, 5.468000000000075}, {5.467999999999847, 5.467999999999961, 5.467999999999961, 5.468000000000188, 5.468000000000131, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.467999999999975, 5.468000000000011, 5.468000000000007, 5.468000000000004, 5.4680000000000035, 5.467999999999989, 5.467999999999996, 5.467999999999996, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.467999999999996, 5.4680000000000035, 5.467999999999996, 5.468000000000025, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.468000000000188}, {5.468000000000188, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.468000000000011, 5.468000000000005, 5.467999999999996, 5.467999999999989, 5.4680000000000035, 5.467999999999996, 5.4680000000000035, 5.468000000000011, 5.467999999999996, 5.467999999999996, 5.4680000000000035, 5.467999999999996, 5.468000000000007, 5.468, 5.468000000000011, 5.4680000000000035, 5.467999999999975, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075}, {5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.4680000000000035, 5.467999999999982, 5.467999999999996, 5.467999999999996, 5.467999999999996, 5.467999999999996, 5.468000000000011, 5.468000000000011, 5.467999999999996, 5.467999999999996, 5.467999999999995, 5.468, 5.467999999999993, 5.468, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.468000000000188, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847}, {5.468000000000302, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999975, 5.467999999999989, 5.467999999999989, 5.467999999999996, 5.468000000000005, 5.468000000000003, 5.467999999999998, 5.468000000000002, 5.467999999999995, 5.468, 5.468000000000002, 5.468000000000005, 5.468, 5.468000000000011, 5.4680000000000035, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.468000000000046, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.467999999999961}, {5.4679999999997335, 5.467999999999847, 5.467999999999961, 5.468000000000188, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000075, 5.468000000000018, 5.467999999999989, 5.468000000000046, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.467999999999998, 5.468000000000002, 5.467999999999997, 5.467999999999998, 5.468000000000001, 5.467999999999998, 5.4680000000000035, 5.467999999999993, 5.4680000000000035, 5.467999999999982, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.4679999999999325, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847}, {5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.468000000000018, 5.467999999999904, 5.468000000000018, 5.467999999999989, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.4680000000000035, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.467999999999996, 5.467999999999998, 5.468, 5.468, 5.468, 5.468, 5.468, 5.468, 5.468000000000011, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.467999999999904, 5.468000000000075, 5.467999999999961, 5.467999999999904, 5.467999999999961, 5.467999999999961, 5.468000000000075}, {5.467999999999847, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.4679999999997335, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000046, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.468, 5.468000000000002, 5.467999999999998, 5.467999999999999, 5.468, 5.467999999999999, 5.468000000000002, 5.467999999999998, 5.468, 5.467999999999996, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.468000000000046, 5.4679999999999325, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000188, 5.467999999999961, 5.468000000000075}, {5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.467999999999904, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000046, 5.468000000000018, 5.4680000000000035, 5.467999999999989, 5.467999999999996, 5.467999999999993, 5.467999999999998, 5.468, 5.468, 5.468, 5.467999999999998, 5.467999999999998, 5.468000000000002, 5.468000000000007, 5.468, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.468000000000075, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000075}, {5.468000000000075, 5.468000000000529, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999975, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.468, 5.4680000000000035, 5.468, 5.467999999999998, 5.468000000000005, 5.4679999999999955, 5.468000000000001, 5.467999999999996, 5.467999999999993, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000131, 5.468000000000075, 5.468000000000302}, {5.468000000000075, 5.46799999999962, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.467999999999904, 5.467999999999989, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.468000000000011, 5.468, 5.4680000000000035, 5.467999999999993, 5.468, 5.467999999999989, 5.467999999999996, 5.467999999999996, 5.468, 5.467999999999998, 5.467999999999996, 5.467999999999989, 5.467999999999996, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075}, {5.468000000000075, 5.468000000000075, 5.468000000000302, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.468000000000075, 5.467999999999904, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.468000000000011, 5.468000000000007, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.467999999999982, 5.467999999999989, 5.467999999999996, 5.467999999999982, 5.468000000000011, 5.468000000000007, 5.468000000000005, 5.467999999999998, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018}, {5.467999999999847, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999975, 5.468000000000011, 5.468000000000011, 5.4680000000000035, 5.467999999999996, 5.467999999999982, 5.467999999999982, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.468000000000032, 5.467999999999975, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.468000000000003, 5.4680000000000035, 5.467999999999989, 5.468000000000011, 5.4680000000000035, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.468000000000018, 5.468000000000075}, {5.467999999999847, 5.467999999999847, 5.468000000000188, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999996, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.467999999999996, 5.468000000000018, 5.468000000000018, 5.4680000000000035, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.468000000000011, 5.468000000000021, 5.468000000000002, 5.468000000000011, 5.4680000000000035, 5.467999999999989, 5.467999999999975, 5.468000000000075, 5.468000000000018, 5.468000000000018, 5.467999999999961}, {5.46799999999962, 5.467999999999847, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.467999999999996, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.467999999999975, 5.4680000000000035, 5.467999999999989, 5.467999999999996, 5.467999999999995, 5.468000000000007, 5.4680000000000035, 5.467999999999975, 5.467999999999989, 5.468000000000075, 5.468000000000018, 5.467999999999961}, {5.468000000000075, 5.468000000000075, 5.4679999999997335, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.468000000000131, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999989, 5.468000000000032, 5.467999999999996, 5.467999999999996, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.468000000000046, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.468000000000011, 5.467999999999998, 5.468000000000018, 5.468000000000032, 5.467999999999989, 5.468000000000018, 5.468000000000018}, {5.467999999999847, 5.467999999999847, 5.468000000000188, 5.468000000000075, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.46799999999979, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.4680000000000035, 5.468000000000018, 5.4680000000000035, 5.467999999999989, 5.468000000000011, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.468000000000075, 5.467999999999904, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.4679999999999325, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000032, 5.4680000000000035, 5.468000000000014, 5.468000000000018, 5.468000000000018, 5.4680000000000035, 5.468000000000032}, {5.467999999999847, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.467999999999989, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.468000000000011, 5.467999999999975, 5.467999999999989, 5.467999999999989, 5.468000000000046, 5.468000000000075, 5.467999999999904, 5.468000000000075, 5.467999999999904, 5.467999999999961, 5.467999999999961, 5.467999999999904, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.4679999999999325, 5.467999999999989, 5.468000000000046, 5.468000000000018, 5.468000000000032, 5.467999999999996, 5.467999999999996, 5.468000000000011, 5.468000000000032}, {5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.467999999999904, 5.468000000000018, 5.468000000000103, 5.467999999999961, 5.468000000000018, 5.4680000000000035, 5.467999999999989, 5.4680000000000035, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.4679999999999325, 5.468000000000046, 5.468000000000018, 5.468000000000018, 5.468000000000007}, {5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000188, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.4680000000000035, 5.467999999999989, 5.467999999999989, 5.468000000000032, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999904, 5.468000000000018, 5.468000000000075, 5.468000000000018, 5.468000000000131, 5.468000000000131, 5.468000000000018, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.4680000000000035}, {5.468000000000302, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.468000000000046, 5.467999999999961, 5.467999999999975, 5.467999999999989, 5.4680000000000035, 5.467999999999975, 5.467999999999989, 5.467999999999961, 5.467999999999989, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000075, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.468000000000018, 5.467999999999961, 5.467999999999904, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999989, 5.468000000000046}, {5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.4680000000000035, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.467999999999989, 5.467999999999989, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.467999999999904, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000075, 5.467999999999904}, {5.467999999999847, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000018, 5.467999999999989, 5.468000000000018, 5.4680000000000035, 5.4680000000000035, 5.467999999999975, 5.467999999999961, 5.467999999999961, 5.468000000000018, 5.468000000000075, 5.467999999999961, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.468000000000188, 5.467999999999961, 5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000131, 5.467999999999961}, {5.467999999999847, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.468000000000131, 5.468000000000018, 5.467999999999961, 5.468000000000018, 5.467999999999989, 5.4680000000000035, 5.467999999999989, 5.468000000000018, 5.468000000000018, 5.468000000000018, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.467999999999847, 5.467999999999961, 5.467999999999961, 5.467999999999847, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.467999999999847, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000188, 5.467999999999961, 5.467999999999961, 5.468000000000075}, {5.467999999999847, 5.468000000000075, 5.467999999999961, 5.468000000000188, 5.468000000000018, 5.468000000000018, 5.467999999999989, 5.468000000000032, 5.468000000000018, 5.467999999999989, 5.467999999999975, 5.468000000000018, 5.467999999999961, 5.467999999999904, 5.468000000000018, 5.467999999999904, 5.467999999999961, 5.467999999999961, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.468000000000075, 5.467999999999847, 5.468000000000075, 5.468000000000188, 5.468000000000188, 5.467999999999961, 5.468000000000302, 5.467999999999961, 5.468000000000188, 5.468000000000188, 5.467999999999961, 5.468000000000075, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.467999999999961, 5.468000000000075, 5.468000000000188, 5.467999999999961}}

AI 绘图提示语参考

在平面中先画一个四边形，并在其四条边对应的顶点处形成镜像点：取四边形的一个对角线的中点作为对称中心，分别把四个顶点关于该中点作镜像得到四个新点，连成对应的镜像四边形。再以两条对角线的向量为方向基，分别将原四边形的每个顶点沿着这两个方向按参数做平移叠加，生成一个二维参数网格中的多份四边形。最后展示随两个参数变化而出现的平移四边形族，并保留上述关于中点的镜像对应关系以突出对称与变换规律。
以上提示语为根据原始绘图命令整理而来，仅供参考。