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立方体错觉III

立方体错觉III
几何画板及绘图内容加载中，请稍等……
2018-11-19 18:27
多边形立体几何变换参数方程函数图像
①本范例演示了三维立方体在二维平面上的投影与错觉现象；②涉及的核心数学概念包括立体几何、多边形、几何变换、参数方程与函数图像；③作图要点：运用了If、Sequence、Polygon、Rotate等GeoGebra命令，通过对象n、t、taux1、PtsC1、taux、Pts、PtsC、C1、f、g、h、i、j等进行动态演示；④适合高中及以上学生学习立体几何、几何变换及参数方程的应用。

GeoGebra 命令及参数

  1. If(0 ≤ t ≤ 1, 1.0E-5, If[1 < t ≤ 2, t - 1, 1]) → taux1
  2. Sequence(Rotate[((taux1 * cos(((i / n * 2) * π))), (taux1 * sin(((i / n * 2) * π)))), π / 6, (0, 0)], i, 1, n) → PtsC1
  3. If(0 ≤ t ≤ 1, t, 1) → taux
  4. Sequence(Rotate[(cos(((i / n * 2) * π)), sin(((i / n * 2) * π))), π / 6, (0, 0)], i, 1, n) → Pts
  5. Sequence(Rotate[((taux * cos(((i / n * 2) * π))), (taux * sin(((i / n * 2) * π)))), π / 6, (0, 0)], i, 1, n) → PtsC
  6. Polygon(Element[Pts, 2], Element[Pts, 3], Element[Pts, 4], (0, 0), Element[Pts, 2]) → C1, f, g, h, i, j
  7. Rotate(C1, (2 * π / 3), (0, 0)) → L1
  8. Rotate(C1, ((2 * 2) * π / 3), (0, 0)) → L2
  9. Rotate(C1, ((3 * 2) * π / 3), (0, 0)) → L3
  10. Polygon(Element[PtsC, 3], Element[PtsC, 4], Element[PtsC, 5], (0, 0), Element[PtsC, 3]) → C2, k, l, m, p, q
  11. Rotate(C2, (2 * π / 3), (0, 0)) → M1
  12. Rotate(C2, ((2 * 2) * π / 3), (0, 0)) → M2
  13. Polygon(Element[PtsC1, 2], Element[PtsC1, 3], Element[PtsC1, 4], (0, 0), Element[PtsC1, 2]) → C3, r, s, a, b, c
  14. Rotate(C2, ((3 * 2) * π / 3), (0, 0)) → M3
  15. Rotate(C3, (2 * π / 3), (0, 0)) → N1
  16. Rotate(C3, ((2 * 2) * π / 3), (0, 0)) → N2
  17. Rotate(C3, ((3 * 2) * π / 3), (0, 0)) → N3
  18. Sequence(Sequence[Translate[Translate[L1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_1
  19. Sequence(Sequence[Translate[Translate[L2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_2
  20. Sequence(Sequence[Translate[Translate[L3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_3
  21. Sequence(Sequence[Translate[Translate[M1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_1
  22. Sequence(Sequence[Translate[Translate[M2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_2
  23. Sequence(Sequence[Translate[Translate[M3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_3
  24. Sequence(Sequence[Translate[Translate[N1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_1
  25. Sequence(Sequence[Translate[Translate[N2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_2
  26. Sequence(Sequence[Translate[Translate[N3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_3

AI 绘图提示语参考

绘制一个立方体的三维投影，包含三个旋转的立方体面，每个面由四个顶点组成，通过旋转和平移生成多个重复的立方体面，形成一个立方体的三维幻象。
以上提示语为根据原始绘图命令整理而来，仅供参考。