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立方体幻象II

立方体幻象II
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2018-11-19 13:43
向量三角函数立体几何变换几何作图
这个范例演示了立方体幻象的视觉效果。它涉及立方体、三角函数、平均值、梯形和标准差等核心数学概念。通过使用Vector、Sequence、Polygon、Rotate等GeoGebra命令，可以构造出动态的立方体变换效果。适合高中数学教学和学习立体几何变换。

GeoGebra 命令及参数

  1. Vector((0, 0), A) → u
  2. Vector((0, 0), B) → v
  3. Sequence(Rotate[(cos(((i / n * 2) * π)), sin(((i / n * 2) * π))), π / 6, (0, 0)], i, 1, n) → Pts
  4. Sequence(Rotate[(((t - 1) * cos(((i / n * 2) * π))), ((t - 1) * sin(((i / n * 2) * π)))), π / 6, (0, 0)], i, 1, n) → PtsC
  5. Polygon(Element[Pts, 2], Element[Pts, 3], Element[Pts, 4], (0, 0), Element[Pts, 2]) → C1, f, g, h, i, j
  6. Rotate(C1, (2 * π / 3), (0, 0)) → L1
  7. Rotate(C1, ((2 * 2) * π / 3), (0, 0)) → L2
  8. Rotate(C1, ((3 * 2) * π / 3), (0, 0)) → L3
  9. Polygon(Element[PtsC, 2], Element[PtsC, 3], Element[PtsC, 4], (0, 0), Element[PtsC, 2]) → C2, k, l, m, p, q
  10. Rotate(C2, (2 * π / 3), (0, 0)) → M1
  11. Rotate(C2, ((2 * 2) * π / 3), (0, 0)) → M2
  12. Rotate(C2, ((3 * 2) * π / 3), (0, 0)) → M3
  13. Polygon(Element[PtsC, 2], Element[PtsC, 3], Element[PtsC, 4], (0, 0), Element[PtsC, 2]) → C3, r, s, a, b, c
  14. Rotate(C3, (2 * π / 3), (0, 0)) → N1
  15. Rotate(C3, ((2 * 2) * π / 3), (0, 0)) → N2
  16. Rotate(C3, ((3 * 2) * π / 3), (0, 0)) → N3
  17. Sequence(Sequence[Translate[L1, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → l_1
  18. Sequence(Sequence[Translate[L2, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → l_2
  19. Sequence(Sequence[Translate[L3, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → l_3
  20. Sequence(Sequence[Translate[N1, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → n_1
  21. Sequence(Sequence[Translate[N2, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → n_2
  22. Sequence(Sequence[Translate[N3, Vector[(i * u) + (j * v)]], i, 1, size], j, 1, size) → n_3
  23. Vector((0, 0), C) → w
  24. Sequence(Sequence[Translate[Translate[M1, Vector[(i * u) + (j * v)]], Vector[(0, 0), C]], i, 1, size], j, 1, size) → m_1
  25. Sequence(Sequence[Translate[Translate[M2, Vector[(i * u) + (j * v)]], Vector[(0, 0), C]], i, 1, size], j, 1, size) → m_2
  26. Sequence(Sequence[Translate[Translate[M3, Vector[(i * u) + (j * v)]], Vector[(0, 0), C]], i, 1, size], j, 1, size) → m_3