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构建长方体

构建长方体
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2014-05-25 05:30
多边形向量立体几何几何作图
①本范例演示如何通过 GeoGebra 构建三维长方体模型；②涉及的核心数学概念包括多边形、向量、平移变换、立体几何等；③作图要点：运用了 Polygon, Line, Point, Segment, Vector, Translate, Sequence 等命令和对象，通过向量平移和序列生成长方体的各个面；④适合高中阶段学生学习立体几何，理解空间图形的构建方法。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → مضلع1, a, b, c, d
  2. Line(E, F) → e
  3. Point(Circle[E, abs(n)]) → G
  4. Segment(E, G) → f
  5. Point(f) → H
  6. Vector(E, H) → u
  7. Translate(A, u) → A'
  8. Translate(B, u) → B'
  9. Translate(C, u) → C'
  10. Translate(D, u) → D'
  11. Polygon(A', B', C', D') → مضلع1', a', b', c', d'
  12. Polygon(B', B, A, A') → مضلع2, b'_1, b_1, a_1, a'_1
  13. Polygon(D', C', C, D) → مضلع3, d'_1, c'_1, c_1, d_1
  14. Sequence(Polygon[A + (i, 0), B + (i, 0), C + (i, 0), D + (i, 0)], i, 0, m) → list1
  15. Sequence(Polygon[A' + (i, 0), B' + (i, 0), C' + (i, 0), D' + (i, 0)], i, 0, m) → list2
  16. Sequence(Polygon[B' + (i, 0), B + (i, 0), A + (i, 0), A' + (i, 0)], i, 0, m) → list3
  17. Sequence(Polygon[C' + (i, 0), C + (i, 0), D + (i, 0), D' + (i, 0)], i, 0, m) → list4
  18. Sequence(Polygon[A - (0, i), B - (0, i), C - (0, i), D - (0, i)], i, 1, r) → list6
  19. Sequence(Polygon[A' - (0, i), B' - (0, i), C' - (0, i), D' - (0, i)], i, 1, r) → list5
  20. Sequence(Polygon[A' - (0, i), A - (0, i), D - (0, i), D' - (0, i)], i, 1, r) → list7
  21. Sequence(Polygon[B' - (0, i), B - (0, i), C - (0, i), C' - (0, i)], i, 1, r) → list8
  22. Sequence(Polygon[B' - (0, i) + (m, 0), B - (0, i) + (m, 0), C - (0, i) + (m, 0), C' - (0, i) + (m, 0)], i, 1, r) → list9
  23. Sequence(Sequence[Polygon[B' - (0, i) + (j, 0), B - (0, i) + (j, 0), C - (0, i) + (j, 0), C' - (0, i) + (j, 0)], i, 1, r], j, 1, m) → list10
  24. Sequence(Sequence[Polygon[A' - (0, i) + (j, 0), A - (0, i) + (j, 0), D - (0, i) + (j, 0), D' - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list11
  25. Sequence(Sequence[Polygon[A - (0, i) + (j, 0), B - (0, i) + (j, 0), C - (0, i) + (j, 0), D - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list12
  26. Sequence(Sequence[Polygon[A' - (0, i) + (j, 0), B' - (0, i) + (j, 0), C' - (0, i) + (j, 0), D' - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list13
  27. Sequence(Translate[list1, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list14
  28. Sequence(Translate[list2, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list15
  29. Sequence(Translate[list3, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list16
  30. Sequence(Translate[list4, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list17
  31. Sequence(Translate[list5, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list18
  32. Sequence(Translate[list6, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list19
  33. Sequence(Translate[list7, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list20
  34. Sequence(Translate[list8, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list21
  35. Sequence(Translate[list9, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list22
  36. Sequence(Translate[list10, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list23
  37. Sequence(Translate[list12, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list24
  38. Sequence(Translate[list13, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list25
  39. Sequence(Translate[list11, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list26

AI 绘图提示语参考

绘制一个三维长方体，先画底面四边形，再通过一条线段确定高度方向，将底面沿该方向平移得到顶面，连接对应顶点形成侧面。随后沿水平方向复制多组长方体，形成一排，再沿垂直方向堆叠多层，构成一个网格状的长方体阵列。最后将整个阵列沿斜向平移多次，形成错落有致的立体堆叠效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。