长方体展开图探索

长方体展开图探索
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2012-12-06 10:44
所属专题 Cuboids & their Nets
①本范例演示长方体的展开图及其结构关系;②涉及核心数学概念包括多边形、立体几何、空间想象能力;③构造要点:使用Sequence、Element、Polygon、Segment等GeoGebra命令绘制展开图各面,并通过R_x, R_y, R_z等变换命令实现三维到二维的展开;④适合初中及以上学生用于理解立体几何与多边形关系,增强空间感知能力。

GeoGebra 命令及参数

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Element(listepoints, 2) → A
  5. Element(listepoints, 1) → E
  6. Element(listepoints, 4) → C_1
  7. Element(listepoints, 3) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Element(listepoints, 6) → B
  10. Element(listepoints, 7) → F
  11. Element(listepoints, 8) → G
  12. Element(listepoints, 5) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Element(listepoints, 3) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(A, B) → p
  27. Segment(B, H) → q
  28. Segment(H, E) → r
  29. Segment(H, G) → s
  30. Segment(B, F) → t
  31. Segment(G, C_1) → d_1
  32. Segment(F, G) → i_1
  33. Segment(F, C) → j_1
  34. Polygon(A, B, F', D') → poly7, a_4, b_3, f', d'
  35. Polygon(E, A, D'', C') → poly8, e_3, a_5, d'', c'
  36. Polygon(B, F'', G', H) → poly9, b_4, f'', g', h_3
  37. Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4
  38. Polygon(A_2, B_2, G'', C''') → poly11, a_6, b_5, g''_1, c'''_1

AI 绘图提示语参考

画一个长方体的展开图,包含六个矩形面,每个面用线条连接,展示长方体的三维结构。先画出三个矩形面,再连接剩余三个面,使展开图清晰可见,体现长方体的空间关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。