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正方体截面演示

正方体截面演示
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2012-02-09 01:23
立体几何几何作图函数图像
所属专题 Volume of Solids
①本范例演示了通过平行于底面的平面截取正方体的几何过程；②涉及的核心数学概念包括立体几何、截面形状、空间想象能力；③作图要点——使用了Sequence（序列）、Element（元素）、Point（点）、Polygon（多边形）、Segment（线段）等GeoGebra命令与对象；④适合高中立体几何教学或学生空间几何能力培养。

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((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Point(listepoints) → A
  5. Point(listepoints) → E
  6. Point(listepoints) → C_1
  7. Point(listepoints) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Point(listepoints) → B
  10. Point(listepoints) → F
  11. Point(listepoints) → G
  12. Point(listepoints) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Point(listepoints) → 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(H, E) → n
  27. Segment(A, B) → p
  28. Segment(B, H) → q
  29. Segment(H, E) → r
  30. Segment(H, G) → s
  31. Segment(B, F) → t
  32. Segment(G, C_1) → d_1
  33. Segment(F, G) → i_1
  34. Segment(F, C) → j_1
  35. Sequence(Mat * Element[plan, k], k, 1, 4) → plan'
  36. Sequence((Element[plan', k, 1, 1], Element[plan', k, 2, 1]), k, 1, 4) → listepoints2
  37. Point(listepoints2) → M
  38. Point(listepoints2) → N
  39. Point(listepoints2) → Q
  40. Point(listepoints2) → R
  41. Polygon(M, N, Q, R) → poly7, m_2, n_2, q_2, r_1
  42. Polygon(Translate[A, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[B, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[H, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[E, Vector[(u - w) / (2 * w) * Vector[G, H]]]) → poly', k_1, l_1, m_1, n_1