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长方体截面演示 by Comeau-Montasse

长方体截面演示 by Comeau-Montasse
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2014-11-11 04:55
向量三角函数解析几何立体几何几何作图
①本范例演示长方体在不同角度下的截面形状变化；②涉及核心数学概念包括立体几何、向量运算、三角函数以及三维坐标变换；③构造要点运用了Sequence, Element, Point, Polygon, Segment, Intersect, Line等GeoGebra命令及对象，如向量u, v, w的构造与旋转矩阵R_x, R_y, R_z的应用；④适合高中及以上学生及数学爱好者用于理解空间几何与变换

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. Point(listepoints) → C
  5. Element(AB, 3, 1) → avant
  6. Element(AC, 3, 1) → dessus
  7. Point(listepoints) → J
  8. Point(listepoints) → K
  9. Point(listepoints) → L
  10. Polygon(J, K, L, C) → poly7, j_2, k_1, l_1, c_5
  11. Point(listepoints) → M
  12. Point(listepoints) → N
  13. Polygon(J, M, N, K) → poly8, j_3, m_1, n_1, k_2
  14. Point(listepoints) → Q
  15. Polygon(K, L, Q, N) → poly9, k_3, l_2, q_1, n_2
  16. Point(listepoints) → A
  17. Polygon(J, C, A, M) → poly1, j, c, a_1, m
  18. Polygon(Q, A, C, L) → poly2, q, a_2, c_1, l
  19. Polygon(A, Q, N, M) → poly3, a_3, q_2, n, m_2
  20. Segment(A, M) → a'_1
  21. Segment(J, C) → j'_1
  22. Segment(K, L) → k'_3
  23. Segment(L, Q) → l'_2
  24. Segment(M, J) → m'
  25. Segment(N, K) → n'_2
  26. Segment(Q, N) → q'_1
  27. Segment(M, N) → m'_1
  28. Segment(Q, A) → q'
  29. Segment(K, J) → j'
  30. Segment(N, K) → l'
  31. Segment(C, L) → l''
  32. Segment(C, A) → l''''
  33. Segment(M, N) → k''''
  34. Segment(C, A) → k'''
  35. Point(j_3) → B
  36. Point(l_1) → D
  37. Point(n_1) → E
  38. Intersect(l_1, k_1) → F
  39. Intersect(c_5, l_1) → G
  40. Line(F, G) → d
  41. Segment(B, E) → e
  42. Line(D, e) → f
  43. Intersect(f, c) → H
  44. Segment(H, D) → g
  45. Segment(B, H) → h
  46. Line(E, h) → i
  47. Intersect(d, i) → O
  48. Intersect(i, k_1) → R
  49. Segment(R, D) → k
  50. Segment(E, R) → p
  51. Line(D, e) → r
  52. Intersect(r, l'_2) → S
  53. Segment(E, S) → s
  54. Line(B, s) → t
  55. Intersect(t, c_5) → T
  56. Segment(T, D) → b_1
  57. Segment(B, T) → d_1
  58. Segment(D, S) → e_1
  59. Polygon(B, E, S, D, T) → poly4, b_2, e_2, s_1, d_2, t_1
  60. Polygon(B, E, R, D, H) → poly5, b_3, e_3, r_1, d_3, h_1