斜二测六面体

斜二测六面体
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2013-12-15 06:14
所属专题 Surface Area
该范例演示了斜二测六面体的绘制方法。涉及的核心数学概念包括立体几何中的六面体及其投影。通过使用GeoGebra命令如Point, Segment, Polygon等,可以构造出六面体的各个面,并通过变换命令如Translate实现六面体的平移。适合高中阶段的学生学习立体几何。

GeoGebra 命令及参数

  1. Point(xAxis) → O
  2. OrthogonalLine(O, xAxis) → k
  3. Point(k) → T
  4. Point(k) → S
  5. OrthogonalLine(S, k) → g_1
  6. Point(g_1) → P
  7. Sequence(Mat * Element[cube, k], k, 1, 9) → cube'
  8. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 9) → listepoints
  9. Element(listepoints, 1) → M
  10. Element(listepoints, 7) → L
  11. Element(listepoints, 8) → K
  12. Element(listepoints, 4) → J
  13. Segment(M, J) → m'
  14. Element(listepoints, 5) → N
  15. Element(listepoints, 2) → A
  16. Segment(A, M) → a'_1
  17. Element(listepoints, 6) → Q
  18. Polygon(K, L, Q, N) → poly6, k_3, l_2, q_1, n_2
  19. Point(n_2) → R
  20. Element(listepoints, 3) → C
  21. Polygon(Q, A, C, L) → poly2, q, a_2, c_1, l
  22. Polygon(J, K, L, C) → poly4, j_2, k_1, l_1, c_5
  23. Line(R, k_1) → e
  24. Intersect(e, l_2) → F
  25. Line(F, q) → f
  26. Intersect(f, a_2) → G
  27. Line(G, a'_1) → g
  28. Intersect(g, m') → H
  29. Element(Element[AE, 3], 1) → droite
  30. Element(AB, 3, 1) → avant
  31. Element(AC, 3, 1) → dessus
  32. Polygon(J, M, N, K) → poly5, j_3, m_1, n_1, k_2
  33. Polygon(J, C, A, M) → poly1, j, c, a_1, m
  34. Polygon(A, Q, N, M) → poly3, a_3, q_2, n, m_2
  35. Segment(J, C) → j'_1
  36. Segment(K, L) → k'_3
  37. Segment(L, Q) → l'_2
  38. Segment(N, K) → n'_2
  39. Segment(Q, N) → q'_1
  40. Segment(M, N) → m'_1
  41. Segment(Q, A) → q'
  42. Segment(K, J) → j'
  43. Segment(N, K) → l'
  44. Segment(C, L) → l''
  45. Segment(C, A) → l''''
  46. Segment(M, N) → k''''
  47. If(i ≟ 1, true, false) → h
  48. Segment(C, A) → k'''
  49. PointIn(poly2) → E
  50. Polygon(A, M, J, C) → poly10, p, s, t, b_1
  51. Polygon(C, F', A) → poly7, a_4, c_2, f'
  52. Polygon(J, R', M) → poly8, m_3, j_1, r'
  53. Segment(R, M) → d_1
  54. Line(J, M) → f_1
  55. Line(C, A) → h_1
  56. Segment(R, H) → e_1
  57. Translate(R_2, A - M) → Q_2
  58. Polygon(A, Q_2, R_2, M) → poly9, a_5, q_3, r_2, m_4
  59. Translate(R_3, C - J) → F_3
  60. Polygon(J, R_3, F_3, C) → poly11, j_4, r_3, f_3, c_3
  61. Angle(Line[M, J], Line[M, R']) → ang
  62. Angle(Line[C, A], Line[C, F']) → ang2
  63. Angle(Line[A, M], Line[A, F']) → ang3
  64. Angle(Line[J, C], Line[J, R']) → ang4
  65. Angle(Line[C, J], Line[C, A]) → ang5

AI 绘图提示语参考

绘制一个斜投影棱柱,首先在x轴上取点O,通过O作x轴的垂线得到点T和S,再通过S作垂线得到点P。接着构造棱柱的各个面,包括顶面、底面和侧面,使用Translate命令将顶面平移得到棱柱的各个侧面。最后连接各个点形成棱柱的各个面,包括顶面、底面和侧面,确保所有线段和多边形正确连接。
以上提示语为根据原始绘图命令整理而来,仅供参考。