正方体的截面 by nandrews

正方体的截面 by nandrews
几何画板及绘图内容加载中,请稍等……
2016-05-10 02:30
这个范例演示了正方体的截面。它涉及立体几何中的平面图形和截面概念。通过使用GeoGebra命令如Polygon、Prism、Point等,可以构造出正方体的各个面和截面。适合初中和高中学生学习立体几何。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Prism(poly1, 4) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Point(edgeFG) → I
  4. OrthogonalLine(I, edgeEH, space) → f
  5. OrthogonalLine(I, b, space) → g
  6. Intersect(b, g) → J
  7. OrthogonalLine(J, d, space) → h
  8. Intersect(edgeEH, f) → K
  9. Intersect(h, faceADHE) → L
  10. Polygon(I, K, L, J) → poly2, i, k, l, j
  11. Point(edgeCG) → M
  12. OrthogonalLine(M, edgeBF, space) → n
  13. OrthogonalLine(M, edgeDH, space) → p
  14. Intersect(p, edgeDH) → N
  15. OrthogonalLine(N, edgeAE, space) → q
  16. Point(q) → O
  17. Point(n) → P
  18. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1
  19. Point(edgeEH) → Q
  20. Intersect(edgeCG, edgeGH) → R
  21. Point(edgeDH) → S
  22. Plane(Q, R, S) → s
  23. IntersectPath(s, e) → poly4, T, U, V, W, t, a_1, b_1, c_1
  24. Intersect(edgeGH, edgeDH) → Z
  25. Intersect(edgeDH, d) → C_1
  26. Intersect(edgeGH, edgeEH) → A_1
  27. Intersect(edgeFG, edgeBF) → B_1
  28. Segment(A_1, B_1) → d_1
  29. Intersect(edgeBF, a) → D_1
  30. Segment(C_1, D_1) → e_1
  31. Point(d_1) → E_1
  32. Intersect(edgeCG, edgeFG) → F_1
  33. Intersect(edgeEH, edgeAE) → G_1
  34. Segment(G_1, C_1) → f_1
  35. Segment(F_1, C_1) → g_1
  36. Midpoint(g_1) → I_1
  37. Midpoint(f_1) → J_1
  38. Plane(E_1, J_1, I_1) → v
  39. IntersectPath(v, e) → poly5, K_1, l_1, L_1, M_1, N_1, O_1, h_1, i_1, j_1, k_1

AI 绘图提示语参考

绘制一个立方体,并展示其与平面FG垂直的截面。首先绘制一个底面ABCD,然后以边FG为轴,构造一个四棱柱。接着在边FG上取点I,作该边的垂线f,与底面BCGF的交点J,再作J到边d的垂线h,与边EH的交点K,以及K到边EF的垂线,与面ADHE的交点L,最后连接I、K、L、J形成截面多边形。
以上提示语为根据原始绘图命令整理而来,仅供参考。