平行六面体截面

平行六面体截面
几何画板及绘图内容加载中,请稍等……
2016-07-09 03:01
该范例展示了平行六面体的截面。涉及的核心数学概念包括立体几何中的截面性质。通过使用GeoGebra命令如RotateText、Mirror、Rotate等,可以构造出平行六面体及其截面。适合高中阶段学生学习立体几何。

GeoGebra 命令及参数

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Mirror(A, Q) → C
  3. Rotate(A, 90°, Q) → B
  4. Mirror(B, Q) → D
  5. Polygon(A, B, C, D) → ABCD, a, b, c, d
  6. PointIn(z = (h * m) + zQ) → A_1
  7. Prism(ABCD, A_1) → Π, B_1, BB1, CC1, DD1, a_1, b_1, c_1, d_1, C_1, D_1, g_1, g_2, g_3, g_4, ABCD1, AA1
  8. Point(d_1) → L
  9. Point(CC1) → N
  10. Point(sp1) → K
  11. PathParameter(K) → k
  12. Plane(K, L, N) → α
  13. IntersectPath(α, Π) → ss1, E, j, l, n, F, G, H, I, J, f, g, i
  14. Line(K, N) → KN
  15. Line(K, L) → KL
  16. Intersect(KN, Line[B, C]) → P1
  17. Intersect(KN, Line[B, B_1]) → P2
  18. Intersect(KN, Line[C_1, B_1]) → P3
  19. If(Distance[P1, B] < Distance[P1, C], Segment[P1, B], Segment[P1, C]) → p1
  20. If(Distance[P2, B] < Distance[P2, B_1], Segment[P2, B], Segment[P2, B_1]) → p2
  21. If(Distance[P3, B_1] < Distance[P3, C_1], Segment[P3, B_1], Segment[P3, C_1]) → p3
  22. If(Distance[P1, K] < Distance[P1, N], Segment[P1, K], Segment[P1, N]) → p_1
  23. Segment(P2, K) → p_2
  24. If(Distance[P3, K] < Distance[P3, N], Segment[P3, K], Segment[P3, N]) → p_3
  25. Intersect(KN, Line[D, C]) → Q1
  26. Intersect(KN, Line[D, D_1]) → Q2
  27. Intersect(KN, Line[C_1, D_1]) → Q3
  28. If(Distance[Q1, C] < Distance[Q1, D], Segment[Q1, C], Segment[Q1, D]) → q1
  29. If(Distance[Q2, D] < Distance[Q2, D_1], Segment[Q2, D], Segment[Q2, D_1]) → q2
  30. If(Distance[Q3, C_1] < Distance[Q3, D_1], Segment[Q3, C_1], Segment[Q3, D_1]) → q3
  31. If(Distance[Q1, K] < Distance[Q1, N], Segment[Q1, K], Segment[Q1, N]) → q_1
  32. Segment(Q2, K) → q_2
  33. If(Distance[Q3, K] < Distance[Q3, N], Segment[Q3, K], Segment[Q3, N]) → q_3
  34. Intersect(KL, Line[D, A]) → R1
  35. Intersect(KL, Line[A_1, A]) → R2
  36. Intersect(KL, Line[D_1, D]) → R3
  37. If(Distance[R1, A] < Distance[R1, D], Segment[R1, A], Segment[R1, D]) → r1
  38. If(Distance[R2, A] < Distance[R2, A_1], Segment[R2, A], Segment[R2, A_1]) → r2
  39. If(Distance[R3, D] < Distance[R3, D_1], Segment[R3, D], Segment[R3, D_1]) → r3
  40. If(Distance[R1, K] < Distance[R1, L], Segment[R1, K], Segment[R1, L]) → r_1
  41. If(Distance[R2, K] < Distance[R2, L], Segment[R2, K], Segment[R2, L]) → r_2
  42. If(Distance[R3, K] < Distance[R3, L], Segment[R3, K], Segment[R3, L]) → r_3
  43. Intersect(KL, Line[A_1, B_1]) → S1
  44. Intersect(KL, Line[C_1, B_1]) → S2
  45. Intersect(KL, Line[C_1, D_1]) → S3
  46. If(Distance[S1, A_1] < Distance[S1, B_1], Segment[S1, A_1], Segment[S1, B_1]) → s1
  47. If(Distance[S2, C_1] < Distance[S2, B_1], Segment[S2, C_1], Segment[S2, B_1]) → s2
  48. If(Distance[S3, C_1] < Distance[S3, D_1], Segment[S3, C_1], Segment[S3, D_1]) → s3
  49. If(Distance[S1, K] < Distance[S1, L], Segment[S1, K], Segment[S1, L]) → s_1
  50. If(Distance[S2, K] < Distance[S2, L], Segment[S2, K], Segment[S2, L]) → s_2
  51. If(Distance[S3, K] < Distance[S3, L], Segment[S3, K], Segment[S3, L]) → s_3

AI 绘图提示语参考

绘制一个平行六面体,其底面为正方形,顶点由旋转和镜像得到。在底面上方取一点作为棱柱的顶点,形成棱柱。在棱柱的棱上选取三个点,通过这三个点确定一个截面平面。该平面与棱柱的各棱相交,形成截面多边形。在截面与棱柱棱的交点处,根据距离判断,绘制出截面与棱柱棱之间的线段,以及截面内部的线段,最终清晰展示出平行六面体被平面截切后的截面形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。