棱柱几何演示

棱柱几何演示
几何画板及绘图内容加载中,请稍等……
2015-02-19 11:42
①本范例演示棱柱的几何构造与性质;②涉及核心概念包括立体几何、多边形、向量、三维空间中的点线面关系;③作图要点运用了PointIn, Polygon, OrthogonalLine, Point, OrthogonalPlane, Vector, Translate, Segment, Plane, Intersect等GeoGebra命令与对象;④适合高中及以上学生及数学爱好者用于立体几何学习和探索。

GeoGebra 命令及参数

  1. PointIn(a) → A
  2. PointIn(a) → B
  3. PointIn(a) → C
  4. PointIn(a) → D
  5. PointIn(a) → E
  6. PointIn(a) → F
  7. PointIn(a) → G
  8. Polygon(A, B, C, D, E, F, G) → poly1, a_1, b, c, d, e, f, g
  9. OrthogonalLine(H, a) → h
  10. Point(h) → I
  11. Polygon(J, K, N, M) → poly2, j, k, n, m
  12. OrthogonalPlane(I, h) → i
  13. Vector(H, I) → u
  14. Translate(poly2, u) → poly2'
  15. Translate(poly1, u) → poly1'
  16. OrthogonalLine(A, a) → l
  17. OrthogonalLine(B, a) → p
  18. OrthogonalLine(C, a) → q
  19. OrthogonalLine(D, a) → r
  20. OrthogonalLine(E, a) → s
  21. OrthogonalLine(F, a) → t
  22. OrthogonalLine(G, a) → b_1
  23. OrthogonalLine(K, a) → c_1
  24. OrthogonalLine(N, a) → d_1
  25. OrthogonalLine(M, a) → e_1
  26. OrthogonalLine(J, a) → f_1
  27. Segment(I, H) → g_1
  28. Point(g_1) → O
  29. Plane(O, a) → o
  30. Intersect(l, i) → P
  31. Intersect(b_1, i) → Q
  32. Intersect(p, i) → R
  33. Intersect(q, i) → S
  34. Intersect(r, i) → T
  35. Intersect(t, i) → U
  36. Intersect(s, i) → V
  37. Intersect(c_1, i) → W
  38. Intersect(f_1, i) → Z
  39. Intersect(d_1, i) → A_1
  40. Intersect(e_1, i) → B_1
  41. Intersect(d_1, o) → C_1
  42. Intersect(e_1, o) → D_1
  43. Intersect(c_1, o) → E_1
  44. Intersect(f_1, o) → F_1
  45. Intersect(s, o) → G_1
  46. Intersect(l, o) → H_1
  47. Intersect(p, o) → I_1
  48. Intersect(q, o) → J_1
  49. Intersect(r, o) → K_1
  50. Intersect(t, o) → L_1
  51. Intersect(b_1, o) → M_1
  52. Polygon(I_1, J_1, K_1, G_1, L_1, M_1, H_1) → poly3, i_1, j_1, k_1, g_2, l_1, m_1, h_1
  53. Polygon(F_1, E_1, C_1, D_1) → poly4, f_2, e_2, c_2, d_2
  54. Segment(W, K) → n_1
  55. Segment(A_1, N) → p_1
  56. Segment(B_1, M) → q_1
  57. Segment(Z, J) → r_1
  58. Segment(R, B) → s_1
  59. Segment(S, C) → t_1
  60. Segment(T, D) → a_2
  61. Segment(V, E) → b_2
  62. Segment(P, A) → h_2
  63. Segment(Q, G) → i_2
  64. Segment(U, F) → j_2

AI 绘图提示语参考

绘制一个棱柱,首先在平面上创建七个点A、B、C、D、E、F、G,然后用这七个点构成一个底面多边形。接着在底面多边形所在的平面上创建一条线h,并在线上创建一个点I,用点I和线h创建一个垂直于底面的平面i。将多边形沿向量u平移,得到另一个平行的多边形。然后创建从每个点到线h的垂线,以及从每个点到平面i的垂线,最后找到这些垂线的交点,形成棱柱的侧面。
以上提示语为根据原始绘图命令整理而来,仅供参考。