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棱柱与棱锥的理解

棱柱与棱锥的理解
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2017-03-29 15:17
多边形向量三角函数立体几何几何作图
①本范例演示棱柱与棱锥的几何构造与性质；②涉及核心数学概念包括多边形、向量、立体几何、三角函数；③作图要点运用了Vector（向量）、Translate（平移）、OrthogonalLine（垂线）、Polygon（多边形）、Midpoint（中点）、Segment（线段）、Mirror（镜像）等GeoGebra命令；④适合高中及以上学生及数学爱好者用于立体几何学习与探索。

GeoGebra 命令及参数

  1. Vector(B_1, Z) → w
  2. Vector(B_1, Y) → v
  3. Vector(B_1, X) → u
  4. Translate(A, Vector[(2 * v)]) → A'
  5. Translate(P, Vector[(2 * v)]) → P'
  6. OrthogonalLine(View3D, yAxis) → a_1
  7. OrthogonalLine(View3D, xAxis) → b_1
  8. Polygon(L, K, N, M) → poly1, l, k_1, n, m
  9. Polygon(K, P, Q, N) → poly2, k_2, p, q, n_1
  10. Polygon(L, M, S, R) → poly3, l_1, m_1, s, r
  11. Polygon(N, V, W, M) → poly4, n_2, v_1, w_1, m_2
  12. Polygon(K, T, U, L) → poly5, k_3, t, u_1, l_2
  13. Polygon(B, Q, P, A) → poly6, b_2, q_1, p_1, a_2
  14. Midpoint(R, M) → D
  15. Translate(S, Vector[(-((2 * v)))]) → S'
  16. Segment(S, C) → e
  17. Translate(M, Vector[(-2 * v)]) → M'
  18. Segment(M, E) → f
  19. Segment(E, C) → h
  20. Translate(N, Vector[(-2 * v)]) → N'
  21. Translate(Q, Vector[(-2 * v)]) → Q'_1
  22. Segment(Q, F) → i
  23. Segment(N, G) → j
  24. Segment(G, F) → d_1
  25. Translate(Q, Vector[(-2 * v)]) → Q'_2
  26. Translate(B, Vector[(-2 * v)]) → B'_1
  27. Segment(B, I) → e_1
  28. Segment(I, H) → f_1
  29. Segment(H, Q) → g_1
  30. Translate(K, Vector[(2 * v)]) → K'
  31. Translate(P, Vector[(2 * v)]) → P'_1
  32. Segment(P, J) → h_1
  33. Segment(J, A_1) → i_1
  34. Segment(A_1, K) → j_1
  35. Segment(B, H_1) → s_1
  36. Segment(H_1, C_1) → c
  37. Segment(C_1, A) → r_1
  38. Midpoint(N, P) → D_1
  39. Midpoint(k_1) → F_1
  40. Segment(A, G_1) → t_1
  41. Segment(G_1, I_1) → c_2
  42. Segment(I_1, P) → d_2
  43. Segment(J, K_1) → f_2
  44. Segment(P, L_1) → e_2
  45. Segment(L_1, K_1) → g_2
  46. Segment(M, W) → h_2
  47. Mirror(L_1, F_1) → O_1
  48. Mirror(K_1, F_1) → P_1
  49. Segment(M, M_1) → i_2
  50. Segment(N_1, J_1) → j_2
  51. Segment(J_1, M_1) → p_2
  52. Polygon(M, E, C, S) → poly7, q_2, r_2, s_2, t_2
  53. Polygon(Q, N, G, F) → poly8, q_3, n_3, g_3, f_3
  54. Polygon(B, Q, H, I) → poly9, b_3, q_4, h_3, i_3
  55. Polygon(J, A_1, K, P) → poly10, j_3, a_3, k_4, p_3
  56. Polygon(C_1, A, B, H_1) → poly11, c_3, a_4, b_4, h_4
  57. Polygon(G_1, I_1, P, A) → poly12, g_4, i_4, p_4, a_5
  58. Polygon(K_1, J, P, L_1) → poly13, k_5, j_4, p_5, l_3
  59. Polygon(M, M_1, J_1, N_1) → poly14, m_3, m_4, j_5, n_4