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长方体体积计算 by singhsaurabhi169

长方体体积计算 by singhsaurabhi169
几何画板及绘图内容加载中，请稍等……
2016-03-11 14:47
解析几何立体几何几何作图
①本范例演示如何通过动态交互计算长方体的体积；②涉及核心数学概念包括体积公式、三维几何、解析几何；③构造过程中运用了Intersect（交点）、Point（点）、OrthogonalLine（垂线）、Segment（线段）、Polygon（多边形）、Circle（圆）、Line（直线）、Midpoint（中点）等GeoGebra命令与对象；④适合高中立体几何教学，可用于演示体积计算与几何作图技巧。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → C
  4. OrthogonalLine(C, yAxis) → a
  5. OrthogonalLine(B, xAxis) → b
  6. Intersect(a, b) → D
  7. Segment(A, B) → c
  8. Segment(B, D) → d
  9. Segment(D, C) → e
  10. Segment(C, A) → f
  11. OrthogonalLine(E, xAxis) → h
  12. OrthogonalLine(F, xAxis) → i
  13. OrthogonalLine(H, yAxis) → j
  14. OrthogonalLine(G, yAxis) → k
  15. Intersect(h, j) → I
  16. Intersect(i, j) → J
  17. Intersect(i, k) → K
  18. Intersect(h, k) → L
  19. Intersect(h, a) → M
  20. Intersect(i, a) → N
  21. Intersect(j, b) → O
  22. Intersect(k, b) → P
  23. Polygon(G, H, E, L, I, M, N, J, O, P, K, F) → poly1, g_1, f_1, e_1, l, h_1, i_1, m, n, j_1, o, p, k_1
  24. Point(xAxis) → Q
  25. Circle(Q, 7 - 2 * g) → q
  26. Intersect(q, xAxis) → R, S
  27. Line(S, T) → r
  28. Circle(S, 5 - 2 * g) → s
  29. Intersect(s, r) → U, V
  30. OrthogonalLine(S, xAxis) → t
  31. Line(V, t) → a_1
  32. Line(Q, t) → b_1
  33. Circle(Q, g) → c_1
  34. Intersect(c_1, b_1) → W, Z
  35. Intersect(t, k) → A_1
  36. Line(A_1, r) → d_1
  37. Intersect(a_1, d_1) → B_1
  38. Line(B_1, k) → l_1
  39. Line(Z, d_1) → m_1
  40. Intersect(m_1, l_1) → C_1
  41. Line(C_1, b_1) → n_1
  42. Line(V, xAxis) → p_1
  43. Intersect(n_1, p_1) → D_1
  44. Polygon(Z, Q, S, A_1) → poly2, z, q_1, s_1, a_2
  45. Polygon(S, V, B_1, A_1) → poly3, s_2, v, b_2, a_3
  46. Polygon(A_1, Z, C_1, B_1) → poly4, a_4, z_1, c_2, b_3
  47. Segment(C_1, D_1) → r_1
  48. Segment(D_1, Q) → t_1
  49. Segment(D_1, V) → d_2
  50. Polygon(E, F, K, L) → poly5, e_2, f_2, k_2, l_2
  51. Polygon(O, J, K, P) → poly7, o_1, j_2, k_3, p_2
  52. Polygon(J, I, M, N) → poly8, j_3, i_2, m_2, n_2
  53. Polygon(I, L, G, H) → poly9, i_3, l_3, g_2, h_2
  54. Polygon(Q, D_1, C_1, Z) → poly10, q_3, d_3, c_3, z_3
  55. Polygon(D_1, V, B_1, C_1) → poly11, d_4, v_1, b_4, c_4
  56. Polygon(L, K, J, I) → poly12, l_4, k_4, j_4, i_4
  57. Polygon(Q, S, V, D_1) → poly13, q_4, s_4, v_2, d_5
  58. Point(yAxis) → E_1
  59. Line(E_1, xAxis) → r_2
  60. Intersect(b, r_2) → F_1
  61. Midpoint(E_1, F_1) → G_1
  62. Segment(E_1, F_1) → t_2
  63. Point(a) → H_1
  64. Line(H_1, yAxis) → e_3
  65. Intersect(e_3, xAxis) → I_1
  66. Midpoint(H_1, I_1) → J_1
  67. Segment(H_1, I_1) → f_3
  68. Midpoint(N, D) → K_1
  69. Polygon(C, A, B, D) → poly14, c_5, a_6, b_5, d_6
  70. Midpoint(Q, S) → L_1
  71. Midpoint(S, V) → M_1
  72. Midpoint(V, B_1) → N_1
  73. Midpoint(A, E) → P_1
  74. OrthogonalLine(O_1, yAxis) → q_2
  75. Intersect(h, q_2) → Q_1
  76. Segment(O_1, Q_1) → g_3
  77. Segment(Q_1, E) → h_3