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立方体与长方体体积计算

立方体与长方体体积计算
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2016-06-21 09:05
解析几何立体几何几何作图
①本范例演示立方体与长方体体积计算的比较与关系；②涉及核心数学概念包括体积公式、算术平均数、连续性、三角形、乘法、概率；③作图要点：使用Point, Segment, Polygon, Intersect, Rotate, Vector, Translate, Textfield等GeoGebra命令和对象构建几何图形与文本；④适合高中阶段学生学习和理解立体几何体积计算及相关数学概念。

GeoGebra 命令及参数

  1. Point(Circle[A, r]) → B
  2. Segment(A, B) → f
  3. Point(Circle[B, r]) → C
  4. Segment(B, C) → g
  5. Point(Circle[C, r]) → D
  6. Segment(C, D) → h
  7. Polygon(D, A, B, C) → poly1, d, a, b, c
  8. Segment(D, B) → i
  9. Segment(A, C) → j
  10. Intersect(j, i) → E
  11. Rotate(D, (-rot), E) → D'
  12. Rotate(A, (-rot), E) → A'
  13. Rotate(B, (-rot), E) → B'
  14. Rotate(C, (-rot), E) → C'
  15. Polygon(D', A', B', C') → poly1', d', a', b', c'
  16. Point(Circle[F, r]) → G
  17. Segment(F, G) → k
  18. Point(Circle[G, r]) → H
  19. Segment(G, H) → m
  20. Point(Circle[H, r]) → I
  21. Segment(H, I) → n
  22. Segment(I, G) → q
  23. Segment(F, H) → s
  24. Intersect(s, q) → J
  25. Point(Circle[A', r]) → K
  26. Segment(A', K) → t
  27. Point(Circle[D', r]) → L
  28. Segment(D', L) → e
  29. Point(Circle[C', r]) → M
  30. Segment(C', M) → f_1
  31. Point(Circle[B', r]) → N
  32. Segment(B', N) → g_1
  33. Polygon(K, N, M, L) → poly2, k_1, n_1, m_1, l_1
  34. Point(Circle[O, airk]) → P
  35. Segment(O, P) → h_1
  36. Vector(P, O) → u
  37. Translate(N, u) → N'
  38. Translate(M, u) → M'
  39. Translate(L, u) → L'
  40. Translate(K, u) → K'
  41. Translate(O, Vector[(0, 0)]) → O'
  42. Translate(P, Vector[(0, 0)]) → P'
  43. Segment(O', P') → i_1
  44. Polygon(N', B', C', M') → poly3, n', b'_1, c'_1, m'
  45. Polygon(M', L', D', C') → poly4, m'_1, l', d'_1, c'_2
  46. Polygon(K', L', D', A') → poly5, k', l'_1, d'_2, a'_1
  47. Polygon(K', N', B', A') → poly6, k'_1, n'_1, b'_2, a'_2
  48. Polygon(N', K', L', M') → poly7, n'_2, k'_2, l'_2, m'_2
  49. Point(Circle[Q, p]) → R
  50. Segment(Q, R) → j_1
  51. Point(Circle[R, l]) → S
  52. Segment(R, S) → p_1
  53. Point(Circle[S, p]) → U
  54. Segment(S, U) → r_1
  55. Polygon(U, Q, R, S) → poly8, u_1, q_1, r_2, s_1
  56. Segment(U, R) → t_1
  57. Segment(S, Q) → a_1
  58. Intersect(a_1, t_1) → T
  59. Rotate(U, (-rot), T) → U'
  60. Rotate(Q, (-rot), T) → Q'
  61. Rotate(R, (-rot), T) → R'
  62. Rotate(S, (-rot), T) → S'
  63. Polygon(U', Q', R', S') → poly8', u', q', r', s'
  64. Point(Circle[Q', ti]) → V
  65. Segment(Q', V) → b_1
  66. Point(Circle[S', ti]) → W
  67. Segment(S', W) → c_1
  68. Point(Circle[U', ti]) → Z
  69. Segment(U', Z) → d_1
  70. Point(Circle[R', ti]) → A_1
  71. Segment(R', A_1) → e_1
  72. Polygon(Z, V, A_1, W) → poly9, z_1, v, a_2, w
  73. Point(Circle[B_1, tbair]) → C_1
  74. Segment(B_1, C_1) → f_2
  75. Vector(B_1, C_1) → v_1
  76. Translate(S', v_1) → S''
  77. Translate(U', v_1) → U''
  78. Translate(Q', v_1) → Q''
  79. Translate(R', v_1) → R''
  80. Polygon(R', R'', S'', S') → poly10, r'_1, r'', s'', s'_1
  81. Polygon(S'', U'', U', S') → poly11, s''_1, u'', u'_1, s'_2
  82. Polygon(R'', Q'', Q', R') → poly12, r''_1, q'', q'_1, r'_2
  83. Polygon(Q'', U'', U', Q') → poly13, q''_1, u''_1, u'_2, q'_2
  84. Polygon(Q'', R'', S'', U'') → poly14, q''_2, r''_2, s''_2, u''_2
  85. Textfield(p) → InputBox1
  86. Textfield(l) → InputBox2
  87. Textfield(ti) → InputBox3
  88. Textfield(r) → InputBox4