立方体的面积化

立方体的面积化
几何画板及绘图内容加载中,请稍等……
2013-10-13 22:18
这个范例展示了如何用一个正方形覆盖一个立方体。它涉及立方体的几何性质和面积化问题。通过使用GeoGebra中的Polygon, Line, Circle等命令,可以构造出一系列几何对象。适合高中数学教学和学习立体几何的学生。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Polygon(A, D, 4) → poly2, e, f, g, h, E, F
  3. Polygon(D, C, 4) → poly3, i, j, k, l, G, H
  4. Polygon(E, D, 4) → poly4, m, n, p, q, I, J
  5. Line(G, B) → r
  6. Circle(B, D) → s
  7. Intersect(s, r, 2) → K
  8. Polygon(B, K, 4) → poly5, t, a_1, b_1, c_1, L, M
  9. Midpoint(b_1) → N
  10. Semicircle(M, L) → d_1
  11. Midpoint(t) → O
  12. Ray(O, N) → e_1
  13. Intersect(d_1, e_1, 1) → P
  14. Polygon(M, P, 4) → poly6, f_1, g_1, h_1, i_1, Q, R
  15. Polygon(P, L, 4) → poly7, j_1, k_1, l_1, m_1, S, T
  16. Polygon(K, F, 4) → poly8, n_1, p_1, q_1, r_1, U, V
  17. Midpoint(M, Q) → W
  18. Polygon(P, W, Q) → poly9, q_2, p_2, w
  19. Polygon(P, M, W) → poly10, w_1, p_3, m_2
  20. Polygon(W, R, M) → poly11, m_3, w_2, r_2
  21. Polygon(W, R, Q) → poly12, q_3, w_3, r_3
  22. Midpoint(c_1) → Z
  23. Polygon(N, Z, M) → poly13, m_4, n_2, z
  24. Midpoint(a_1) → A_1
  25. Polygon(A_1, N, L) → poly14, l_2, a_2, n_3
  26. Polygon(A_1, O, K) → poly15, k_2, a_3, o
  27. Polygon(O, Z, B) → poly16, b_2, o_1, z_1
  28. Line(D, q_1) → s_1
  29. OrthogonalLine(D, s_1) → t_1
  30. Polygon(A_1, O, Z, N) → poly17, a_4, o_2, z_2, n_4
  31. Intersect(s_1, b) → B_1
  32. Intersect(s_1, q) → C_1
  33. Intersect(t_1, h) → D_1
  34. Intersect(t_1, k) → E_1
  35. Polygon(D_1, D, A) → poly18, a_5, d_2, d_3
  36. Polygon(A, D, B_1, B) → poly19, a_6, d_4, b_3, b_4
  37. Polygon(D, E_1, G, C) → poly20, d_5, e_2, g_2, c_2
  38. Polygon(B_1, D, C) → poly21, c_3, b_5, d_6
  39. Polygon(D_1, F, E, D) → poly22, d_7, f_2, e_3, d_8
  40. Polygon(E, C_1, D) → poly23, d_9, e_4, c_4
  41. Polygon(C_1, J, H, D) → poly24, c_5, j_2, h_2, d_{10}
  42. Polygon(D, H, E_1) → poly25, e_5, d_{11}, h_3
  43. Vector(D, F) → u
  44. Translate(D_1, u) → F_1
  45. Translate(D, u) → D'
  46. Translate(A, u) → A'
  47. Polygon(F_1, D', A') → poly18', a', f_3, d'
  48. Translate(A, u) → A'_1
  49. Translate(D, u) → D'_1
  50. Translate(B_1, u) → G_1
  51. Translate(B, u) → B'
  52. Polygon(A'_1, D'_1, G_1, B') → poly19', a'_1, d'_1, g_3, b'
  53. Vector(D, K) → v
  54. Translate(E, v) → E'
  55. Translate(C_1, v) → H_1
  56. Translate(D, v) → D'_2
  57. Polygon(E', H_1, D'_2) → poly23', d'_2, e', h_4
  58. Translate(D_1, v) → I_1
  59. Translate(F, v) → F'
  60. Translate(E, v) → E'_1
  61. Translate(D, v) → D'_3
  62. Polygon(I_1, F', E'_1, D'_3) → poly22', i_2, f', e'_1, d'_3
  63. Vector(D, U) → u_1
  64. Translate(B_1, u_1) → J_1
  65. Translate(D, u_1) → D'_4
  66. Translate(C, u_1) → C'
  67. Polygon(J_1, D'_4, C') → poly21', c', j_3, d'_4
  68. Translate(D, u_1) → D'_5
  69. Translate(E_1, u_1) → K_1
  70. Translate(G, u_1) → G'
  71. Translate(C, u_1) → C'_1
  72. Polygon(D'_5, K_1, G', C'_1) → poly20', d'_5, k_3, g', c'_1
  73. Vector(D, V) → v_1
  74. Translate(C_1, v_1) → L_1
  75. Translate(J, v_1) → J'
  76. Translate(H, v_1) → H'
  77. Translate(D, v_1) → D'_6
  78. Polygon(L_1, J', H', D'_6) → poly24', l_3, j', h', d'_6
  79. Translate(D, v_1) → D'_7
  80. Translate(H, v_1) → H'_1
  81. Translate(E_1, v_1) → M_1
  82. Polygon(D'_7, H'_1, M_1) → poly25', m_5, d'_7, h'_1
  83. Vector(W, J') → u_2
  84. Translate(W, u_2) → W'
  85. Translate(R, u_2) → R'
  86. Translate(Q, u_2) → Q'
  87. Polygon(W', R', Q') → poly12', q', w', r'
  88. Vector(W, G') → v_2
  89. Vector(W, F') → s_2
  90. Vector(W, B') → t_2
  91. Translate(W, s_2) → W'_1
  92. Translate(R, s_2) → R'_1
  93. Translate(M, s_2) → M'
  94. Polygon(W'_1, R'_1, M') → poly11', m', w'_1, r'_1
  95. Translate(P, t_2) → P'
  96. Translate(M, t_2) → M'_1
  97. Translate(W, t_2) → W'_2
  98. Polygon(P', M'_1, W'_2) → poly10', w'_2, p', m'_1
  99. Translate(P, v_2) → P'_1
  100. Translate(W, v_2) → W'_3
  101. Translate(Q, v_2) → Q'_1
  102. Polygon(P'_1, W'_3, Q'_1) → poly9', q'_1, p'_1, w'_3
  103. Vector(T, R'_1) → u_3
  104. Translate(poly7, u_3) → poly7'
  105. Midpoint(T, L) → N_1
  106. Midpoint(B, D) → O_1
  107. Midpoint(A, E) → P_1
  108. Midpoint(E, H) → Q_1
  109. Midpoint(C, H) → R_1

AI 绘图提示语参考

绘制一个立方体,并用一个正方形覆盖它。首先,使用四个顶点A、D、C、E构造四个正方形,然后通过这些正方形的边构造一系列线段和圆,接着利用这些线段和圆构造多个交点,最后通过这些交点和顶点构造多个正方形,最终覆盖整个立方体。
以上提示语为根据原始绘图命令整理而来,仅供参考。