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(a + b)的立方体几何表示

(a + b)的立方体几何表示
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2020-01-03 16:35
立体几何几何作图
①这个范例通过几何方式演示了(a + b)的立方体体积计算；②涉及的核心数学概念包括立体几何、体积计算、多边形构造；③作图要点提炼了使用GeoGebra命令如点、立方体、线、交点、球体、距离、多边形、垂线、棱柱、中点等；④适合高中及以上学生学习和理解多项式体积公式及几何关系。

GeoGebra 命令及参数

  1. Point(Circle[J, Distance[L, J], Segment[L, J]]) → K
  2. Cube(L, J, K) → i, M, faceKMQP, faceNOPQ, edgeLM, edgeJL, edgeJK, edgeKM, edgeLN, edgeMQ, edgeNQ, edgeNO, N, edgeJO, edgeOP, edgeKP, edgePQ, O, P, Q, faceJKML, faceLMQN, faceJLNO, faceJKPO
  3. Line(A, xAxis) → h
  4. Line(A, zAxis) → f
  5. Intersect(f, faceNOPQ) → R
  6. Line(R, h) → j
  7. Intersect(edgeOP, j) → U
  8. Sphere(A, d) → e
  9. Line(A, yAxis) → g
  10. Intersect(f, e) → B, C
  11. Intersect(h, e) → D, E
  12. Intersect(g, e) → F, G
  13. Line(R, g) → k
  14. Intersect(edgeNO, k) → S
  15. Distance(R, U) → XR
  16. Intersect(edgeNQ, j) → T
  17. Distance(R, A) → ZR
  18. Distance(T, Q) → YR
  19. Line(V, j) → l
  20. Line(G, l) → m
  21. Line(E, g) → n
  22. Line(W, g) → p
  23. Intersect(m, n) → Z
  24. Intersect(l, n) → A_1
  25. Intersect(l, p) → B_1
  26. Intersect(m, p) → C_1
  27. Polygon(Z, C_1, B_1, A_1) → q1, z_1, c_1, b_1, a_1
  28. Line(D, n) → q
  29. Intersect(m, q) → F_1
  30. Intersect(l, q) → G_1
  31. Line(D_1, q) → r
  32. Intersect(r, l) → E_1
  33. Intersect(m, r) → H_1
  34. Polygon(E_1, H_1, F_1, G_1) → q2, e_1, h_1, f_1, g_1
  35. Line(F, h) → s
  36. Line(I_1, s) → t
  37. Intersect(r, s) → J_1
  38. Intersect(q, s) → K_1
  39. Intersect(q, t) → L_1
  40. Intersect(r, t) → M_1
  41. Intersect(k, s) → N_1
  42. Intersect(t, p) → O_1
  43. Intersect(s, p) → P_1
  44. Intersect(s, n) → Q_1
  45. Intersect(t, n) → R_1
  46. Polygon(M_1, J_1, K_1, L_1) → q3, m_1, j_1, k_1, l_1
  47. Polygon(R_1, Q_1, P_1, O_1) → q4, r_1, q_1, p_1, o_1
  48. OrthogonalLine(A_1, q1) → i_1
  49. OrthogonalLine(B_1, q1) → n_1
  50. OrthogonalLine(C_1, q1) → s_1
  51. OrthogonalLine(Z, q1) → t_1
  52. OrthogonalLine(E_1, q2) → d_1
  53. OrthogonalLine(G_1, q2) → f_2
  54. OrthogonalLine(H_1, q2) → g_2
  55. OrthogonalLine(F_1, q2) → h_2
  56. OrthogonalPlane(C, f) → p_2
  57. Intersect(d_1, p_2) → S_1
  58. Intersect(g_2, p_2) → T_1
  59. Intersect(h_2, p_2) → U_1
  60. Intersect(f_2, p_2) → V_1
  61. Intersect(t_1, p_2) → W_1
  62. Intersect(i_1, p_2) → Z_1
  63. Intersect(s_1, p_2) → A_2
  64. Intersect(n_1, p_2) → B_2
  65. Polygon(W_1, A_2, B_2, Z_1) → q5, w_1, a_2, b_2, i_2
  66. Polygon(T_1, U_1, V_1, S_1) → q6, j_2, u_1, v_1, k_2
  67. OrthogonalLine(O_1, q4) → l_2
  68. OrthogonalLine(P_1, q4) → m_2
  69. OrthogonalLine(Q_1, q4) → n_2
  70. OrthogonalLine(R_1, q4) → q_2
  71. OrthogonalLine(J_1, q3) → r_2
  72. OrthogonalLine(M_1, q3) → s_2
  73. OrthogonalLine(L_1, q3) → t_2
  74. OrthogonalLine(K_1, q3) → c_2
  75. Intersect(l_2, p_2) → C_2
  76. Intersect(m_2, p_2) → D_2
  77. Intersect(n_2, p_2) → E_2
  78. Intersect(q_2, p_2) → F_2
  79. Intersect(s_2, p_2) → G_2
  80. Intersect(t_2, p_2) → H_2
  81. Intersect(r_2, p_2) → I_2
  82. Intersect(c_2, p_2) → J_2
  83. Polygon(G_2, H_2, J_2, I_2) → q7, d_2, e_2, f_3, g_3
  84. Polygon(F_2, C_2, D_2, E_2) → q8, h_3, i_3, j_3, k_3
  85. OrthogonalPlane(B, f) → p_3
  86. Intersect(n_1, p_3) → K_2
  87. Intersect(i_1, p_3) → L_2
  88. Intersect(t_1, p_3) → M_2
  89. Intersect(s_1, p_3) → N_2
  90. Intersect(f_2, p_3) → O_2
  91. Intersect(d_1, p_3) → P_2
  92. Intersect(g_2, p_3) → Q_2
  93. Intersect(h_2, p_3) → R_2
  94. Polygon(K_2, L_2, M_2, N_2) → q9, l_3, m_3, n_3, q_3
  95. Polygon(O_2, P_2, Q_2, R_2) → q10, o_2, r_3, s_3, t_3
  96. Intersect(r_2, p_3) → S_2
  97. Intersect(c_2, p_3) → T_2
  98. Intersect(t_2, p_3) → U_2
  99. Intersect(s_2, p_3) → V_2
  100. Intersect(n_2, p_3) → W_2
  101. Intersect(q_2, p_3) → Z_2
  102. Intersect(m_2, p_3) → A_3
  103. Intersect(l_2, p_3) → B_3
  104. Polygon(Z_2, W_2, A_3, B_3) → q11, z_2, w_2, a_3, b_3
  105. Polygon(U_2, T_2, S_2, V_2) → q12, u_2, c_3, d_3, v_2
  106. Prism(q6, ZR) → v, G_3, edge10, edge11, edge12, edge9, edge13, edge15, edge16, edge14, H_3, I_3, J_3, face8, face9, face7, face6, face10
  107. Prism(q7, ZR) → w, K_3, edge17, edge18, edge20, edge19, edge21, edge23, edge24, edge22, L_3, M_3, N_3, face11, face13, face14, face12, face15
  108. Prism(q8, ZR) → e_3, O_3, edge28, edge25, edge26, edge27, edge29, edge31, edge32, edge30, P_3, Q_3, R_3, face17, face16, face18, face19, face20
  109. Prism(q5, ZR) → o_3, S_3, edge33, edge35, edge36, edge34, edge37, edge39, edge40, edge38, T_3, U_3, V_3, face22, face24, face23, face21, face25
  110. Prism(q9, u_3) → v_3, W_3, edge41, edge42, edge43, edge44, edge45, edge47, edge48, edge46, Z_3, A_4, B_4, face26, face28, face29, face27, face30
  111. Prism(q11, ZL) → w_3, C_4, edge50, edge49, edge51, edge52, edge53, edge55, edge56, edge54, D_4, E_4, F_4, face31, face32, face34, face33, face35
  112. Prism(q10, a_4) → b_4, G_4, edge57, edge58, edge59, edge60, edge61, edge63, edge64, edge62, H_4, I_4, J_4, face36, face38, face39, face37, face40
  113. Prism(q12, c_4) → d_4, K_4, edge67, edge66, edge65, edge68, edge69, edge71, edge72, edge70, L_4, M_4, N_4, face43, face41, face42, face44, face45
  114. Midpoint(edge58) → D_3
  115. Midpoint(edge9) → C_9
  116. Midpoint(edge14) → C_10
  117. Midpoint(edge22) → E10
  118. Midpoint(edge21) → E_3
  119. Midpoint(T_3, U_3) → C_3

AI 绘图提示语参考

画一个立方体，再在立方体内部构造一个球体，球体与立方体的一个面相交于两点，并画出立方体的对角线。接着，在立方体的一个面上画出两条线段，这两条线段与立方体的对角线相交于一点，并连接这个交点与立方体的一个顶点，形成两个三角形。最后，在立方体的外部画出三个三角形，这些三角形与立方体的三个面相交，并连接这些交点。
以上提示语为根据原始绘图命令整理而来，仅供参考。