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三等分长方体体积

三等分长方体体积
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2015-03-26 06:40
立体几何几何作图
①本范例演示如何通过构造几何体将长方体体积三等分；②涉及核心数学概念包括体积计算、相似三角形、几何变换；③构造过程中运用了Pyramid（棱锥）、Plane（平面）、IntersectPath（路径相交）、PointIn（点在路径上）、Volume（体积）、Point（点）、Polygon（多边形）、Prism（棱柱）等GeoGebra命令与对象；④适合高中阶段立体几何教学与探究，可用于理解体积关系与空间几何构造。

GeoGebra 命令及参数

  1. Pyramid(G, F_2, D_2, C_2, A_2) → b, face1, edge5, edge6, edge7, edge8, face2, face3, face4, face5, edge1, edge2, edge3, edge4
  2. Pyramid(H, B_2, D_3, F, A_3) → d, face6, edge13, edge14, edge15, edge16, face7, face8, face9, face10, edge9, edge10, edge11, edge12
  3. Pyramid(E, B, D, C, A) → a, faceBDCE, edgeAE, edgeAB_1, edgeAD_1, edgeAC_1, faceABE, faceABD_1, faceACD_1, faceACE, edgeBE, edgeBD_1, edgeCD_1, edgeCE
  4. Plane(J, faceACE) → l
  5. IntersectPath(l, a) → poly4, poly6, i_1, j_1, p_1, q_1, V, W, Z, A_1, F_1, G_1, g_1, h_1
  6. IntersectPath(l, b) → poly5, poly7, m_1, n_1, r_1, s_1, B_1, C_1, D_1, E_1, H_1, I_1, k_1, l_1
  7. PointIn(faceABE) → PointfaceABE
  8. PointIn(faceACE) → PointfaceACE
  9. PointIn(poly5) → Pointpoly5_1
  10. PointIn(poly4) → Pointpoly4_1
  11. PointIn(poly5) → Pointpoly5_2
  12. PointIn(poly4) → Pointpoly4_2
  13. Volume(d) → volumed
  14. Point(d) → Pointd_1
  15. Volume(b) → volumeb
  16. Point(b) → Pointb_1
  17. Volume(d) → o_1
  18. Point(d) → Pointd_2
  19. Volume(d) → l_2
  20. Point(d) → Pointd_3
  21. Volume(b) → m_2
  22. Point(b) → Pointb
  23. Volume(a) → volumea
  24. Point(a) → Pointa
  25. Volume(d) → n_2
  26. Point(d) → Pointd
  27. PointIn(poly5) → Pointpoly5
  28. PointIn(poly4) → Pointpoly4
  29. Plane(I, face10) → c
  30. IntersectPath(c, b) → poly1, L, M, N, O, k, m, q, r
  31. IntersectPath(c, d) → poly2, poly3, a_1, b_1, c_1, d_1, P, Q, R, S, T, U, s, t
  32. Plane(K, face1) → e_1
  33. IntersectPath(e_1, d) → poly8, poly10, a_2, b_2, g_2, h_2, J_1, K_1, L_1, M_1, R_1, S_1, f_1, t_1
  34. IntersectPath(e_1, a) → poly9, poly11, e_2, f_2, i_2, j_2, N_1, O_1, P_1, Q_1, T_1, U_1, c_2, d_2
  35. Polygon(D, B, E, C) → poly12, d_3, b_3, e_3, c_3
  36. Prism(poly12, height) → u_2, V_1, edge17, edge18, edge19, edge20, edge21, edge22, edge23, edge24, W_1, Z_1, E_2, face11, face12, face13, face14, face15
  37. Volume(u_2) → volumeu2
  38. Point(u_2) → Pointu2
  39. PointIn(poly2) → Pointpoly2
  40. PointIn(poly1) → Pointpoly1
  41. PointIn(poly8) → Pointpoly8
  42. PointIn(poly9) → Pointpoly9

AI 绘图提示语参考

绘制一个长方体，并将其体积三等分。首先建立长方体，然后通过几何构造创建平面和棱锥，利用交路径找到分割点，计算各部分体积，最后展示三等分后的长方体。
以上提示语为根据原始绘图命令整理而来，仅供参考。