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可变立方体：动态调整棱长与体积的交互演示

可变立方体：动态调整棱长与体积的交互演示
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2018-04-27 03:11
多边形立体几何几何作图滑块动画
本范例通过GeoGebra构建一个可交互调整的立方体，直观展示棱长变化对体积、表面积及对角面的影响。核心数学概念包括立体几何中的棱柱体积公式、表面积计算、空间直角坐标系下的点线面关系，以及利用滑块（slider）实现参数化动态调整。作图要点：使用Polygon命令绘制底面正方形，Prism命令生成棱柱，Angle命令标注二面角；通过定义变量n、A、C、D、B等控制顶点坐标，并利用按钮（button1-3）和文本（text1-4）显示实时数值。适合中学几何教学或大学入门立体几何课程，帮助学生理解三维图形的参数化建模与动态可视化。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Prism(q1, n) → f, I, edgeAI, edgeBJ, edgeCK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, faceABJI, faceBCKJ, faceCDLK, faceADLI, faceIJKL
  3. Polygon(E, F, G, H, M, N, O, P) → poly1, e_1, f_1, g, h, m, n_1, o, p
  4. Prism(poly1, 0) → i, Q, faceFGSR, faceGHTS, faceHMUT, faceMNVU, faceNOWV, faceOPZW, faceEPZQ, faceQRSTUVWZ, edgeEQ, edgeFR, R, edgeGS, edgeHT, edgeMU, edgeNV, edgeOW, edgePZ, edgeQR, edgeRS, edgeST, edgeTU, S_2, edgeUV, edgeVW, edgeWZ, edgeQZ, T, U, V, W, Z, faceEFRQ
  5. Prism(faceQRSTUVWZ, k) → l, I_1, face12, face13, face14, face15, face16, face17, face11, face18, edge17, edge18, J_1, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge27, edge28, edge29, K_1, edge30, edge31, edge32, edge26, L_1, M_1, N_1, O_1, P_1, face10
  6. Polygon(A_1, B_1, 4) → poly2, q, r, s, t, C_1, D_1
  7. Polygon(E_1, F_1, 8) → poly3, g_1, H_1, Q_1, R_1, S_1, T_1, h_1, i_1, j_1, k_1, l_1, m_1, p_1, G_1
  8. Polygon(U_1, V_1, W_1, Z_1, A_2) → poly4, u_1, v_1, w_1, z_1, a_2
  9. Polygon(S, B_2, C_2, D_2, E_2) → poly5, s_1, b_2, c_2, d_2, e_2
  10. Angle(E_2, D_2, C_2) → α
  11. Angle(C_2, B_2, S) → β
  12. Angle(D_2, C_2, B_2) → γ
  13. Angle(A_2, Z_1, W_1) → δ
  14. Angle(W_1, V_1, U_1) → ε
  15. Angle(Z_1, W_1, V_1) → ζ
  16. Polygon(F_2, G_2, H_2) → t1, h_2, f_2, g_2
  17. Polygon(I_2, J_2, K_2) → t2, k_2, i_2, j_2
  18. Polygon(L_2, M_2, 6) → poly6, q_1, Q_2, r_1, t_1, b_1, c_1, d_1, N_2, O_2, P_2
  19. Polygon(L_3, M_3, 6) → poly6_1, q_2, Q_3, r_2, t_2, b_3, c_3, d_3, N_3, O_3, P_3
  20. Polygon(R_2, T_2, 3) → poly7, l_2, m_2, n_2, U_2
  21. Polygon(V_2, W_2, 3) → poly8, p_2, s_2, f_3, Z_2
  22. Polygon(A_3, B_3, 5) → poly9, g_3, h_3, i_3, j_3, k_3, C_3, D_3, E_3
  23. Polygon(F_3, G_3, 5) → poly10, l_3, m_3, n_3, p_3, q_3, H_3, I_3, J_3
  24. Polygon(K_3, R_3, 4) → poly11, r_3, s_3, t_3, a_3, S_3, T_3
  25. Polygon(U_3, V_3, 4) → poly12, e_3, f_4, g_4, h_4, W_3, Z_3