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两立方差分第二部分

两立方差分第二部分
几何画板及绘图内容加载中，请稍等……
2016-03-19 12:51
立体几何微积分最值优化几何作图
①本范例演示两立方差分的几何表示与相关图形现象；②涉及核心数学概念包括立方差公式、相似三角形、中值定理、立体几何优化问题及切线；③构造要点：使用 GeoGebra 命令如 Intersect（相交）、Point（点）、Polygon（多边形）等创建和操作几何对象；④适合高中及以上数学学习者，用于理解代数与几何的联系及优化问题。

GeoGebra 命令及参数

  1. Intersect(yAxis, xAxis) → A
  2. Point(yAxis) → B
  3. Point(yAxis) → C
  4. Point(xAxis) → D
  5. Point(xAxis) → E
  6. Point(zAxis) → J
  7. Point(zAxis) → K
  8. Intersect(yAxis, zAxis) → M
  9. Polygon(F, B, C, G) → poly2, f_1, b_1, c, g
  10. Polygon(H, F, G, I) → poly3, h, f_2, g_1, i
  11. Polygon(E, D, F, H) → poly4, e, d_1, f_3, h_1
  12. Polygon(D, L, J, A) → poly5, d_2, l, j, a_1
  13. Polygon(J, N, B, A) → poly6, j_1, n, b_2, a_2
  14. Polygon(L, O, F, D) → poly7, l_1, o, f_4, d_3
  15. Polygon(O, N, B, F) → poly8, o_1, n_1, b_3, f_5
  16. Polygon(K, J, N, R) → poly13, k_1, j_3, n_4, r_2
  17. Polygon(S, E, D, P) → poly15, s, e_1, d_4, p_3
  18. Polygon(E, H, V, S) → poly16, e_2, h_2, v, s_1
  19. Polygon(H, V, T, I) → poly18, h_3, v_2, t, i_1
  20. Polygon(T, W, G, I) → poly19, t_1, w, g_2, i_2
  21. Polygon(U, C, G, W) → poly22, u_1, c_1, g_3, w_3
  22. Polygon(U, R, B, C) → poly23, u_2, r_4, b_4, c_2
  23. Polygon(N, O, L, J) → poly1, n_5, o_5, l_5, j_5
  24. Polygon(K, P, L, J) → poly14, k_2, p_2, l_4, j_4
  25. Polygon(A, D, F, B) → poly24, a, d, f, b
  26. Polygon(L, O, F, D) → poly9, l_2, o_2, f_6, d_5
  27. Polygon(O, N, B, F) → poly10, o_3, n_2, b_5, f_7
  28. Polygon(Q, R, N, O) → poly11, q, r, n_3, o_4
  29. Polygon(P, Q, O, L) → poly12, p, q_1, o_6, l_3
  30. Polygon(V, Q, F, H) → poly17, v_1, q_2, f_8, h_4
  31. Polygon(Q, W, G, F) → poly20, q_3, w_1, g_4, f_9
  32. Polygon(P, Q, R, K) → poly21, p_1, q_4, r_1, k
  33. Polygon(Q, R, K, P) → poly25, q_5, r_3, k_3, p_4
  34. Polygon(W, U, R, Q) → poly26, w_2, u, r_5, q_6
  35. Polygon(V, T, W, Q) → poly27, v_3, t_2, w_4, q_7
  36. Polygon(S, P, Q, V) → poly28, s_2, p_5, q_8, v_4