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金字塔剖分

金字塔剖分
几何画板及绘图内容加载中，请稍等……
2019-04-25 18:23
函数立体几何最值优化参数方程几何作图
①本范例演示金字塔的几何剖分与艺术化呈现；②涉及的核心数学概念包括立体几何、参数方程、函数图像与几何作图；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Translate（平移）、Plane（平面）、Centroid（质心）、Pyramid（金字塔）、IntersectPath（路径相交）等GeoGebra命令与对象；④适合高中及以上学段，用于学习立体几何构造、参数方程应用及优化问题。

GeoGebra 命令及参数

  1. Polygon(A, B, D, C) → p0, a, b, d, c
  2. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (1 - 1)) - 1, 0)]) → P1
  3. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (2 - 1)) - 1, 0)]) → P2
  4. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (3 - 1)) - 1, 0)]) → P3
  5. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (4 - 1)) - 1, 0)]) → P4
  6. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (5 - 1)) - 1, 0)]) → P5
  7. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (6 - 1)) - 1, 0)]) → P6
  8. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (7 - 1)) - 1, 0)]) → P7
  9. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (8 - 1)) - 1, 0)]) → P8
  10. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (9 - 1)) - 1, 0)]) → P9
  11. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (10 - 1)) - 1, 0)]) → P10
  12. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (11 - 1)) - 1, 0)]) → P11
  13. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (12 - 1)) - 1, 0)]) → P12
  14. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (13 - 1)) - 1, 0)]) → P13
  15. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (14 - 1)) - 1, 0)]) → P14
  16. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (15 - 1)) - 1, 0)]) → P15
  17. Plane(P1) → PO1
  18. Plane(P2) → PO2
  19. Plane(P3) → PO3
  20. Plane(P4) → PO4
  21. Plane(P5) → PO5
  22. Plane(P6) → PO6
  23. Plane(P7) → PO7
  24. Plane(P8) → PO8
  25. Plane(P9) → PO9
  26. Plane(P10) → PO10
  27. Plane(P11) → PO11
  28. Plane(P12) → PO12
  29. Plane(P13) → PO13
  30. Plane(P14) → PO14
  31. Plane(P15) → PO15
  32. Polygon((o, (-o) + t, (-o)), ((-o), (-o) + t, (-o)), ((-o), o + t, (-o)), (o, o + t, (-o))) → base, f, g, h, i
  33. Centroid(base) → T
  34. Pyramid(base, (x(T), y(T), z(T) + 0.9)) → s, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  35. IntersectPath(PO1, s) → S1_1, F_2, G_2, H_2, I_2, h_3, i_3, j_3, k_3
  36. IntersectPath(PO2, s) → S2_1, B_2, C_2, D_2, E_2, d_2, e_2, f_3, g_3
  37. IntersectPath(PO3, s) → S3_1, V_1, W_1, Z_1, A_2, t_2, a_2, b_2, c_2
  38. IntersectPath(PO4, s) → S4_1, E, F, T_1, U_1, j, k, r_2, s_2
  39. IntersectPath(PO5, s) → S5_1, G, H, I, J, l, m, p, q
  40. IntersectPath(PO6, s) → S6_1, K, L, M, N, r, e, f_1, g_1
  41. IntersectPath(PO7, s) → S7_1, O, P, Q, R, h_1, i_1, j_1, k_1
  42. IntersectPath(PO8, s) → S8_1, S, U, V, W, l_1, m_1, n_1, p_1
  43. IntersectPath(PO9, s) → S9_1, Z, A_1, B_1, C_1, q_1, r_1, s_1, t_1
  44. IntersectPath(PO10, s) → S10_1, D_1, E_1, F_1, G_1, a_1, b_1, c_1, d_1
  45. IntersectPath(PO11, s) → S11_1, H_1, I_1, J_1, K_1, e_1, f_2, g_2, h_2
  46. IntersectPath(PO12, s) → S12_1, L_1, M_1, N_1, O_1, i_2, j_2, k_2, l_2
  47. IntersectPath(PO13, s) → S13_1, P_1, Q_1, R_1, S_1, m_2, n_2, p_2, q_2
  48. IntersectPath(PO14, s) → S14_1, J_2, K_2, L_2, M_2, l_3, m_3, n_3, p_3
  49. IntersectPath(PO15, s) → S15_1, N_2, O_2, P_2, Q_2, q_3, r_3, s_3, t_3