金字塔体积公式的推导（几何构造与分数化简）

GeoGebra 命令及参数

1. Line(E, F) → f
2. Rotate(A, a, f) → A'
3. Rotate(B, a, f) → B'
4. Rotate(D, a, f) → D'
5. Line(F, G) → g
6. Rotate(C, a, g) → C'
7. Rotate(B, a, g) → B'_{1}
8. Rotate(D, a, g) → D'_{1}
9. Polygon(G, F, B'_{1}, C') → q1, g_1, f_1, b'_{1}, c'
10. Polygon(B'_{1}, D'_{1}, C') → t1, h, i, d'_{1}
11. Polygon(F, B'_{1}, D'_{1}) → t2, j, f_2, k
12. Polygon(D'_{1}, G, F) → t3, f_3, l, g_2
13. Polygon(D'_{1}, C', G) → t4, g_3, m, n
14. Polygon(A', B', F, E) → q2, a', b', f_4, e
15. Polygon(D', A', B') → t5, p, d', q
16. Polygon(F, B', D') → t6, r, f_5, s
17. Polygon(E, D', A') → t7, t, e_1, b_{2}
18. Polygon(F, E, D') → t8, c, f_6, e_2
19. Line(C, G) → d
20. Rotate(H, a, d) → H'
21. Rotate(E, a, d) → E'
22. Rotate(F, a, d) → F'
23. Rotate(D, a, d) → D'_{2}
24. Polygon(G, H', E', F') → q3, g_4, h', e', f'
25. Polygon(D'_{2}, H', E') → t9, h_1, d'_{2}, i_1
26. Polygon(D'_{2}, F', E') → t10, j_1, k_1, l_1
27. Polygon(D'_{2}, G, F') → t11, m_1, n_1, g_5
28. Polygon(D'_{2}, G, H') → t12, p_1, q_1, g_6
29. Segment(B, F) → r_1
30. Segment(A, B) → s_1
31. Segment(B, C) → t_1
32. Segment(C, D) → a_1
33. Segment(D, A) → b_1
34. Segment(A, E) → c_1
35. Segment(E, F) → d_1
36. Segment(F, G) → h_2
37. Segment(C, G) → l_2
38. Segment(G, H) → i_2
39. Segment(D, H) → j_2
40. Segment(H, E) → k_2