维度变化时体积如何改变——圆锥、圆柱与球体的动态演示

GeoGebra 命令及参数

1. Segment(A_1, B_1) → a
2. Segment(B_1, C_1) → b
3. Segment(C_1, D_1) → c
4. Segment(D_1, A_1) → d
5. Polygon(A_1, B_1, C_1, D_1) → poly1, a_1, b_1, c_1, d_1
6. Polygon(A_2, B_2, C_2, D_2) → poly2, a_2, b_2, c_2, d_2
7. Ellipse(E, E_1, B) → f
8. Segment(E, E_1) → g
9. OrthogonalLine(E, g) → h
10. Circle(E, l_1) → k
11. Intersect(k, h) → C, D
12. OrthogonalLine(E_1, g) → i
13. Circle(E_1, l_1) → p
14. Intersect(p, i) → F, G
15. Segment(E + (-0.05, 0), D + (-0.05, 0)) → j
16. Point(f) → I
17. Segment(E, E_1) → e
18. Line(I, j) → m
19. Circle(I, l_1) → q
20. Intersect(q, m) → H, J
21. Ellipse(D, G_1, J) → r
22. Segment(J, I) → n
23. Polygon(E, E_1, G_1, D) → poly3, e_1, e_2, g_1, d_3
24. Ellipse(R_1, R_2, K) → s
25. Segment(R_1, R_2) → t
26. OrthogonalLine(R_1, t) → f_1
27. OrthogonalLine(R_2, t) → h_1
28. Circle(R_1, l_2) → k_1
29. Circle(R_2, l_2) → p_1
30. Intersect(k_1, f_1) → L, M
31. Intersect(p_1, h_1) → N, O
32. Segment(R_1 + (-0.055, 0), M + (-0.055, 0)) → i_1
33. Point(s) → P
34. Line(P, i_1) → m_1
35. Circle(P, l_2) → q_1
36. Intersect(q_1, m_1) → Q, R
37. Segment(P, R) → n_1
38. Ellipse(M, O, R) → s_1
39. Polygon(R_1, R_2, O, M) → poly4, r_3, r_4, o, m_2
40. Midpoint(e) → S
41. Segment(S, E_1) → ra_1
42. Segment(R_1, R_2) → across
43. Midpoint(across) → T
44. Segment(T, R_2) → ra_2
45. Segment(E_1 + (0.05, 0), G + (0.05, 0)) → l
46. Segment(R_2 + (0.055, 0), O + (0.055, 0)) → j_1