垫圈体积：旋转体与微积分的可视化演示

GeoGebra 命令及参数

1. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], A) → B'
2. Segment(B, B') → l
3. Cylinder(B, B', r) → a, c, d, b
4. Dilate(E, If[2 < j ≤ 3, 3 - j, 0], C) → E'
5. Segment(E, E') → f
6. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], C) → G'
7. Dilate(F, If[1 < j ≤ 2, 2 - j, 0], E) → F'
8. Segment(G, G') → g
9. Segment(F, F') → i
10. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], H) → A'
11. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], D) → A'_1
12. Circle(A', A'_1, I) → k
13. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], B) → A'_2
14. Cylinder(A, A'_2, e) → m, p, q, n
15. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], A) → A'_3
16. Segment(G, A'_3) → s
17. Dilate(A, If[6 < j ≤ 7, 7 - j, 0], B) → A'_4
18. Vector(A, A'_4) → u
19. Translate(m, u) → m'
20. Cylinder(A, A'_4, e) → o, t, c_1, v
21. Dilate(B, If[7 < j ≤ 8, 8 - j, 0], J) → B'_1
22. Vector(B, B'_1) → w
23. Translate(m', w) → m''
24. Dilate(J, If[8 < j ≤ 9, 9 - j, 0], K) → J'
25. Segment(J, J') → f_1
26. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], L) → C'
27. Vector(C, C') → u_1
28. Translate(E, u_1) → E'_1
29. Translate(E', u_1) → E''
30. Segment(E'_1, E'') → f'
31. Translate(G, u_1) → G'_1
32. Translate(G', u_1) → G''
33. Segment(G'_1, G'') → g'
34. Translate(F, u_1) → F'_1
35. Translate(F', u_1) → F''
36. Segment(F'_1, F'') → i'
37. Dilate(K, If[9 < j ≤ 10, 10 - j, 0], M) → K'
38. Dilate(O, If[9 < j ≤ 10, 10 - j, 0], N) → O'
39. Segment(K, K') → g_1
40. Segment(O, O') → h_1
41. Rotate(J, π, Line[(0, 0, 0), (0, 0, 1)]) → J'_1
42. Rotate(J', π, Line[(0, 0, 0), (0, 0, 1)]) → J''
43. Segment(J'_1, J'') → i_1
44. Rotate(G, π, Line[(0, 0, 0), (0, 0, 1)]) → G'_2
45. Rotate(A'_3, π, Line[(0, 0, 0), (0, 0, 1)]) → P
46. Segment(G'_2, P) → s'