无字证明：环体体积

GeoGebra 命令及参数

1. Segment(G, (x(G), y(G) - R)) → r_1
2. CircleArc((0, R / (1 - Extend)), O, L, xOyPlane) → s
3. Intersect(r_1, s, 1) → Q
4. Vector(Q, G) → u
5. CurveCartesian(t - sin(t), 1 - cos(t), t, 0, 6.28319) → b
6. Ray((0, 0), (1, 0)) → i
7. Point(Segment[(0, 1), (6.28319, 1)]) → H
8. Segment(H, (x(H), 0)) → j
9. Midpoint(j) → I
10. Circle(L, 1 / (1 - Extend)) → p
11. Circle((0, 0), 1 / (1 - Extend)) → q
12. Intersect(p, q, 1) → M
13. Intersect(p, q, 2) → N
14. Segment((0, 0), (6.283185307179586, 0)) → e
15. Vector(G, L) → v
16. Segment(G, Q) → d
17. Center(s) → B
18. Midpoint(O, L) → D
19. Sequence(((R * sin((i * (1 - Extend))) / (1 - Extend)), (R - (R * cos((i * (1 - Extend))))) / (1 - Extend)), i, 0, (2 * π), (2 * π / m)) → l1
20. Sequence(Vector[Element[l1, i], Element[l1, i + 1]], i, 1, Length[l1]) → l2
21. Sequence(Circle[Element[l1, i], r, Vector[Element[l2, i]]], i, 1, Length[l1]) → l3
22. Circle(G, R, xOyPlane) → h
23. Distance(Element[l1, 2], Element[l1, 3]) → haut
24. Sequence(Cylinder[Element[l3, i], haut], i, 1, Length[l1]) → l4
25. Element(l3, Section) → c
26. Midpoint(C, A) → F
27. Vector(F, A) → w
28. Vector(F, C) → a
29. Circle(J, r) → f
30. Point(f) → P
31. Circle(J, r) → g
32. Segment(J, P) → k
33. Midpoint(J, P) → S