球体体积证明 by Michael Oster

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Circle(A, B) → c
4. Distance(A, B) → r
5. Point(xAxis) → D
6. Circle(D, r) → h
7. Sphere(A, r) → a
8. Cylinder(h, r) → b, d, e
9. Cylinder(h, (-r)) → f, g, i
10. Point(xAxis) → C
11. OrthogonalLine(C, xOyPlane) → j
12. Segment(E, C) → k
13. Point(k) → G
14. IntersectPath(l, a) → p
15. IntersectPath(l, b) → q
16. Surface((u * cos(θ)) + Distance[A, D], (u * sin(θ)), u, θ, 0, 6.283185307179586, u, (-r), r) → m
17. IntersectPath(l, f) → s
18. OrthogonalLine(D, l) → n
19. Surface(x(H) + (u * cos(θ)), (u * sin(θ)), z(G), u, z(G), r, θ, 0, 6.283185307179586) → o
20. Segment(A, B) → t
21. Intersect(h, xAxis, 2) → J
22. Segment(D, J) → a_1
23. Segment(A, I) → b_1
24. Segment(D, H) → c_1
25. Intersect(u, p) → K, L
26. Segment(I, L) → d_1
27. Segment(A, L) → e_1
28. Segment(H, N) → f_1
29. Segment(C, G) → g_1
30. Segment(A, L) → h_1
31. Polygon(A, I, L) → poly1, l_1, a_2, i_1
32. Segment(S, R) → j_1
33. Polygon(S, R, D) → poly2, d_2, s_1, r_1
34. Segment(D, S) → k_1
35. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → v
36. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → w
37. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → m_1
38. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → n_1
39. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → o_1
40. If(Step ≠ 10, Step ≟ Step + 1, Step ≟ 0) → p_1