旋转体体积与圆盘/垫圈法演示

GeoGebra 命令及参数

1. Point(offsetYaxis) → axis
2. Point(offsetXaxis) → a_f
3. Point(offsetXaxis) → b_f
4. Segment(a_f + (0, sliderXoffset2), b_f + (0, sliderXoffset2)) → innerslider
5. Point(innerslider) → a_g
6. Point(innerslider) → b_g
7. Sequence((af_x + i, axis_y), i, 0, Δx * (n - 1), Δx) → list_{centers}
8. Sequence((af_x + i + leftright * Δx, f(af_x + i + leftright * Δx)), i, 0, Δx * (n - 1), Δx) → listf_{points}
9. Sequence(If[(x(Element[list_{centers}, i]) < ag_x) ∨ (x(Element[list_{centers}, i]) > bg_x - Δx), Corner[1] + (-1, -1), (x(Element[listf_{points}, i]), g(x(Element[listf_{points}, i])))], i, 1, n) → listg_{points}
10. Function(f, af_x, bf_x) → f_1
11. Sequence(abs(y(Element[listf_{points}, i]) - y(Element[list_{centers}, i])), i, 1, n) → listf_{radii}
12. Sequence((0, Element[listf_{radii}, i] * sqrt(1 - tilt^(2))), i, 1, n) → listf_c
13. Sequence(Ellipse[Element[listf_{foci1}, i], Element[listf_{foci2}, i], Element[listf_{radii}, i]], i, 1, n) → listf_{ellipses1}
14. Sequence(Segment[Element[listf_{points}, i] - (leftright * Δx, 0), Element[listf_{points}, i] + ((1 - leftright) * Δx, 0)], i, 1, n) → listf_{segments1}
15. Mirror(listf_{segments1}, axisline) → listf_{segments2}
16. Textfield(f) → inputBox1
17. Integral(π * (f(x) - axis_y)^(2), af_x, bf_x) → Vf_{actual}
18. Segment(a_f, (af_x, axis_y)) → segment_a
19. Segment(b_f, (bf_x, axis_y)) → segment_b
20. Sequence(If[(x(Element[list_{centers}, i]) < ag_x) ∨ (x(Element[list_{centers}, i]) > bg_x - Δx), 0, abs(y(Element[listg_{points}, i]) - y(Element[list_{centers}, i]))], i, 1, n) → listg_{radii}
21. Function(g, ag_x, bg_x) → g_1
22. Sequence((0, Element[listg_{radii}, i] * sqrt(1 - tilt^(2))), i, 1, n) → listg_c
23. Sequence(Ellipse[Element[listg_{foci1}, i], Element[listg_{foci2}, i], Element[listg_{radii}, i]], i, 1, n) → listg_{ellipses1}
24. Textfield(g) → inputBox2
25. Translate(listf_{ellipses1}, Vector[(0, 0), (Δx, 0)]) → listf_{ellipses2}
26. Translate(listg_{ellipses1}, Vector[(0, 0), (Δx, 0)]) → listg_{ellipses2}
27. Sequence(Segment[Element[listg_{points}, i] - (leftright * Δx, 0), Element[listg_{points}, i] + ((1 - leftright) * Δx, 0)], i, 1, n) → listg_{segments1}
28. Mirror(listg_{segments1}, axisline) → listg_{segments2}
29. Integral(π * (g(x) - axis_y)^(2), ag_x, bg_x) → Vg_{actual}
30. Corner(6) → A
31. Segment(a_g, (ag_x, axis_y)) → segmenti_a
32. Segment(b_g, (bg_x, axis_y)) → segmenti_b
33. Segment((x(a_f), sliderXoffset3), (x(b_f), sliderXoffset3)) → ellipseslider
34. Point(ellipseslider) → highlight
35. Element(list_{centers}, ellipsenumber) → ellipsecenter
36. Element(listf_{radii}, ellipsenumber) → ellipsef_a
37. Element(listf_{ellipses2}, ellipsenumber) → ellipsef
38. CurveCartesian(x(ellipsecenter) + ellipsef_b * cos(t), y(ellipsecenter) + ellipsef_a * sin(t), t, 1.5707963267948966, 4.71238898038469) → ellipsehalf1_f
39. Element(listf_{segments1}, ellipsenumber) → segmentf1
40. Element(listf_{segments2}, ellipsenumber) → segmentf2
41. Element(listg_{ellipses2}, ellipsenumber) → ellipseg
42. Element(listg_{radii}, ellipsenumber) → ellipseg_a
43. Circle((0, 0), ellipseg_a) → d
44. Circle((Δx / tilt, 0), ellipseg_a) → e
45. Intersect(d, e) → B, C, ,
46. CurveCartesian(x(ellipsecenter) + ellipseg_b * cos(t), y(ellipsecenter) + ellipseg_a * sin(t), t, -β, β) → ellipsepart_g
47. CurveCartesian(x(ellipsecenter) + Δx + ellipsef_b * cos(t), y(ellipsecenter) + ellipsef_a * sin(t), t, 1.5708, 4.71238898038469) → ellipsehalf2_f
48. CurveCartesian(x(ellipsecenter) + Δx + ellipsef_b * cos(t), y(ellipsecenter) + ellipsef_a * sin(t), t, -1.5708, 1.5707963267948966) → ellipsehalf3_f
49. Polygon({(0, ellipsef_a), (Δx, ellipsef_a), (Δx, -ellipsef_a), (0, -ellipsef_a)} + ellipsecenter) → poly1, , , ,
50. Function(-f(x) + 2 * axis_y, af_x, bf_x) → f_2
51. Function(-g(x) + 2 * axis_y, ag_x, bg_x) → g_2
52. CurveCartesian(x(ellipsecenter) + Δx + ellipseg_b * cos(t), y(ellipsecenter) + ellipseg_a * sin(t), t, π - β, π + β) → ellipsepartb_g