圆的面积转化为平行四边形

GeoGebra 命令及参数

1. Segment(E, (x(E) + 2, y(E))) → a
2. Point(a) → F
3. Min(x(F) - x(E), 1) → k
4. Point(yAxis) → O
5. Sequence(If[k < 1, (x(O) + ((l * sin((i * φ))) * cos((i * φ)) / sin(φ)), y(O) + ((l * sin((i * φ))) * sin((i * φ)) / sin(φ))), (x(O) + (l * i), y(O))], i, 0, (2 * n)) → list2
6. Sequence((x(O) + sin((i * θ)), y(O) + 1 - cos((i * θ))), i, 0, (2 * n)) → list1
7. Max(x(F) - x(E) - 1, 0) → k'
8. Rotate((x(O) + 0, y(O) + 1), ((-k) * θ / 2), O) → A
9. Rotate(O, ((-k) * θ / 2), O) → O'
10. Rotate(Element[list1, 1], ((-k) * θ / 2), O) → B
11. Sector(Rotate[Circle[(x(O) + 0, y(O) + 1), O], ((-k) * θ / 2), O], Rotate[O, ((-k) * θ / 2), O], Rotate[Element[list1, 1], ((-k) * θ / 2), O]) → c
12. Rotate((x(O) + 0, y(O) + 1), ((-k) * θ / 2), O) → C
13. Rotate(O, ((-k) * θ / 2), O) → O'_1
14. Rotate(Element[list1, 1], ((-k) * θ / 2), O) → D
15. Arc(Rotate[Circle[(x(O) + 0, y(O) + 1), O], ((-k) * θ / 2), O], O'_1, D) → d
16. CurveCartesian(t - sin(t), 1 - cos(t), t, 0, 6.28319) → b
17. Circle((0, 1), 1) → h
18. Ray((0, 0), (1, 0)) → i
19. Point(Segment[(0, 1), (6.28319, 1)]) → H
20. Segment(H, (x(H), 0)) → j
21. Midpoint(j) → I
22. Midpoint(a) → J
23. Circle(L, 1 / (1 - m)) → p
24. Circle((0, 0), 1 / (1 - m)) → q
25. Intersect(p, q, 1) → M
26. Intersect(p, q, 2) → N
27. Circle((0, 1), 1) → c_1
28. Segment((0, 0), (6.283185307179586, 0)) → e
29. Segment(G, (x(G), y(G) - 1)) → r
30. Sequence(Sector[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]]], i, 1, n) → list3
31. Sequence(Sector[Rotate[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)]], i, n + 1, (2 * n)) → list4
32. CircleArc((0, 1 / (1 - m)), O, L) → s
33. Segment(Q, R) → g
34. OrthogonalLine(R, i) → f_1
35. Intersect(f_1, g) → S
36. Point(f_1) → T
37. Segment(S, T) → g_1