圆的周长与面积探索

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Circle(A, B) → c
3. Polygon(A, B, 4) → poly1, a, b, d, e, C, D
4. Polygon(C, B, 4) → poly2, c_1, b_1, f, g, E, F
5. Polygon(F, E, 4) → poly3, f_1, e_1, h, i, G, H
6. Dilate(B, 3.141592653589793, A) → B'_1
7. Dilate(C, 3.141592653589793, D) → C'
8. Polygon(H, C', B'_1, G) → poly4, h_1, c', b', g_1
9. CircleArc(B, E, A) → k
10. Dilate(B, 6.283185307179586, A) → B'_2
11. Dilate(B, 4, A) → B'_3
12. Dilate(B, 5, A) → B'_4
13. Dilate(B, 6, A) → B'
14. Sequence(Text[k + " r", K + (k, 0)], k, 0, 6) → list1
15. Circle(M, 1) → q
16. Rotate(J, (-α), M) → J'
17. Mirror(J', M) → J''_1
18. Segment(J''_1, J') → j
19. Mirror(D, A) → D'_1
20. Sequence(Segment[Rotate[D'_1, (k * 3.141592653589793 / 2^(l)) + 3.141592653589793 / 2^(l + 1), A], Rotate[D, (k * 3.141592653589793 / 2^(l)) + 3.141592653589793 / 2^(l + 1), A]], k, 0, 2^(l) - 1) → list3
21. Rotate(D, 3.141592653589793 / 2^(l + 1), A) → D'_2
22. Rotate(D, ((-3.141592653589793)) / 2^(l + 1), A) → D'
23. CircleSector(A, D', D'_2) → r
24. Midpoint(A, D') → N
25. Mirror(A, N) → A'
26. Mirror(D', N) → D''
27. Mirror(D'_2, N) → O
28. Sector(Mirror[Circle[A, D'], N], D'', O) → r'
29. Sequence(Sector[Translate[Circle[A, D'], Vector[(k * v)]], Translate[D', Vector[(k * v)]], Translate[D'_2, Vector[(k * v)]]], k, 1, 2^(l) - 1) → list2
30. Sequence(Sector[Translate[Mirror[Circle[A, D'], N], Vector[(k * v)]], Translate[D'', Vector[(k * v)]], Translate[O, Vector[(k * v)]]], k, 1, 2^(l) - 1) → list4
31. Sequence(Text[k / 2 + " d", I + (k, 0)], k, 0, 6) → list5
32. Sequence(Text[k / 2 + " C ", R + ((k * 3.141592653589793), 0)], k, 0, 2) → list6
33. CircleArc(G, B'_3, E) → p
34. CircleArc(B'_4, B', B'_3) → t
35. CircleArc(A, B, S) → d_1
36. Rotate(J', 1, M) → J''
37. Rotate(J'', 1, M) → J'''
38. Rotate(J''', 1, M) → T
39. Rotate(T, 1, M) → T'
40. Rotate(T', 1, M) → T''_1
41. Rotate(T''_1, 1, M) → U