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Frank's Circles 问题：改变圆的数量

Frank's Circles 问题：改变圆的数量
几何画板及绘图内容加载中，请稍等……
2015-06-06 01:48
圆几何作图
①这个范例演示如何通过分割区域为几何形状来解决一个挑战性问题；②涉及的核心数学概念包括面积、圆、周长、几何作图等；③作图要点：使用了 Point, Circle, Intersect, CircleArc, Segment, Polygon, CircleSector 等GeoGebra命令和对象；④适合高中数学教学，用于几何作图和问题解决能力的培养。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Circle(A, r) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, r) → d
  5. Intersect(d, xAxis, 2) → C
  6. Circle(C, r) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(d, e, 2) → F
  10. Intersect(c, d, 2) → G
  11. CircleArc(A, D, G) → f
  12. CircleArc(B, G, F) → g
  13. CircleArc(C, F, E) → h
  14. CircleArc(B, E, D) → k
  15. Segment(A, D) → a
  16. Polygon(D, A, G, B) → poly1, d_1, a_1, g_1, b
  17. Polygon(E, B, F, C) → poly2, e_1, b_1, f_1, c_1
  18. CircleSector(A, D, G) → p
  19. CircleSector(B, E, D) → q
  20. CircleSector(B, G, F) → r_1
  21. CircleSector(C, F, E) → s
  22. Intersect(e, xAxis, 2) → H
  23. Circle(H, r) → t
  24. Intersect(c, g_1, 1) → I
  25. Intersect(c, d, 2) → J
  26. Intersect(c, d, 1) → K
  27. CircleArc(I, J, K) → h_1
  28. CircleSector(I, J, K) → k_1
  29. Intersect(e, t, 1) → L
  30. Intersect(e, xAxis, 2) → M
  31. Intersect(e, t, 2) → N
  32. Intersect(d, t, 1) → O
  33. Polygon(L, M, N, O) → poly3, l_1, m, n_1, o
  34. Intersect(d, e, 1) → P
  35. CircleSector(O, L, P) → p_1
  36. Intersect(d, e, 2) → Q
  37. CircleSector(O, Q, N) → q_1
  38. CircleSector(M, N, L) → s_1
  39. CircleArc(O, L, P) → t_1
  40. CircleArc(O, Q, N) → c_2
  41. CircleArc(M, N, L) → d_2
  42. Intersect(t, xAxis, 2) → R
  43. Circle(R, r) → e_2
  44. Intersect(t, e_2, 1) → S
  45. Intersect(t, e_2, 2) → T
  46. Polygon(S, R, T, M) → poly4, s_2, r_2, t_2, m_1
  47. CircleSector(M, S, L) → f_2
  48. CircleSector(M, N, T) → g_2
  49. CircleSector(R, T, S) → h_2
  50. CircleArc(M, S, L) → k_2
  51. CircleArc(M, N, T) → p_2
  52. CircleArc(R, T, S) → q_2