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圆的面积分割法

圆的面积分割法
几何画板及绘图内容加载中，请稍等……
2017-12-22 21:52
圆三角函数几何作图
所属专题 Mathematics Form 2
这个范例演示了如何通过分割圆来计算其面积。核心数学概念包括圆的面积公式和几何作图。使用了If, Div, Line, Point, Distance, Sequence, Rotate, CircleSector, Vector, Translate, Circle, Zip, Segment, Intersect, CircleArc, Midpoint, OrthogonalLine, LineBisector, Semicircle, Angle, SelectedIndex等GeoGebra命令。适合初中及以上学生学习圆的面积计算方法。

GeoGebra 命令及参数

  1. If(r ≤ 1, 0, r - 1) → r_2
  2. Div(n, 2) → BNum
  3. Line(A, yAxis) → g
  4. Point(g) → O
  5. Distance(A, O) → OA
  6. Sequence((x(A) + (t * HPj), y(A)), t, 1, CurSector) → ListH
  7. Sequence((x(A) + (0.5 * HPj) + (t * HPj), y(A) + VPj), t, 0, CurSector - 1) → ListV
  8. Rotate(SP4b, α / 2, SP4a) → F
  9. CircleSector(SP4a, F, SP4c) → TSektor2
  10. If(b > 1, 1, b) → k
  11. Rotate(O, (((-k) * α)) / 2, A) → SP1a
  12. Rotate(A, α, O) → SP0
  13. Rotate(SP0, (((-k) * α)) / 2, A) → SP1b
  14. Vector(A, SP1b) → v
  15. Translate(SP1b, Vector[((CurSector - 1) * v)]) → SP2c
  16. Translate(SP1a, Vector[((CurSector - 1) * v)]) → SP2a
  17. Rotate(A, (0.5 * α), O) → SP0b
  18. Rotate(A, (1.5 * α), O) → SP0a
  19. Line(A, xAxis) → f
  20. Circle(O, A) → c
  21. Rotate(SP2a, ((-h) * α), ListH(CurSector)) → SP3a
  22. Rotate(SP2c, α, SP2a) → SP2b
  23. Rotate(SP2b, ((-h) * α), ListH(CurSector)) → SP3b
  24. Zip(CircleSector[p, q, r], p, Take[ListV, 2], q, ListH, r, Take[ListH, 2]) → ListHSector
  25. Sequence(Rotate[SP1b, (p * α), SP1a], p, 1, n - 1) → ListPSector1
  26. Zip(CircleSector[SP1a, p, q], p, Append[SP1b, ListPSector1], q, ListPSector1) → ListCSector1
  27. Sequence(Rotate[SP3b, (p * α), SP3a], p, 1, n - CurSector - 1) → ListPSector2
  28. Zip(CircleSector[SP3a, p, q], p, Append[SP3b, ListPSector2], q, ListPSector2) → ListCSector2
  29. Segment(O, A) → i
  30. If(b ≟ n, true, false) → IsMax
  31. Circle(A, Jejari) → d
  32. Intersect(d, g, 2) → C
  33. Rotate(A, β, C) → D
  34. CircleArc(C, A, D) → e
  35. Circle(A, ((2 * π) * OA)) → p
  36. Midpoint(O, A) → E
  37. OrthogonalLine(O, g) → m
  38. CircleSector(SP2a, SP2c, SP2b) → Sektor2
  39. CircleSector(SP1a, A, SP1b) → Sektor1
  40. Zip(CircleSector[p, q, r], p, Take[ListV, 2, BNum], q, Take[ListH, 1, BNum - 1], r, Take[ListH, 2, BNum]) → ListASector1
  41. Zip(CircleSector[p, q, r], p, Take[ListV, BNum + 2], q, Take[ListH, BNum + 1], r, Take[ListH, BNum + 2]) → ListASector2
  42. If(Genap ≟ true, Midpoint[SP4a, SP4b], Midpoint[SP4a, SP4c]) → Pt1
  43. OrthogonalLine(SP4a, f) → Tengah
  44. CircleSector(SP4a, SP4b, F) → TSektor1
  45. Intersect(p, f) → G, B
  46. Segment(A, B) → j
  47. If(r > 1, 1, r) → r_1
  48. Circle(O, A) → c_1
  49. Midpoint(A, B) → M
  50. CircleSector(SP4a, SP4b, SP4c) → ASektor1
  51. Rotate(SP4a, α / 2, SP4b) → H
  52. CircleSector(SP4b, H, SP4d) → ASektor1a
  53. CircleSector(SP4b, SP4a, H) → ASektor1b
  54. Rotate(ListASector2, ((r_1 * 180))°, Pt1) → ListRASector
  55. Rotate(ASektor1, ((r_1 * 180))°, Pt1) → ARSektor1
  56. Rotate(F, ((r_1 * 180))°, Pt1) → F'
  57. Rotate(SP4a, ((r_1 * 180))°, Pt1) → J
  58. Segment(J, F') → f_1
  59. LineBisector(A, SP4a) → g_1
  60. LineBisector(SP4c, O) → h_1
  61. Intersect(g_1, h_1) → I
  62. Rotate(TSektor2, (r_2 * (180° - α / 2)), I) → TRSektor2
  63. Semicircle(A, SP4b) → s
  64. Midpoint(A, SP4b) → K
  65. Rotate(SP4b, ((r_2 * 180))°, K) → SP4e
  66. Vector(SP4b, SP4e) → t
  67. Translate(ASektor1b, t) → ATSektor1b
  68. Rotate(Sektor2, ((-h) * α), ListH(CurSector)) → Sektor3
  69. Point(f) → L
  70. Angle(O, A, L) → γ
  71. SelectedIndex(Bahasa) → nn
  72. If(nn ≟ 1, "r", "j") → text1

AI 绘图提示语参考

绘制一个圆，并将其分割成多个扇形区域，展示如何通过分割圆来计算其面积。首先画一个圆心为O、半径为OA的圆，然后通过旋转和移动操作，将圆分割成多个扇形区域，最后展示这些扇形如何组合成整个圆。
以上提示语为根据原始绘图命令整理而来，仅供参考。