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圆扇形与相关矩形面积关系

圆扇形与相关矩形面积关系
几何画板及绘图内容加载中，请稍等……
2020-05-15 03:14
圆三角函数几何作图
①本范例演示圆内扇形与其相关矩形的面积关系；②涉及核心数学概念包括圆面积、扇形面积、矩形面积、三角函数等；③作图要点：使用 GeoGebra 命令如 Intersect（交点）、Circle（圆）、Rotate（旋转）、Angle（角度）、CircleSector（扇形）、Segment（线段）、Midpoint（中点）、Mirror（镜像）等构建图形；④适合高中数学教学，用于理解扇形与矩形面积计算及几何变换。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 4) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, 18°, A) → B'
  5. Angle(B, A, B') → α
  6. CircleSector(A, B, B') → d
  7. Segment(A, B') → f
  8. Midpoint(f) → C
  9. Mirror(d, C) → d'
  10. Point(d') → D
  11. Segment(D, B') → g
  12. Midpoint(g) → E
  13. Mirror(d', E) → d''
  14. Point(d'') → F
  15. Segment(D, F) → h
  16. Midpoint(h) → G
  17. Mirror(d'', G) → d'''
  18. Point(d''') → H
  19. Segment(H, F) → i
  20. Midpoint(i) → I
  21. Mirror(d''', I) → e
  22. Point(e) → J
  23. Segment(H, J) → j
  24. Midpoint(j) → K
  25. Mirror(e, K) → e'
  26. Point(e') → L
  27. Segment(L, J) → k
  28. Midpoint(k) → M
  29. Mirror(e', M) → e''
  30. Point(e'') → N
  31. Segment(L, N) → l
  32. Midpoint(l) → O
  33. Mirror(e'', O) → e'''
  34. Point(e''') → P
  35. Segment(P, N) → m
  36. Midpoint(m) → Q
  37. Mirror(e''', Q) → p
  38. Point(p) → R
  39. Segment(P, R) → n
  40. Midpoint(n) → S
  41. Mirror(p, S) → p'
  42. Point(p') → T
  43. Segment(T, R) → q
  44. Midpoint(q) → U
  45. Mirror(p', U) → p''
  46. Point(p'') → V
  47. Segment(T, V) → r
  48. Midpoint(r) → W
  49. Mirror(p'', W) → p'''
  50. Point(p''') → Z
  51. Segment(Z, V) → s
  52. Midpoint(s) → A_1
  53. Mirror(p''', A_1) → t
  54. Point(t) → B_1
  55. Segment(Z, B_1) → a
  56. Midpoint(a) → C_1
  57. Mirror(t, C_1) → t'
  58. Point(t') → D_1
  59. Segment(D_1, B_1) → b
  60. Midpoint(b) → E_1
  61. Mirror(t', E_1) → t''
  62. Point(t'') → F_1
  63. Segment(D_1, F_1) → f_1
  64. Midpoint(f_1) → G_1
  65. Mirror(t'', G_1) → t'''
  66. Segment(A, B) → g_1
  67. Midpoint(g_1) → H_1
  68. Mirror(d, H_1) → d'_1
  69. Point(d'_1) → I_1
  70. Segment(I_1, B) → h_1
  71. Midpoint(h_1) → J_1
  72. Mirror(d'_1, J_1) → c_1
  73. Point(c_1) → K_1
  74. Segment(I_1, K_1) → i_1
  75. Midpoint(i_1) → L_1
  76. Mirror(c_1, L_1) → d_1
  77. Point(d_1) → M_1
  78. Segment(M_1, K_1) → j_1
  79. Midpoint(j_1) → N_1
  80. Mirror(d_1, N_1) → e_1
  81. Intersect(c, xAxis, 1) → O_1
  82. Rotate(O_1, 10°, A) → P_1
  83. Angle(O_1, A, P_1) → β
  84. CircleSector(A, O_1, P_1) → k_1