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求阴影部分占整体的几分之几

求阴影部分占整体的几分之几
几何画板及绘图内容加载中，请稍等……
2018-03-24 03:49
多边形向量几何作图
所属专题 Perimeter & Area
本示例动态展示了Ed Southall在Twitter上发布的一个面积问题的解决方案。它涉及分数和几何作图。通过使用Polygon, Midpoint, Segment, Rotate, Dilate, Vector, Translate等GeoGebra命令，可以构造出一个几何图形，展示阴影部分占整体的比例。适合初中及以上学生学习几何和分数概念。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(h) → F
  3. Midpoint(f) → G
  4. Midpoint(g) → H
  5. Midpoint(i) → I
  6. Polygon(F, C, H) → t1, h_1, f_1, c
  7. Midpoint(c) → J
  8. Midpoint(A, E) → K
  9. Midpoint(E, D) → L
  10. Midpoint(E, B) → M
  11. Segment(A, B) → n
  12. Segment(B, C) → p
  13. Segment(C, D) → q
  14. Segment(D, A) → r
  15. Rotate(F, If[0 < b ≤ 1, (b * π), π], J) → F'_1
  16. Rotate(C, If[0 < b ≤ 1, (b * π), π], J) → C'_1
  17. Rotate(H, If[0 < b ≤ 1, (b * π), π], J) → H'_1
  18. Polygon(F'_1, C'_1, H'_1) → t1', h'_1, f'_1, c'_1
  19. Segment(H'_1, C'_1) → s
  20. Segment(C'_1, F'_1) → t
  21. Segment(F'_1, H'_1) → d
  22. Segment(F, H) → e
  23. Dilate(E, If[2 < b ≤ 3, 3 - b, 0], I) → E'
  24. Vector(E, E') → u
  25. Translate(F'_1, u) → P
  26. Translate(C'_1, u) → Q
  27. Translate(H'_1, u) → R
  28. Polygon(P, Q, R) → t1'', r_1, p_1, q_1
  29. Translate(F'_1, u) → A_1
  30. Translate(H'_1, u) → B_1
  31. Segment(A_1, B_1) → d'_1
  32. Segment(A_1, E') → g_1
  33. Segment(E', B_1) → i_1
  34. Dilate(E, If[3 < b ≤ 4, 4 - b, 0], B) → E'_1
  35. Vector(E, E'_1) → v
  36. Translate(P, v) → P'
  37. Translate(Q, v) → Q'
  38. Translate(R, v) → R'
  39. Polygon(P', Q', R') → t1''', r', p', q'
  40. Translate(A_1, v) → S
  41. Translate(E', v) → E''
  42. Segment(S, E'') → j_1
  43. Translate(E', v) → E''_1
  44. Translate(B_1, v) → T
  45. Segment(E''_1, T) → k_1
  46. Translate(A_1, v) → U
  47. Translate(B_1, v) → V
  48. Segment(U, V) → l_1
  49. Dilate(G, If[4 < b ≤ 5, 5 - b, 0], A) → G'
  50. Vector(G, G') → w
  51. Translate(P', w) → P''
  52. Translate(Q', w) → Q''
  53. Translate(R', w) → R''
  54. Polygon(P'', Q'', R'') → t2, r'', p'', q''
  55. Translate(U, w) → U'
  56. Translate(V, w) → V'
  57. Segment(U', V') → m_1
  58. Translate(E''_1, w) → C_1
  59. Translate(T, w) → T'
  60. Segment(C_1, T') → n_1
  61. Rotate(P'', If[6 < b ≤ 7, ((b - 6) * π), π], K) → P'''
  62. Rotate(Q'', If[6 < b ≤ 7, ((b - 6) * π), π], K) → Q'''
  63. Rotate(R'', If[6 < b ≤ 7, ((b - 6) * π), π], K) → R'''
  64. Polygon(P''', Q''', R''') → t2', r''', p''', q'''
  65. Rotate(U', If[6 < b ≤ 7, ((b - 6) * π), π], K) → U''
  66. Rotate(V', If[6 < b ≤ 7, ((b - 6) * π), π], K) → V''
  67. Segment(U'', V'') → s_1
  68. Segment(A, G) → t_1
  69. Rotate(A, If[6 < b ≤ 7, ((b - 6) * π), π], K) → A'
  70. Rotate(G, If[6 < b ≤ 7, ((b - 6) * π), π], K) → G'_1
  71. Segment(A', G'_1) → a_1
  72. Segment(V'', A') → b_1
  73. Rotate(P', If[6 < b ≤ 7, ((b - 6) * π), π], M) → P''_1
  74. Rotate(Q', If[6 < b ≤ 7, ((b - 6) * π), π], M) → Q''_1
  75. Rotate(R', If[6 < b ≤ 7, ((b - 6) * π), π], M) → R''_1
  76. Polygon(P''_1, Q''_1, R''_1) → t3, r''_1, p''_1, q''_1
  77. Rotate(G, If[6 < b ≤ 7, ((b - 6) * π), π], M) → G'_2
  78. Rotate(B, If[6 < b ≤ 7, ((b - 6) * π), π], M) → B'
  79. Rotate(E, If[6 < b ≤ 7, ((b - 6) * π), π], M) → E'_2
  80. Segment(E'_2, G'_2) → c_1
  81. Segment(G'_2, B') → d_1
  82. Segment(B', E'_2) → e_1
  83. Rotate(P, If[6 < b ≤ 7, ((b - 6) * π), π], L) → P'_1
  84. Rotate(Q, If[6 < b ≤ 7, ((b - 6) * π), π], L) → Q'_1
  85. Rotate(R, If[6 < b ≤ 7, ((b - 6) * π), π], L) → R'_1
  86. Polygon(P'_1, Q'_1, R'_1) → t1'''_1, r'_1, p'_1, q'_1
  87. Rotate(D, If[6 < b ≤ 7, ((b - 6) * π), π], L) → D'
  88. Rotate(I, If[6 < b ≤ 7, ((b - 6) * π), π], L) → I'
  89. Rotate(E, If[6 < b ≤ 7, ((b - 6) * π), π], L) → E'_3
  90. Segment(E'_3, I') → f_2
  91. Segment(I', D') → g_2
  92. Segment(D', E'_3) → h_2
  93. Polygon(F, C, H) → t4, h_3, f_3, c_2
  94. Polygon(F, E, H) → t5, h_4, f_4, e_2
  95. Polygon(E, H, B) → t6, b_2, e_3, h_5