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六边形的秘密！

六边形的秘密！
几何画板及绘图内容加载中，请稍等……
2017-08-06 10:57
多边形变换几何作图
这是一个动态且可修改的六边形（凸或凹）现象演示。它展示了六边形内部发生的各种几何现象。该范例涉及相似三角形、多边形等核心数学概念。通过使用GeoGebra中的Polygon、Segment、Midpoint、Line等命令，可以构造出六边形及其相关几何元素。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  2. Segment(F, A) → g
  3. Segment(A, B) → h
  4. Segment(B, C) → i
  5. Segment(C, D) → j
  6. Segment(D, E) → k
  7. Segment(E, F) → l
  8. Midpoint(l) → G
  9. Midpoint(g) → H
  10. Midpoint(h) → I
  11. Midpoint(i) → J
  12. Midpoint(j) → K
  13. Midpoint(k) → L
  14. Line(A, G) → m
  15. Line(E, H) → n
  16. Intersect(m, n) → M
  17. Line(F, L) → p
  18. Line(D, G) → q
  19. Intersect(p, q) → N
  20. Line(C, L) → r
  21. Line(E, K) → s
  22. Intersect(r, s) → O
  23. Line(D, J) → t
  24. Line(B, K) → f_1
  25. Intersect(t, f_1) → P
  26. Line(C, I) → g_1
  27. Line(A, J) → h_1
  28. Intersect(g_1, h_1) → Q
  29. Line(B, H) → i_1
  30. Line(F, I) → j_1
  31. Intersect(i_1, j_1) → R
  32. Polygon(M, N, O, P, Q, R) → poly2, m_1, n_1, o, p_1, q_1, r_1
  33. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], I) → A'
  34. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], J) → B'
  35. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], K) → C'
  36. Dilate(D, If[0 < u ≤ 1, 1 - u, 0], L) → D'
  37. Dilate(E, If[0 < u ≤ 1, 1 - u, 0], G) → E'
  38. Dilate(F, If[0 < u ≤ 1, 1 - u, 0], H) → F'
  39. Segment(A, A') → k_1
  40. Segment(B, B') → l_1
  41. Segment(C, C') → s_1
  42. Segment(D, D') → t_1
  43. Segment(E, E') → a_1
  44. Segment(F, F') → b_1
  45. Rotate(A, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], I) → A'_1
  46. Rotate(A', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], I) → A''
  47. Segment(A'_1, A'') → c_1
  48. Rotate(B, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], J) → B'_1
  49. Rotate(B', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], J) → B''
  50. Segment(B'_1, B'') → d_1
  51. Rotate(C, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], K) → C'_1
  52. Rotate(C', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], K) → C''
  53. Segment(C'_1, C'') → e_1
  54. Rotate(D, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → D'_1
  55. Rotate(D', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → D''
  56. Segment(D'_1, D'') → f_2
  57. Rotate(E, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], G) → E'_1
  58. Rotate(E', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], G) → E''
  59. Segment(E'_1, E'') → g_2
  60. Rotate(F, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], H) → F'_1
  61. Rotate(F', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], H) → F''
  62. Segment(F'_1, F'') → h_2
  63. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], G) → A'_2
  64. Dilate(E, If[2 < u ≤ 3, 3 - u, 0], H) → E'_2
  65. Segment(A, A'_2) → i_2
  66. Segment(E, E'_2) → j_2
  67. Dilate(F, If[3 < u ≤ 4, 4 - u, 0], L) → F'_2
  68. Dilate(D, If[3 < u ≤ 4, 4 - u, 0], G) → D'_2
  69. Segment(F, F'_2) → k_2
  70. Segment(D, D'_2) → l_2
  71. Dilate(C, If[4 < u ≤ 5, 5 - u, 0], L) → C'_2
  72. Dilate(E, If[4 < u ≤ 5, 5 - u, 0], K) → E'_3
  73. Segment(C, C'_2) → m_2
  74. Segment(E, E'_3) → n_2
  75. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], J) → D'_3
  76. Dilate(B, If[5 < u ≤ 6, 6 - u, 0], K) → B'_2
  77. Segment(B, B'_2) → p_2
  78. Segment(D, D'_3) → q_2
  79. Dilate(C, If[6 < u ≤ 7, 7 - u, 0], I) → C'_3
  80. Dilate(A, If[6 < u ≤ 7, 7 - u, 0], J) → A'_3
  81. Segment(A, A'_3) → r_2
  82. Segment(C, C'_3) → s_2
  83. Dilate(B, If[7 < u ≤ 8, 8 - u, 0], H) → B'_3
  84. Dilate(F, If[7 < u ≤ 8, 8 - u, 0], I) → F'_3
  85. Segment(F, F'_3) → t_2
  86. Segment(B, B'_3) → a_2
  87. Dilate(R, If[15 < u ≤ 16, 16 - u, 0], M) → R'
  88. Segment(R, R') → b_2
  89. Dilate(R, If[16 < u ≤ 17, 17 - u, 0], P) → R'_1
  90. Vector(R, R'_1) → v
  91. Translate(R, v) → R'_2
  92. Translate(R', v) → R''
  93. Segment(R'_2, R'') → c_2
  94. Dilate(M, If[17 < u ≤ 18, 18 - u, 0], N) → M'
  95. Segment(M, M') → d_2
  96. Dilate(M, If[18 < u ≤ 19, 19 - u, 0], Q) → M'_1
  97. Vector(M, M'_1) → w
  98. Translate(M, w) → M'_2
  99. Translate(M', w) → M''
  100. Segment(M'_2, M'') → e_2
  101. Dilate(N, If[19 < u ≤ 20, 20 - u, 0], O) → N'
  102. Segment(N, N') → f_3
  103. Dilate(N, If[20 < u ≤ 21, 21 - u, 0], R) → N'_1
  104. Vector(N, N'_1) → u_1
  105. Translate(N, u_1) → N'_2
  106. Translate(N', u_1) → N''
  107. Segment(N'_2, N'') → g_3