积极 AI Logo 积极 AI

正六边形的性质

正六边形的性质
几何画板及绘图内容加载中，请稍等……
2018-02-26 18:02
多边形角几何作图
所属专题 Folding paper, doing geometry figures
该范例演示了正六边形的性质，包括边长、对角线长度、内角和外角等。涉及的核心数学概念有：多边形、角度、几何作图。使用了Polygon、Midpoint、Rotate、CircleArc、Intersect等GeoGebra命令进行构造。适合初中及以上学生学习几何图形的性质。

GeoGebra 命令及参数

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment((sqrt(2) / 4, 0), (sqrt(2) / 4, 1)) → f
  3. Segment((sqrt(2) / 2, 0), (sqrt(2) / 2, 1)) → g
  4. Segment(((3 * sqrt(2) / 4), 0), ((3 * sqrt(2) / 4), 1)) → h
  5. Midpoint(B, D) → E
  6. Rotate(D, -90°, E) → DD
  7. CircleArc(E, DD, D) → e
  8. Intersect(e, h, 1) → F
  9. CircleArc(E, F, D) → k
  10. AngularBisector(F, E, D) → i
  11. Intersect(i, c) → G
  12. Segment(E, G) → j
  13. Polygon(A, C, G, E, B) → veelhoek1, a_1, c_1, g_1, e_1, b_1
  14. Polygon(E, D, G) → driehoek1, g_2, e_2, d_1
  15. Rotate(E, (((-(s - 1)) * 180))°, g_1) → E'
  16. Rotate(D, (((-(s - 1)) * 180))°, g_1) → D'
  17. Rotate(G, (((-(s - 1)) * 180))°, g_1) → G'
  18. Polygon(E', D', G') → driehoek1', g', e', d'
  19. Polygon(E, F, G) → driehoek2, g_3, e_3, f_1
  20. Segment(E, D) → l
  21. Segment(D, G) → m
  22. OrthogonalLine(F, a_1) → n
  23. Intersect(j, d') → II
  24. Intersect(n, j) → R
  25. Intersect(n, a_1) → S
  26. Segment(R, S) → p
  27. Segment(F, S) → q
  28. Mirror(F, g) → H
  29. Mirror(G, g) → I
  30. Segment(I, E) → r
  31. CircleArc(E, B, H) → t
  32. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  33. Rotate(I, (((s - 3) * 180))°, r) → I'
  34. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  35. Rotate(B, (((s - 3) * 180))°, r) → B'
  36. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  37. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  38. Segment(B, E) → h_1
  39. Segment(B, I) → j_1
  40. Mirror(R, g) → TT
  41. Mirror(S, g) → SS
  42. Segment(SS, TT) → k_1
  43. Segment(SS, H) → l_1
  44. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  45. Circle(G, C) → p_1
  46. Intersect(d', f_1) → J
  47. Intersect(d', f_1) → K
  48. Intersect(d', f_1) → L
  49. Intersect(d', f_1) → M
  50. Intersect(p_1, f_1) → N,
  51. CircleArc(G, N, C) → q_1
  52. Line(G, F) → m_1
  53. Intersect(m_1, a_2) → O
  54. Segment(O, F) → n_1
  55. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  56. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  57. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  58. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  59. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  60. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  61. Mirror(O, n_1) → O'_1
  62. Mirror(C, n_1) → C'_1
  63. Mirror(G, n_1) → G'_2
  64. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  65. Mirror(O, g) → O'_2
  66. Mirror(C, g) → C'_2
  67. Mirror(G, g) → G'_3
  68. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  69. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  70. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  71. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  72. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  73. Intersect(c', o_1) → V
  74. Intersect(c', o_1) → W
  75. Intersect(c', o_1) → Z
  76. Line(I, H) → r_1
  77. Intersect(o_1, r_1) → T
  78. Segment(O, C) → s_1
  79. Segment(C, G) → t_1
  80. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  81. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  82. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  83. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  84. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  85. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  86. Segment(E, T) → f_2
  87. Segment(T, E) → j_2
  88. Intersect(Segment[O, N], j_2) → A_1
  89. Segment(A_1, E) → k_2
  90. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  91. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  92. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  93. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  94. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  95. Mirror(N, g) → NN
  96. CircleArc(I, A, NN) → d_2
  97. Segment(I, T) → l_2
  98. Intersect(g'_2, l_2) → B_1
  99. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  100. Segment(I, A) → m_2
  101. Segment(A, O) → p_2
  102. Mirror(H, Segment[I, G]) → HH
  103. Mirror(HH, g) → GG
  104. Intersect(n_2, g) → C_1
  105. Polygon(I, T, C_1, NN) → vierhoek5, i_7, t_5, c_4, nn
  106. Segment(HH, H) → q_2
  107. Segment(GG, F) → r_2
  108. Polygon(GG, F, G) → driehoek6, g_9, gg, f_3
  109. Polygon(I, H, HH) → driehoek7, hh, i_8, h_3
  110. Rotate(GG, (((s - 9) * 180))°, q) → GG'
  111. Rotate(F, (((s - 9) * 180))°, q) → F'
  112. Rotate(G, (((s - 9) * 180))°, q) → G'_5
  113. Polygon(GG', F', G'_5) → driehoek6', g'_5, gg', f'
  114. Rotate(I, (((s - 9) * 180))°, f) → I'_3
  115. Rotate(H, (((s - 9) * 180))°, f) → H'
  116. Rotate(HH, (((s - 9) * 180))°, f) → HH'
  117. Polygon(I'_3, H', HH') → driehoek7', hh', i'_3, h'
  118. Segment(HH, E) → s_2
  119. Segment(H, B_1) → j_3
  120. Segment(E, GG) → k_3
  121. Segment(T, F) → l_3
  122. Polygon(E, HH, H, T, F, GG) → veelhoek4, e_9, hh_1, h_4, t_6, f_4, gg_1
  123. Segment(C_1, T) → m_3
  124. Angle(HH, E, GG) → α
  125. Angle(HH, E, GG) → β
  126. Angle(H', HH, E) → γ
  127. Angle(T, H', HH) → δ
  128. Angle(F, T, H') → ε
  129. Angle(GG, F, T) → ζ
  130. Angle(E, GG, F) → η
  131. Midpoint(E, T) → MM
  132. Circle(MM, E) → d_3
  133. Point(d_3) → PP
  134. Mirror(PP, MM) → PP'
  135. Line(PP, PP') → n_3
  136. Circle(MM, 0.55) → p_3
  137. Line(E, T) → q_3
  138. Intersect(p_3, q_3) → F_1, G_1
  139. Segment(F_1, G_1) → r_3
  140. Sequence(Segment[Rotate[F_1, ((nnn * 30))°, MM], Rotate[G_1, ((nnn * 30))°, MM]], nnn, 1, 6) → lijst_1

AI 绘图提示语参考

绘制一个正六边形，包括其边、对角线、内角和外角。首先绘制六边形的顶点A、C、D、B，然后连接这些顶点形成六边形。接着构造六边形的对角线和中心点E，通过旋转和对称构造六边形的其他部分，最终形成多个三角形和四边形，展示正六边形的对称性和角度特性。
以上提示语为根据原始绘图命令整理而来，仅供参考。