轴对称与正多边形的探究

轴对称与正多边形的探究
几何画板及绘图内容加载中,请稍等……
2012-09-03 20:11
本范例展示了轴对称图形和正多边形的性质。通过轴对称变换,可以观察到正多边形的对称轴和对称性。涉及的核心数学概念包括轴对称、正多边形和几何作图。使用了Polygon, Line, Mirror等GeoGebra命令进行构造。适合初中及以上学生学习几何对称性和正多边形的相关知识。

GeoGebra 命令及参数

  1. Polygon(A, B, n) → poli1, c, a, b, f_1, g_1, C, E, H
  2. Polygon(A_1, B_1, n_1) → poli1_1, c_1, I, a_1, d, i_{17}, r_2, s_4, C_1, V_9, W_9
  3. Polygon(A_2, B_2, n_2) → poli1_2, c_2, O, a_2, e, h_1, i_1, j_1, C_2, U_2, N
  4. Polygon(A_3, B_3, n_3) → poli1_3, c_3, a_3, g, C_3
  5. Polygon(A_4, B_4, n_4) → poli1_4, c_4, I_{10}, P, Q, a_4, f, l_{17}, k_1, l_1, m_1, C_4, H_{10}
  6. Polygon(A_5, B_5, n_5) → poli1_5, c_5, R, S, Z, a_5, h, q_1, r_1, s_1, t_1, C_5, M
  7. Polygon(A_6, B_6, n_6) → poli1_6, c_6, a_6, i, C_6
  8. Polygon(A_7, B_7, n_7) → poli1_7, c_7, E_1, I_1, J_1, a_7, l, b_2, d_2, f_2, g_2, C_7, D_1
  9. Polygon(A_8, B_8, n_8) → poli1_8, c_8, a_8, m, j_2, k_2, C_8, K_1, L_1
  10. Polygon(A_9, B_9, n_9) → poli1_9, c_9, M_1, N_1, O_1, a_9, j, l_2, m_2, q_2, s_2, C_{17}, D
  11. Polygon(A_{10}, B_{10}, n_{10}) → poli1_{10}, c_{10}, a_{10}, q, t_2, C_{16}, Q_1
  12. Polygon(A_{11}, B_{11}, n_{11}) → poli1_{11}, c_{11}, R_1, a_{11}, k, m_4, b_3, d_3, C_{15}, F_1, T
  13. Polygon(A_{12}, B_{12}, n_{12}) → poli1_{12}, c_{12}, U_1, V_1, Z_1, a_{12}, r, e_3, f_3, i_3, k_3, C_{14}, T_1
  14. Polygon(A_{13}, B_{13}, n_{13}) → poli1_{13}, c_{13}, E_2, a_{13}, p, p_1, l_3, m_3, C_{13}, P_1, D_2
  15. Polygon(A_{14}, B_{14}, n_{14}) → poli1_{14}, c_{14}, G_2, H_2, I_2, a_{14}, s, p_3, q_3, r_3, s_3, C_{12}, F_2
  16. Polygon(A_{15}, B_{15}, n_{15}) → poli1_{15}, c_{15}, a_{15}, t, b_1, p_2, C_{11}, F, G
  17. Polygon(A_{16}, B_{16}, n_{16}) → poli1_{16}, c_{16}, L, a_{16}, d_1, j_3, t_4, m_5, C_{10}, K_{10}, J
  18. Polygon(A_{17}, B_{17}, n_{17}) → poli1_{17}, c_{17}, J_2, a_{17}, e_1, t_3, b_4, d_4, C_9, W_1, K
  19. Polygon(G_1, H_1, 3) → poli2, s_7, g_3, h_3, S_1
  20. Line(U, h_3) → e_2
  21. Line(V, g_3) → h_2
  22. Line(W, s_7) → i_2
  23. Mirror(poli1, i_2) → poli1'
  24. Mirror(poli1_1, i_2) → poli3
  25. Mirror(poli1_2, i_2) → poli4
  26. Mirror(poli1_3, i_2) → poli5
  27. Mirror(poli1_4, i_2) → poli6
  28. Mirror(poli1_5, i_2) → poli7
  29. Mirror(poli1_6, i_2) → poli8
  30. Mirror(poli1_7, i_2) → poli9
  31. Mirror(poli1_8, i_2) → poli10
  32. Mirror(poli1_9, i_2) → poli11
  33. Mirror(poli1_{10}, i_2) → poli12
  34. Mirror(poli1_{11}, i_2) → poli13
  35. Mirror(poli1_{12}, i_2) → poli14
  36. Mirror(poli1_{13}, i_2) → poli15
  37. Mirror(poli1_{14}, i_2) → poli16
  38. Mirror(poli1_{15}, i_2) → poli17
  39. Mirror(poli1_{16}, i_2) → poli18
  40. Mirror(poli1_{17}, i_2) → poli19
  41. Mirror(poli2, i_2) → poli2'
  42. Mirror(poli1, h_2) → poli1'_1
  43. Mirror(poli1_1, h_2) → poli20
  44. Mirror(poli1_2, h_2) → poli21
  45. Mirror(poli1_3, h_2) → poli22
  46. Mirror(poli1_4, h_2) → poli23
  47. Mirror(poli1_5, h_2) → poli24
  48. Mirror(poli1_6, h_2) → poli25
  49. Mirror(poli1_7, h_2) → poli26
  50. Mirror(poli1_8, h_2) → poli27
  51. Mirror(poli1_9, h_2) → poli28
  52. Mirror(poli1_{10}, h_2) → poli29
  53. Mirror(poli1_{11}, h_2) → poli30
  54. Mirror(poli1_{12}, h_2) → poli31
  55. Mirror(poli1_{13}, h_2) → poli32
  56. Mirror(poli1_{14}, h_2) → poli33
  57. Mirror(poli1_{15}, h_2) → poli34
  58. Mirror(poli1_{16}, h_2) → poli35
  59. Mirror(poli1_{17}, h_2) → poli36
  60. Mirror(poli2, h_2) → poli2'_1
  61. Mirror(poli1, e_2) → poli1'_2
  62. Mirror(poli1_1, e_2) → poli37
  63. Mirror(poli1_2, e_2) → poli38
  64. Mirror(poli1_3, e_2) → poli39
  65. Mirror(poli1_4, e_2) → poli40
  66. Mirror(poli1_5, e_2) → poli41
  67. Mirror(poli1_6, e_2) → poli42
  68. Mirror(poli1_7, e_2) → poli43
  69. Mirror(poli1_8, e_2) → poli44
  70. Mirror(poli1_9, e_2) → poli45
  71. Mirror(poli1_{10}, e_2) → poli46
  72. Mirror(poli1_{11}, e_2) → poli47
  73. Mirror(poli1_{12}, e_2) → poli48
  74. Mirror(poli1_{13}, e_2) → poli49
  75. Mirror(poli1_{14}, e_2) → poli50
  76. Mirror(poli1_{15}, e_2) → poli51
  77. Mirror(poli1_{16}, e_2) → poli52
  78. Mirror(poli1_{17}, e_2) → poli53
  79. Mirror(poli2, e_2) → poli2'_2

AI 绘图提示语参考

绘制多个正多边形,并展示它们的对称轴和对称性。首先创建多个正多边形,然后通过镜像操作,沿两条不同的直线进行对称变换,观察对称后的图形。最终图形应包含多个原始正多边形及其镜像,以及用于对称变换的两条直线,清晰展示轴对称的性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。