积极 AI Logo 积极 AI

通用几何常数与正多边形

通用几何常数与正多边形
几何画板及绘图内容加载中，请稍等……
2019-03-08 13:23
多边形
①本范例演示了如何通过 GeoGebra 构造正多边形并探索其通用几何常数；②涉及的核心数学概念包括正多边形构造、几何变换、旋转、几何均值等；③作图要点：使用了 Circle（圆）、Point（点）、Segment（线段）、Rotate（旋转）、AttachCopyToView（视图附着）、Polygon（多边形）等 GeoGebra 命令；④适合高中及以上数学学习者，用于理解几何变换与多边形性质。

GeoGebra 命令及参数

  1. Circle(C, m_0) → g_1
  2. Point(g_1) → G
  3. Point(g_1) → D
  4. Segment(G, D) → f
  5. Rotate(D, 36°, C) → D'
  6. Segment(G, D') → g
  7. Rotate(D', 36°, C) → D''
  8. Segment(G, D'') → h
  9. Rotate(D'', 36°, C) → D'''
  10. Segment(G, D''') → u
  11. Rotate(D''', 36°, C) → E
  12. Segment(G, E) → w
  13. Rotate(E, 36°, C) → E'
  14. Segment(G, E') → a
  15. Rotate(E', 36°, C) → E''
  16. Segment(G, E'') → b
  17. Rotate(E'', 36°, C) → E'''
  18. Segment(G, E''') → c
  19. Rotate(E''', 36°, C) → F
  20. Segment(G, F) → d
  21. Rotate(F, 36°, C) → F'
  22. Segment(G, F') → e
  23. Segment(C, D) → m
  24. Circle(A, m_0) → hhh
  25. Point(hhh) → B
  26. Rotate(B, (-(60°)), A) → B'_1
  27. Rotate(B, 60°, A) → B'
  28. Rotate(B', 60°, A) → B''
  29. Rotate(B'', 60°, A) → B'''
  30. Rotate(B''', 60°, A) → K
  31. AttachCopyToView(PolyLine[(12.100000000000005,0.2599999999999979), (NaN,NaN), (12.100000000000005,0.2599999999999979), (12.080000000000004,0.19999999999999787), (12.020000000000005,0.2199999999999979), (12.020000000000005,0.29999999999999793), (12.020000000000005,0.379999999999998), (12.020000000000005,0.4599999999999981), (12.080000000000004,0.41999999999999804), (12.140000000000004,0.359999999999998), (12.160000000000004,0.29999999999999793), (12.160000000000004,0.2199999999999979), (12.140000000000004,0.15999999999999784), (12.060000000000004,0.15999999999999784), (12.000000000000004,0.17999999999999786), (11.960000000000004,0.2399999999999979), (11.960000000000004,0.31999999999999795), (11.960000000000004,0.399999999999998), (12.040000000000004,0.399999999999998), (12.140000000000004,0.399999999999998), (12.220000000000004,0.399999999999998), (12.260000000000005,0.33999999999999797), (12.280000000000005,0.2599999999999979), (12.280000000000005,0.17999999999999786), (12.220000000000004,0.2599999999999979), (12.220000000000004,0.33999999999999797), (12.200000000000005,0.4599999999999981), (12.160000000000004,0.5399999999999981), (12.120000000000005,0.5999999999999982), (12.040000000000004,0.5999999999999982), (11.960000000000004,0.5799999999999982), (11.880000000000004,0.5999999999999982), (11.880000000000004,0.6799999999999982), (11.800000000000004,0.7399999999999982), (11.880000000000004,0.6799999999999982), (11.920000000000005,0.6199999999999982), (11.940000000000005,0.5599999999999982), (12.040000000000004,0.5399999999999981), (12.160000000000004,0.49999999999999806), (12.220000000000004,0.4599999999999981), (12.180000000000005,0.399999999999998), (12.140000000000004,0.33999999999999797), (12.180000000000005,0.399999999999998), (12.240000000000004,0.41999999999999804), (12.280000000000005,0.33999999999999797), (12.280000000000005,0.2599999999999979), (12.320000000000004,0.15999999999999784), (12.340000000000005,0.2199999999999979), (12.260000000000005,0.2199999999999979), (12.180000000000005,0.2199999999999979), (12.100000000000005,0.19999999999999787), (12.000000000000004,0.19999999999999787), (11.900000000000004,0.19999999999999787), (11.860000000000005,0.2599999999999979), (11.840000000000005,0.31999999999999795), (11.800000000000004,0.379999999999998), (11.880000000000004,0.379999999999998), (11.940000000000005,0.33999999999999797), (12.000000000000004,0.29999999999999793), (12.060000000000004,0.359999999999998), (12.040000000000004,0.2799999999999979), (NaN,NaN), (7.460000000000003,-1.7000000000000035), true], 1, (-5.120000000000001, -5.000000000000006), (18.720000000000006, 6.620000000000003), (0, 581), (1192, 0)) → stroke1
  32. Segment(C, D') → h_1
  33. Segment(C, D'') → i
  34. Segment(C, D''') → j
  35. Segment(C, E) → l
  36. Segment(C, E') → p
  37. Segment(C, E'') → q
  38. Segment(C, E''') → r
  39. Segment(C, F) → s
  40. Segment(F', C) → t
  41. Polygon(E', E'', E''', F, F', D, D', D'', D''', E) → poly1, e', e_2, e'', e''', f_2, f', d_1, d', d'', d'''
  42. Polygon(E', E'', E''', F, F', D, D', D'', D''', E) → poly2, e'_1, e_3, e''_1, e'''_1, f_3, f'_1, d_2, d'_1, d''_1, d'''_1