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新六边形探索

新六边形探索
几何画板及绘图内容加载中，请稍等……
2019-03-08 11:45
多边形变换几何作图
本范例展示了几何学中的新概念。通过使用GeoGebra中的Circle, Point, Segment, Rotate, Line, Intersect等命令，可以构造出一个六边形，并探索其几何性质。适合初中及以上学生学习几何变换和多边形特性。

GeoGebra 命令及参数

  1. Circle(A, m_0) → e_1
  2. Point(e_1) → B
  3. Segment(A, B) → m
  4. Rotate(B, 60°, A) → B'
  5. Rotate(B', 60°, A) → B''
  6. Rotate(B'', 60°, A) → B'''
  7. Rotate(B''', 60°, A) → K
  8. Rotate(B, (-(60°)), A) → B'_1
  9. Point(e_1) → L
  10. Segment(L, K) → b
  11. Segment(L, B''') → a
  12. Segment(L, B'') → f
  13. Segment(L, B') → e
  14. Segment(L, B'_1) → c
  15. Segment(L, B) → d
  16. Circle(C, m_0) → c_1
  17. Point(c_1) → D
  18. Line(D, C) → j_1
  19. Intersect(c_1, j_1, 2) → I
  20. 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
  21. Segment(A, B') → h
  22. Segment(A, B'') → i
  23. Segment(A, B''') → j
  24. Segment(K, A) → l
  25. Segment(A, B'_1) → p
  26. Polygon(K, B''', B'', B', B, B'_1) → poly1, k_1, b''', b'', b', b_1, b'_1

AI 绘图提示语参考

画一个正六边形，从中心点出发依次绘制六个顶点，每个顶点通过旋转前一个顶点60度得到，然后用线段依次连接相邻顶点形成六边形，再从中心点向每个顶点绘制线段，最后将中心点和每个顶点连接起来，展示六边形的对称性和旋转特性。
以上提示语为根据原始绘图命令整理而来，仅供参考。