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旋转多边形 by John Golden

旋转多边形 by John Golden
几何画板及绘图内容加载中，请稍等……
2016-03-23 01:38
多边形变换几何作图
①本范例演示通过旋转四边形并利用其与自身的交点构造复杂多边形的过程；②涉及的核心数学概念包括旋转、对称性、多边形构造、交点计算；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Rotate（旋转）、Intersect（交点）、Sequence（序列）、PolyLine（多段线）、Rotgon（旋转多边形）等GeoGebra命令/对象；④适合高中及以上数学学习者，用于理解变换几何与复杂图形构造。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Rotate(A, (360 * ° / N), E) → A'
  3. Rotate(B, (360 * ° / N), E) → B'
  4. Rotate(C, (360 * ° / N), E) → C'
  5. Rotate(D, (360 * ° / N), E) → D'
  6. Polygon(A', B', C', D') → poly1', a', b', c', d'
  7. Intersect(poly1, poly1') → F, G, F_1, F_2, F_3, F_4, F_5, F_6, F_7, F_8
  8. Polygon({Intersect[poly1, poly1']}) → poly2
  9. Polygon(F_1, D, C) → poly3, c_1, f_1, d_1
  10. Polygon(F_2, A, G) → poly4, g, f_2, a_1
  11. Polygon(F, C, B) → poly5, b_1, f, c_2
  12. Sequence(Rotate[poly2, ((i * 360) * ° / N), E], i, 1, N) → list1
  13. Sequence(Polygon[Rotate[F_1, ((i * 360) * ° / N), E], Rotate[D, ((i * 360) * ° / N), E], Rotate[C, ((i * 360) * ° / N), E]], i, 1, N) → list2
  14. Sequence(Polygon[Rotate[F_2, ((i * 360) * ° / N), E], Rotate[A, ((i * 360) * ° / N), E], Rotate[G, ((i * 360) * ° / N), E]], i, 1, N) → list3
  15. Sequence(Polygon[Rotate[F, ((i * 360) * ° / N), E], Rotate[C, ((i * 360) * ° / N), E], Rotate[B, ((i * 360) * ° / N), E]], i, 1, N) → list4
  16. Sequence(Polygon[Rotate[A, ((i * 360) * ° / N), E], Rotate[B, ((i * 360) * ° / N), E], Rotate[C, ((i * 360) * ° / N), E], Rotate[D, ((i * 360) * ° / N), E]], i, 1, N) → list5
  17. Polygon(F_2, F_3, F_4) → poly6, f_4, f_3, f_5
  18. Sequence(Polygon[Rotate[F_2, ((i * 360) * ° / N), E], Rotate[F_3, ((i * 360) * ° / N), E], Rotate[F_4, ((i * 360) * ° / N), E]], i, 1, N) → list6
  19. PolyLine(A, B, C, D, A) → h
  20. Rotate(A', (360 * ° / N), E) → A''
  21. Rotate(B', (360 * ° / N), E) → B''
  22. Rotate(C', (360 * ° / N), E) → C''
  23. Rotate(D', (360 * ° / N), E) → D''
  24. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
  25. Intersect(poly1'', poly1) → H, I, H_1, H_2, H_3, H_4, H_5, H_6, H_7, H_8
  26. Polygon(H, I, D) → poly7, i, j, k
  27. Polygon({Intersect[poly1, poly1'']}) → poly9
  28. Sequence(Rotate[poly9, ((i * 360) * ° / N), E], i, 1, N) → list8
  29. Polygon(F, H, B) → poly8, b_2, f_6, h_1
  30. Sequence(Polygon[Rotate[F, ((i * 360) * ° / N), E], Rotate[H, ((i * 360) * ° / N), E], Rotate[B, ((i * 360) * ° / N), E]], i, 1, N) → list9
  31. Polygon(G, H, D) → poly10, d_2, g_1, h_2
  32. Sequence(Polygon[Rotate[G, ((i * 360) * ° / N), E], Rotate[H, ((i * 360) * ° / N), E], Rotate[D, ((i * 360) * ° / N), E]], i, 1, N) → list10
  33. Sequence(Polygon[Rotate[H, ((i * 360) * ° / N), E], Rotate[I, ((i * 360) * ° / N), E], Rotate[B, ((i * 360) * ° / N), E]], i, 1, N) → list7
  34. Rotgon(E, N, F, F_2, H_1) → list11