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谢尔宾斯基等腰直角三角形曲线

谢尔宾斯基等腰直角三角形曲线
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2017-10-22 08:19
测试改名0多边形几何作图
①本范例演示了如何通过迭代构造谢尔宾斯基等腰直角三角形曲线；②涉及的核心数学概念包括分形几何、等腰直角三角形、迭代、自相似性；③作图要点——从下方『构造摘要』提炼用到了Segment（线段）、Polygon（多边形）、PolyLine（多段线）、Rotate（旋转）等GeoGebra命令/对象；④适合高中及以上学生学习分形几何、几何作图及算法思想。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, D) → h
  4. Polygon(B, A, 4) → poly1, i, j, k, l, E, F
  5. Polygon(B, C, 4) → poly2, m, n, p, q, G, H
  6. Polygon(D, C, 4) → poly3, r, s, t, a, I, J
  7. PolyLine(A, E, B, G, C, I, D) → b
  8. Segment(A, D) → c
  9. Rotate(Rotate[PolyLine[Dilate[A, f / c, A], Dilate[E, f / c, A], Dilate[B, f / c, A], Dilate[G, f / c, A], Dilate[C, f / c, A], Dilate[I, f / c, A], Dilate[D, f / c, A]], Angle[c, f], A], π, Midpoint[f]) → d
  10. Rotate(Rotate[Rotate[PolyLine[Dilate[A, g / c, A], Dilate[E, g / c, A], Dilate[B, g / c, A], Dilate[G, g / c, A], Dilate[C, g / c, A], Dilate[I, g / c, A], Dilate[D, g / c, A]], Angle[c, f], A], π, Midpoint[f]], Angle[f, g] + π, B) → e
  11. Rotate(Translate[Rotate[Rotate[PolyLine[Dilate[A, h / c, A], Dilate[E, h / c, A], Dilate[B, h / c, A], Dilate[G, h / c, A], Dilate[C, h / c, A], Dilate[I, h / c, A], Dilate[D, h / c, A]], Angle[c, f], A], π, Midpoint[f]], D - B], Angle[f, h], D) → f_1