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Sierpinski Isosceles Right Triangles Curve

Sierpinski Isosceles Right Triangles Curve
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2017-10-22 08:19
TrianglePolygonGeometric Construction
This example demonstrates the iterative construction of the Sierpinski Isosceles Right Triangles Curve, a fractal geometry illustration. Key math concepts include fractals, isosceles right triangles, iteration, and self-similarity. The construction uses commands like Segment, Polygon, PolyLine, and Rotate in GeoGebra. Suitable for high school students and above to learn about fractal geometry, geometric constructions, and algorithmic thinking.

GeoGebra Commands & Parameters

  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