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Fractal Triangle and Incircle

Fractal Triangle and Incircle
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2021-11-27 17:14
TriangleCircle
This example demonstrates the relationship between a fractal triangle and its incircle. It involves fractal geometry and the concept of an incircle. Using GeoGebra commands such as Segment, Incircle, Mirror, and Polygon, a series of similar triangles are constructed, each with an incircle that is tangent to the incircle of the original triangle. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Incircle(A, B, C) → c
  5. Mirror(l1, Midpoint[A, C]) → l1'
  6. Mirror(l7, Midpoint[A, C]) → l7'
  7. Mirror(l6, Midpoint[A, C]) → l6'
  8. Mirror(l5, Midpoint[A, C]) → l5'
  9. Mirror(l4, Midpoint[A, C]) → l4'
  10. Mirror(l3, Midpoint[A, C]) → l3'
  11. Mirror(l2, Midpoint[A, C]) → l2'
  12. Polygon(A, B, C) → t1, c_1, a, b

AI Drawing Prompt Reference

Draw a triangle by selecting three points and constructing its three sides, then construct the incircle of the original triangle. Next, use symmetry about a line that passes through the midpoint of a relevant side (linked to the triangle’s construction) to mirror the lines/edges corresponding to the triangle, creating multiple copies that form a chain of similar triangles. Keep the original incircle visible to highlight the relationship between the fractal-like triangular construction and the incircle. Finally, outline the original triangle as a polygon, preserving the key geometric structure and tangency context.
The prompt above was compiled from the original drawing commands and is for reference only.