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Cairo Tiling Construction 1

Cairo Tiling Construction 1
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2014-11-24 20:54
PolygonVectorOptimizationGeometric Construction
This example demonstrates the construction of a Cairo Tiling, a complex pattern formed by rotating and reflecting polygons. It involves core mathematical concepts like polygon construction, rotation, reflection, vector operations, and sequence generation. The construction uses commands and objects such as Point, Rotate, Polygon, Segment, Mirror, Vector, and Sequence in GeoGebra. Suitable for high school students learning geometric transformations, tiling patterns, and spatial geometry concepts.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Rotate(C, -90*°, A) → C'
  3. Rotate(C, 90*°, B) → C'_1
  4. Polygon(C, A, C', C'_1, B) → poly1, c, a, c', c'_1, b
  5. Rotate(B, -90*°, A) → B'
  6. Rotate(A, 90*°, B) → A'
  7. Segment(A, C') → d
  8. Segment(C', C'_1) → e
  9. Segment(C'_1, B) → f
  10. Segment(C', B') → g
  11. Segment(C'_1, A') → h
  12. Rotate(cell, 90*°, B) → cell'
  13. Mirror(A, B) → A'_1
  14. Vector(A, A'_1) → u
  15. Vector(A, A') → v
  16. Sequence(Sequence[Translate[tile, Vector[(m * u) + (n * v)]], m, -3, 3], n, -3, 3) → tiling

AI Drawing Prompt Reference

Draw a Cairo tiling pattern by first creating point A on the y-axis, then rotating points C and B around A to generate C', C'_1, and B'. Use these points to construct polygon poly1. Next, create A' and B' and use them to generate line segments d, e, f, g, and h. Then, rotate cell around B to generate cell', and mirror A to generate A'_1. Finally, use A'_1 and A' to generate vectors u and v, and translate tile to create the entire Cairo tiling pattern.
The prompt above was compiled from the original drawing commands and is for reference only.