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Wallpaper p4g Pattern

Wallpaper p4g Pattern
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2014-08-04 12:57
TransformationGeometric Construction
This example demonstrates the p4g wallpaper pattern and its symmetry. Key mathematical concepts include symmetry, transformation, and geometric construction. Using commands like Midpoint, Vector, Mirror, and Rotate in GeoGebra, you can construct a p4g symmetric pattern. Suitable for middle school students and teachers.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → E
  2. Midpoint(B, D) → F
  3. Midpoint(D, C) → G
  4. Midpoint(C, A) → H
  5. Midpoint(C, B) → I
  6. Vector(A, B) → u
  7. Vector(A, C) → v
  8. Vector(C, D) → w
  9. Vector(B, D) → a
  10. Segment(H, F) → b
  11. Segment(E, G) → c
  12. Segment(J, K) → e
  13. Segment(K, L) → f
  14. Segment(K, M) → g
  15. Segment(K, N) → h
  16. Segment(H, E) → j
  17. Mirror(cell1a, j) → cell1b
  18. Rotate(cell1, 90*°, I) → cell2
  19. Rotate(cell1, 180*°, I) → cell3
  20. Rotate(cell1, 270*°, I) → cell4
  21. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  22. Line(H, E) → l
  23. Line(E, F) → m
  24. Line(F, G) → n
  25. Line(G, H) → p
  26. Line(A, D) → q
  27. Line(C, B) → r
  28. LineBisector(C, G) → s
  29. LineBisector(G, D) → t
  30. LineBisector(C, H) → a_1
  31. LineBisector(H, A) → b_1