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p4m Symmetry Transformation

p4m Symmetry Transformation
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2014-08-08 10:55
VectorTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates p4m symmetry transformation, involving translation, rotation, and mirroring. Using GeoGebra commands such as Midpoint, Vector, Rotate, etc., complex geometric shapes are constructed. Suitable for middle school students learning geometric transformations.

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(I, A) → j
  17. Segment(I, E) → k
  18. Line(A, D) → l
  19. Line(C, B) → m
  20. Line(H, F) → n
  21. Line(E, G) → p
  22. Line(G, F) → q
  23. Line(F, E) → r
  24. Line(E, H) → s
  25. Line(H, G) → t
  26. Mirror(cell1a, c) → cell1b
  27. Rotate(cell1, 90*°, I) → cell2
  28. Rotate(cell1, 180*°, I) → cell3
  29. Rotate(cell1, 270*°, I) → cell4
  30. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling

AI Drawing Prompt Reference

Draw a square and then perform translation, rotation, and mirroring around the center point to create a p4m symmetric pattern. First, find the midpoints of each side of the square, then create vectors representing the direction of the sides. Next, construct the diagonals and auxiliary line segments, and finally generate a complex geometric pattern through translation, rotation, and mirroring.
The prompt above was compiled from the original drawing commands and is for reference only.