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p4m Frame

p4m Frame
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2014-07-27 22:06
TransformationGeometric Construction
This example demonstrates the construction of a p4m frame. Key mathematical concepts include symmetry, transformation, and geometric construction. Using GeoGebra commands such as Midpoint, Vector, Segment, Line, Mirror, and Rotate, the geometric structure of the p4m frame is built. 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(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