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Wallpaper Symmetry Group p4g

Wallpaper Symmetry Group p4g
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2017-11-03 00:36
TransformationGeometric Construction
In collections Wallpaper Symmetry Groups
This example illustrates the p4g wallpaper symmetry group. It involves symmetry, transformations, and geometric construction. Using commands like Intersect, Vector, OrthogonalLine, Circle, Sequence, and Mirror, you can construct patterns with p4g symmetry. Suitable for high school geometry education to help students understand symmetry and transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. OrthogonalLine(A, u) → f
  4. Circle(A, B) → c
  5. Intersect(c, f, 2) → C
  6. Vector(A, C) → v
  7. Sequence(Rotate[pic1, (a * π / 2)], a, 0, 3) → L_1
  8. OrthogonalLine(C, v) → g
  9. OrthogonalLine(B, u) → h
  10. Mirror(L_1, h) → L_2
  11. Mirror(L_1, g) → L_3
  12. Mirror(L_3, h) → L_4
  13. Sequence(Sequence[Translate[L_1, Vector[((4 * a) * u) + ((4 * b) * v)]], a, -10, 10], b, -10, 10) → L_5
  14. Sequence(Sequence[Translate[L_2, Vector[((4 * a) * u) + ((4 * b) * v)]], a, -10, 10], b, -10, 10) → L_6
  15. Sequence(Sequence[Translate[L_3, Vector[((4 * a) * u) + ((4 * b) * v)]], a, -10, 10], b, -10, 10) → L_7
  16. Sequence(Sequence[Translate[L_4, Vector[((4 * a) * u) + ((4 * b) * v)]], a, -10, 10], b, -10, 10) → L_8