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Wallpaper Symmetry Group p2

Wallpaper Symmetry Group p2
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2017-10-31 05:56
VectorTransformationGeometric Construction
In collections Wallpaper Symmetry Groups
This example demonstrates the construction of a wallpaper symmetry group p2 in two-dimensional space, showcasing symmetry principles, vector constructions, linear functions, and trigonometric functions. Key GeoGebra commands used include Intersect, Vector, Sequence, and Rotate, with objects like points O, B, vectors u, A, v, and lines L_1, L_2, L_3. It is suitable for high school and advanced students studying spatial geometry and symmetry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(O, B) → u
  3. Vector(O, A) → v
  4. Sequence(Sequence[(a * A) + (b * B), a, -10, 10], b, -10, 10) → L_1
  5. Rotate(pic1, π, Midpoint[A, B]) → pic1'
  6. Sequence(Sequence[Translate[pic1', (a * A) + (b * B)], a, -10, 10], b, -10, 10) → L_2
  7. Sequence(Sequence[Translate[pic1, (a * A) + (b * B)], a, -10, 10], b, -10, 10) → L_3