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Wallpaper Symmetry Group p4

Wallpaper Symmetry Group p4
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2017-11-02 21:31
VectorGeometric Construction
In collections Wallpaper Symmetry Groups
This example demonstrates the geometric pattern and symmetry of the wallpaper symmetry group p4. Core math concepts include symmetry, fractions, parallelograms, unit circles, exponential functions, and trapezoids. Construction highlights involve GeoGebra commands/objects like Intersect, Vector, OrthogonalLine, Circle, and Sequence. Suitable for high school mathematics teaching or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. OrthogonalLine(A, u, xOyPlane) → f
  4. Circle(A, B) → c
  5. Intersect(f, c) → D, E
  6. Vector(A, E) → v
  7. Sequence(Rotate[pic2, (a * π / 2)], a, 0, 3) → L_1
  8. Sequence(Sequence[Translate[L_1, Vector[((2 * a) * u) + ((2 * b) * v)]], a, -10, 10], b, -10, 10) → L_2