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Wallpaper Symmetry Group pmg

Wallpaper Symmetry Group pmg
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2017-11-01 21:52
VectorFunctionCoordinate GeometryTransformationGeometric Construction
In collections Wallpaper Symmetry Groups
This example demonstrates the symmetry of the wallpaper group pmg. Core mathematical concepts include symmetry, limits, linear functions, addition, straight lines, and hypothesis testing. Construction highlights the use of GeoGebra commands: Intersect, Vector, OrthogonalLine, Point, Midpoint, Mirror, Line, Sequence; objects include A, B, u, f, C, v, g, h, pic1, D, E, F, pic1', i, pic1'_1, pic1'', L_1, L_2, L_3, L_4. Suitable for high school and above learning symmetry and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. OrthogonalLine(A, u) → f
  4. Point(f) → C
  5. Vector(A, C) → v
  6. OrthogonalLine(C, v) → g
  7. OrthogonalLine(B, u) → h
  8. Midpoint(C, D) → E
  9. Midpoint(D, B) → F
  10. Mirror(pic1, E) → pic1'
  11. Line(D, B) → i
  12. Mirror(pic1, i) → pic1'_1
  13. Mirror(pic1', i) → pic1''
  14. Sequence(Sequence[Translate[pic1, Vector[((2 * a) * u) + ((2 * b) * v)]], a, -10, 10], b, -10, 10) → L_1
  15. Sequence(Sequence[Translate[pic1', Vector[((2 * a) * u) + ((2 * b) * v)]], a, -10, 10], b, -10, 10) → L_2
  16. Sequence(Sequence[Translate[pic1'_1, Vector[((2 * a) * u) + ((2 * b) * v)]], a, -10, 10], b, -10, 10) → L_3
  17. Sequence(Sequence[Translate[pic1'', Vector[((2 * a) * u) + ((2 * b) * v)]], a, -10, 10], b, -10, 10) → L_4