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Wallpaper Symmetry Group cm

Wallpaper Symmetry Group cm
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2017-11-01 03:21
Coordinate GeometryTransformationParametric EquationGeometric Construction
This example demonstrates the symmetry patterns and transformations of Wallpaper Symmetry Group cm. Core math concepts include symmetry, transformation, parametric equations, and coordinate geometry. Construction highlights involve GeoGebra commands/objects like Intersect (intersection), Vector (vector), OrthogonalLine (perpendicular line), Point (point), LineBisector (angle bisector), and Sequence (sequence). Suitable for high school students and teachers learning geometric transformations, symmetry, and parametric equations.

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. LineBisector(A, B) → g
  7. LineBisector(A, C) → h
  8. Sequence(Translate[Mirror[pic1, h], Vector[((2 * a) * ((0.5 * v) + u))]], a, -10, 10) → L_1
  9. Sequence(Translate[pic1, Vector[(((2 * a) + 1) * ((0.5 * v) + u))]], a, -10, 10) → L_2
  10. Sequence(Translate[L_1, Vector[(a * v)]], a, -10, 10) → L_3
  11. Sequence(Translate[L_2, Vector[(a * v)]], a, -10, 10) → L_4