Wallpaper Symmetry Group pg Demo

Wallpaper Symmetry Group pg Demo
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2017-11-01 03:01
In collections Wallpaper Symmetry Groups
This example demonstrates the geometric symmetry of Wallpaper Symmetry Group pg, showcasing translation, rotation, and other symmetric operations through graphical transformations. Core mathematical concepts include symmetry, translation transformations, vector operations, and analytical geometry. Key construction elements utilize GeoGebra commands and objects such as Intersect (intersection), Vector (vector), OrthogonalLine (perpendicular line), Point (point), LineBisector (angle bisector), Translate (translation), and Sequence (sequence). Suitable for high school and above learners to understand the application of symmetry and transformations in mathematics.

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, C) → g
  7. LineBisector(A, B) → h
  8. Translate(Mirror[pic1, g], u) → pic2
  9. Sequence(Sequence[Translate[pic1, Vector[((2 * a) * u) + (b * v)]], a, -10, 10], b, -10, 10) → L_1
  10. Sequence(Sequence[Translate[pic2, Vector[((2 * a) * u) + (b * v)]], a, -10, 10], b, -10, 10) → L_2