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p4g Geometric Transformation

p4g Geometric Transformation
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2014-08-08 10:52
VectorMatrixTransformation
In collections Symmetry, Transformation and Tessellation
This example demonstrates p4g symmetry transformations, involving key mathematical concepts such as geometric transformations and matrices. Using GeoGebra commands like Midpoint, Vector, Segment, Mirror, and Rotate, complex geometric shapes are constructed. Suitable for high school mathematics education and learning, especially for topics on geometric transformations and matrix transformations.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → E
  2. Midpoint(B, D) → F
  3. Midpoint(D, C) → G
  4. Midpoint(C, A) → H
  5. Midpoint(C, B) → I
  6. Vector(A, B) → u
  7. Vector(A, C) → v
  8. Vector(C, D) → w
  9. Vector(B, D) → a
  10. Segment(H, F) → b
  11. Segment(E, G) → c
  12. Segment(J, K) → e
  13. Segment(K, L) → f
  14. Segment(K, M) → g
  15. Segment(K, N) → h
  16. Segment(H, E) → j
  17. Mirror(cell1a, j) → cell1b
  18. Rotate(cell1, 90*°, I) → cell2
  19. Rotate(cell1, 180*°, I) → cell3
  20. Rotate(cell1, 270*°, I) → cell4
  21. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  22. Line(H, E) → l
  23. Line(E, F) → m
  24. Line(F, G) → n
  25. Line(G, H) → p
  26. Line(A, D) → q
  27. Line(C, B) → r
  28. LineBisector(C, G) → s
  29. LineBisector(G, D) → t
  30. LineBisector(C, H) → a_1
  31. LineBisector(H, A) → b_1

AI Drawing Prompt Reference

Draw a square ABCD, then construct its diagonals using midpoints E, F, G, H. Draw vectors u, v, w, a. Use midpoints and vectors to draw segments b, c, e, f, g, h, j. Perform mirror and rotation operations to get cell1b, cell2, cell3, cell4. Finally, use translation to generate the tiling pattern tiling.
The prompt above was compiled from the original drawing commands and is for reference only.