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Geogebra Symmetry Pattern Construction

Geogebra Symmetry Pattern Construction
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2014-08-04 13:08
VectorSequence
This example demonstrates the construction of symmetric geometric patterns using GeoGebra, involving core math concepts like symmetry, vectors, sequences, and geometric transformations. Key GeoGebra commands and objects used include Point, Midpoint, Vector, Segment, Mirror, Sequence, Line. Suitable for high school mathematics teaching or geometric construction learning.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a symmetric geometric pattern using multiple points and line segments, constructed by calculating midpoints and vectors to form basic units, then expand the pattern through mirroring and sequence transformations to demonstrate symmetry, resulting in a complex geometric structure.
The prompt above was compiled from the original drawing commands and is for reference only.