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Symmetry and Parametric Curves Construction

Symmetry and Parametric Curves Construction
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2014-08-04 12:47
Parametric EquationGeometric Construction
This example demonstrates the geometric construction of complex patterns using symmetry, rotation, and vectors; core math concepts include symmetry, parametric curves, geometric transformations, centroid calculation; construction highlights from the summary involve commands like Segment, Rotate, Midpoint, Mirror, Vector, Sequence, Line; suitable for high school and above students to understand parametric equations, geometric transformations, and their applications in design.

GeoGebra Commands & Parameters

  1. Segment(C, B) → h
  2. Segment(L, M) → c
  3. Segment(M, N) → d
  4. Segment(M, P) → e
  5. Segment(M, Q) → f
  6. Rotate(cell1a, 240*°, E) → cell1c
  7. Rotate(cell1a, 120*°, E) → cell1b
  8. Midpoint(A, B) → H
  9. Segment(E, H) → b
  10. Mirror(cell1, h) → cell2
  11. Midpoint(C, A) → G
  12. Midpoint(B, D) → I
  13. Midpoint(D, C) → J
  14. Midpoint(C, B) → K
  15. Vector(A, B) → u
  16. Vector(A, C) → v
  17. Segment(E, G) → a
  18. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  19. Vector(B, D) → w
  20. Vector(C, D) → g
  21. Segment(F, J) → j
  22. Segment(F, I) → k
  23. Segment(E, F) → i
  24. Segment(A, E) → p
  25. Segment(E, C) → q
  26. Segment(E, B) → r
  27. Segment(F, C) → s
  28. Segment(F, B) → t
  29. Segment(F, D) → a_1
  30. Line(C, B) → b_1
  31. Line(C, A) → c_1
  32. Line(A, B) → d_1