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Tessellation by Ben Sparks

Tessellation by Ben Sparks
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2016-11-02 21:36
PolygonVectorGeometric Construction
This example demonstrates the concept of tessellation. It involves key mathematical concepts such as polygons and vectors. Using GeoGebra commands like Segment, Line, Vector, Translate, etc., various polygon tessellation patterns can be constructed. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Line(A, g) → h
  4. Line(C, f) → i
  5. Vector(A, B) → u
  6. Vector(B, C) → v
  7. Segment(A, E) → k
  8. Segment(E, F) → m
  9. Segment(F, G) → n_1
  10. Segment(G, B) → p
  11. Segment(B, H) → q
  12. Segment(H, I) → r
  13. Segment(I, J) → s
  14. Segment(J, K) → t
  15. Segment(K, L) → a
  16. Segment(L, C) → b
  17. Translate(edge1, v) → edge1'
  18. Translate(edge2, Vector[(-u)]) → edge2'
  19. Flatten(Sequence[Sequence[(tt * u) + (ss * v), tt, (-n), n], ss, (-n), n]) → veclist
  20. Intersect(i, h) → D
  21. Segment(A, D) → j
  22. Segment(D, C) → l
  23. Polygon(Join[{edge1, edge2, Reverse[edge1'], Reverse[edge2']}]) → poly1
  24. Zip(Translate[poly1, Vector[vec]], Vector[vec], veclist) → tessel
  25. Polygon(A, B, C, D) → pshape, a_1, b_1, c_1, d_1
  26. Zip(Polygon[Translate[A, Vector[vec]], Translate[B, Vector[vec]], Translate[C, Vector[vec]], Translate[D, Vector[vec]]], Vector[vec], veclist) → ptessel