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Hexagonal Slide Puzzle

Hexagonal Slide Puzzle
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2019-08-16 23:50
PolygonVectorGeometric ConstructionSlider Animation
This example demonstrates a simple hexagonal tile tessellation transformation. The core mathematical concepts include geometric transformations, specifically translation. Using GeoGebra commands such as Vector, Translate, Sequence, and Polygon, a translated hexagonal pattern can be constructed. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

  1. Vector(E, B) → u
  2. Translate(L, u) → L'
  3. Translate(K, u) → K'
  4. Vector(C, A) → v
  5. Translate(H, Vector[(-v)]) → H'
  6. Translate(G, Vector[(-v)]) → G'
  7. Vector(E, D) → w
  8. Translate(J, w) → J'
  9. Translate(I, w) → I'
  10. Sequence(Polygon[Translate[A, Vector[(i * w)]], Translate[G, Vector[(i * w)]], Translate[H, Vector[(i * w)]], Translate[B, Vector[(i * w)]], Translate[K', Vector[(i * w)]], Translate[L', Vector[(i * w)]], Translate[F, Vector[(i * w)]], Translate[J', Vector[(i * w)]], Translate[I', Vector[(i * w)]], Translate[D, Vector[(i * w)]], Translate[H', Vector[(i * w)]], Translate[G', Vector[(i * w)]], Translate[C, Vector[(i * w)]], Translate[L, Vector[(i * w)]], Translate[K, Vector[(i * w)]], Translate[E, Vector[(i * w)]], Translate[I, Vector[(i * w)]], Translate[J, Vector[(i * w)]]], i, -5, 5) → l1
  11. Polygon(A, B, F, D, C, E) → poly1, a, b, f, d, c, e
  12. Sequence(Translate[l1, Vector[(i * v)]], i, -5, 5) → l2
  13. Polygon(A, G, H', G', C, L, K, E, I, J, H, B, K', L', F, J', I', D) → poly2, a_1, d_1, h', g', c_1, l, k, e_1, i, j, g, h, b_1, k', l', f_1, j', i'
  14. Sequence(Polygon[Translate[A, Vector[(((2 * i) + 1) * w)]], Translate[G, Vector[(((2 * i) + 1) * w)]], Translate[H, Vector[(((2 * i) + 1) * w)]], Translate[B, Vector[(((2 * i) + 1) * w)]], Translate[K', Vector[(((2 * i) + 1) * w)]], Translate[L', Vector[(((2 * i) + 1) * w)]], Translate[F, Vector[(((2 * i) + 1) * w)]], Translate[J', Vector[(((2 * i) + 1) * w)]], Translate[I', Vector[(((2 * i) + 1) * w)]], Translate[D, Vector[(((2 * i) + 1) * w)]], Translate[H', Vector[(((2 * i) + 1) * w)]], Translate[G', Vector[(((2 * i) + 1) * w)]], Translate[C, Vector[(((2 * i) + 1) * w)]], Translate[L, Vector[(((2 * i) + 1) * w)]], Translate[K, Vector[(((2 * i) + 1) * w)]], Translate[E, Vector[(((2 * i) + 1) * w)]], Translate[I, Vector[(((2 * i) + 1) * w)]], Translate[J, Vector[(((2 * i) + 1) * w)]]], i, -3, 2) → l3
  15. Sequence(Polygon[Translate[A, Vector[((2 * i) * w)]], Translate[G, Vector[((2 * i) * w)]], Translate[H, Vector[((2 * i) * w)]], Translate[B, Vector[((2 * i) * w)]], Translate[K', Vector[((2 * i) * w)]], Translate[L', Vector[((2 * i) * w)]], Translate[F, Vector[((2 * i) * w)]], Translate[J', Vector[((2 * i) * w)]], Translate[I', Vector[((2 * i) * w)]], Translate[D, Vector[((2 * i) * w)]], Translate[H', Vector[((2 * i) * w)]], Translate[G', Vector[((2 * i) * w)]], Translate[C, Vector[((2 * i) * w)]], Translate[L, Vector[((2 * i) * w)]], Translate[K, Vector[((2 * i) * w)]], Translate[E, Vector[((2 * i) * w)]], Translate[I, Vector[((2 * i) * w)]], Translate[J, Vector[((2 * i) * w)]]], i, -2, 2) → l4
  16. Sequence(Translate[l3, Vector[((2 * i) * v)]], i, -3, 2) → l5
  17. Sequence(Translate[l4, Vector[((2 * i) * v)]], i, -3, 2) → l6
  18. Sequence(Translate[l4, Vector[(((2 * i) + 1) * v)]], i, -3, 2) → l7
  19. Sequence(Translate[l3, Vector[(((2 * i) + 1) * v)]], i, -3, 2) → l8