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Euclidean Mosaic: Geometric Construction and Transformation

Euclidean Mosaic: Geometric Construction and Transformation
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2025-08-19 01:45
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This example demonstrates the construction of Euclidean mosaics, highlighting geometric transformations such as translation, reflection, and rotation. Key mathematical concepts include geometric construction, transformation, and symmetry. The construction involves GeoGebra commands like Join, Translate, Mirror, Circle, and Sequence, with dynamic visualization using Intersect. Suitable for middle s

GeoGebra Commands & Parameters

  1. Join(Sequence[Rotate[p1, (k * pi / 4)], k, 0, 7]) → lista1
  2. Translate(lista1, t) → tras1
  3. Mirror(p2, xAxis) → p2'
  4. Join(Join[Sequence[Rotate[{p2, p2'}, (k * pi / 2)], k, 0, 3]]) → lista2
  5. Translate(lista2, t) → tras2
  6. Circle((0, 0), 4) → c
  7. Mirror(tras1, c) → inv1
  8. Mirror(tras2, c) → inv2
  9. Corner(1, 1) → Export_1
  10. Corner(1, 3) → Export_2
  11. Mirror(p3, xAxis) → p3'
  12. Join(Join[{Sequence[Rotate[{p3, p3'}, (k * pi / 2)], k, 0, 1], Sequence[Rotate[{p5}, (k * pi / 2)], k, 0, 3]}]) → lista3
  13. Translate(lista3, t) → tras3
  14. Mirror(tras3, c) → inv3
  15. Join(Join[Sequence[Rotate[{p4}, (k * pi / 2)], k, 0, 1]]) → lista4
  16. Translate(lista4, t) → tras4
  17. Mirror(tras4, c) → inv4
  18. Sequence({random(), random(), random()}, k, 1, númeroListas) → listaAzar
  19. Sequence(If[oscuro, {1, 1, 1}, {0, 0, 0}], k, 1, númeroListas) → listaBorde
  20. Mirror(negro01, y = x) → negro01'
  21. Mirror(negro02, y = x) → negro02a
  22. Mirror(negro02a, yAxis) → negro02b
  23. Mirror(negro02, xAxis) → negro02c
  24. Join({Sequence[Rotate[{negro01, negro01'}, (k * pi / 2)], k, 0, 3], negro02, negro02a, negro02b, negro02c}) → negro
  25. Translate(negro, t) → negroT
  26. Mirror(negroT, c) → negro'
  27. Segment(A, B) → f
  28. Segment(C, D) → g
  29. Circle(E, 3) → d
  30. Circle(E, 3) → e
  31. Intersect(Line[F, G], Line[polígono1V(10), polígono1V(9)]) → H