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Square and Rhombus Tiling

Square and Rhombus Tiling
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2014-08-05 09:38
PolygonTransformationGeometric Construction
This example demonstrates the tiling pattern formed by combining squares and rhombuses. It involves core mathematical concepts such as polygons, symmetry, vector operations, and coordinate geometry. The construction utilizes GeoGebra commands like Segment, Circle, Point, Line, Intersect, Polygon, Midpoint, Rotate, Vector, and Sequence. It is suitable for high school mathematics education, helping students understand geometric transformations and the principles of tiling patterns.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. Circle(A, B) → c_2
  3. Point(c_2) → C
  4. Line(C, a_2) → d_2
  5. Segment(A, C) → b_2
  6. Line(B, b_2) → e_2
  7. Intersect(d_2, e_2) → D
  8. Polygon(C, D, 4) → poly2, l, m, n, p, G, H
  9. Polygon(D, B, 4) → poly3, q, r, s, t, I, J
  10. Midpoint(J, B) → O
  11. Rotate(B, -90*°, O) → B'
  12. Rotate(C, -90*°, O) → C'
  13. Segment(C', B') → c
  14. Polygon(A, C, 4) → poly1, h_2, i, j, k, E, F
  15. Segment(E, H) → a
  16. Segment(C, B) → b
  17. Polygon(B, A, 4) → poly4, a_1, b_1, c_1, d_1, K, L
  18. Segment(C, D) → f_2
  19. Segment(B, D) → g_2
  20. Midpoint(F, C) → M
  21. Midpoint(G, C) → N
  22. Midpoint(K, B) → P
  23. Vector(E, L) → u
  24. Vector(K, J) → v
  25. Sequence(Sequence[Translate[tile1, Vector[(n * u) + (m * v)]], n, -3, 3], m, -3, 3) → list1
  26. Segment(M, P) → g_1
  27. Segment(P, O) → h_1
  28. Segment(O, N) → i_1
  29. Segment(N, M) → j_1
  30. OrthogonalLine(M, h_2) → e_1
  31. OrthogonalLine(P, a_1) → f_1
  32. OrthogonalLine(N, l) → k_1
  33. OrthogonalLine(O, q) → l_1
  34. Intersect(e_1, f_1) → Q
  35. Intersect(k_1, l_1) → R
  36. Segment(M, Q) → d
  37. Segment(P, Q) → e
  38. Segment(Q, R) → f
  39. Segment(N, R) → g
  40. Segment(O, R) → h
  41. Rotate(set1, 90*°, O) → set2
  42. Rotate(set1, 180*°, O) → set3
  43. Rotate(set1, 270*°, O) → set4
  44. Sequence(Sequence[Translate[tile2, Vector[(n * u) + (m * v)]], n, -3, 3], m, -3, 3) → list2

AI Drawing Prompt Reference

Draw a tiling pattern composed of squares and rhombuses, showcasing symmetry and geometric transformations. Start by creating two squares and two rhombuses, then use rotation and translation to form a repeating tessellation. Ensure the pattern has high symmetry and clearly shows how the squares and rhombuses fit together.
The prompt above was compiled from the original drawing commands and is for reference only.