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Rotate a Triangle to Create Tessellations

Rotate a Triangle to Create Tessellations
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2014-04-04 05:09
TrianglePolygonTransformationGeometric Construction
In collections Create a Rotation Tessellation using a Triangle
This example demonstrates how to create a tessellation by rotating a triangle. It involves core math concepts like Rotation, Polygon, Plane Figures, Unit Circle, and Complex Numbers. The construction uses GeoGebra commands such as Polygon, Segment, Rotate, Midpoint, and PointIn. Suitable for middle school and above students learning geometric transformations and tessellation construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Segment(A, D) → d
  3. Segment(D, E) → e
  4. Segment(E, F) → f
  5. Segment(F, G) → g
  6. Segment(G, H) → h
  7. Segment(H, B) → i
  8. Rotate(A, -60*°, B) → A'
  9. Rotate(B, -60*°, B) → B'
  10. Segment(A', B') → a'
  11. Rotate(A, -60*°, B) → A'_1
  12. Rotate(D, -60*°, B) → D'
  13. Segment(A'_1, D') → d'
  14. Rotate(D, -60*°, B) → D'_1
  15. Rotate(E, -60*°, B) → E'
  16. Segment(D'_1, E') → e'
  17. Rotate(E, -60*°, B) → E'_1
  18. Rotate(F, -60*°, B) → F'
  19. Segment(E'_1, F') → f'
  20. Rotate(F, -60*°, B) → F'_1
  21. Rotate(G, -60*°, B) → G'
  22. Segment(F'_1, G') → g'
  23. Rotate(G, -60*°, B) → G'_1
  24. Rotate(H, -60*°, B) → H'
  25. Segment(G'_1, H') → h'
  26. Rotate(H, -60*°, B) → H'_1
  27. Rotate(B, -60*°, B) → B'_1
  28. Segment(H'_1, B'_1) → i'
  29. Midpoint(c) → I
  30. Segment(C, J) → j
  31. Segment(J, K) → k
  32. Segment(K, I) → l
  33. Rotate(A'_1, -180*°, I) → L
  34. Rotate(C, -180*°, I) → C'
  35. Rotate(J, -180*°, I) → J'
  36. Segment(C', J') → j'
  37. Rotate(J, -180*°, I) → J'_1
  38. Rotate(K, -180*°, I) → K'
  39. Segment(J'_1, K') → k'
  40. Rotate(K, -180*°, I) → K'_1
  41. Rotate(I, -180*°, I) → I'
  42. Segment(K'_1, I') → l'
  43. Rotate(A', -180*°, I) → A''
  44. Polygon(F, E, D', E', F', G', H', B, H, G, D, A, J', K', I, K, J, C) → poly2, f_1, c_1, d'_1, e'_1, f'_1, g'_1, h'_1, b_1, h_1, g_1, e_1, d_1, a_1, j'_1, k'_1, i_1, k_1, j_1
  45. PointIn(poly2) → M
  46. PointIn(poly2) → N

AI Drawing Prompt Reference

Draw a triangle and rotate it around one of its vertices three times, each time by 60 degrees, to create six identical triangles. Connect the corresponding sides of these rotated triangles to form a complex geometric pattern. Inside the pattern, draw a small triangle at the center and rotate it 180 degrees to get another small triangle. Finally, select two random points inside the final geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.