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Create Tessellation Based on Triangle Rotation

Create Tessellation Based on Triangle Rotation
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2014-04-04 05:08
Triangle
In collections Create a Rotation Tessellation using a Triangle
This example demonstrates how to create a tessellation based on triangle rotation. Key mathematical concepts include rotation, geometric transformations, and geometric construction. Using GeoGebra commands such as Polygon, Segment, Rotate, and Midpoint, a series of rotated triangles are constructed to form a beautiful tessellation pattern. Suitable for middle school and above students to learn about geometric transformations and tessellations.

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''