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Translation Tessellation Step 8

Translation Tessellation Step 8
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2014-03-28 10:11
PolygonVectorTransformation
In collections Translation Tesselation
This example demonstrates the 8th step of translation tessellation. It involves translation transformations and polygon construction. Using commands like Polygon, Segment, Vector, and Translate, a translation tessellation can be constructed. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(A, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(J, B) → k
  7. Segment(H, J) → i
  8. Vector(A, D) → u
  9. Translate(A, u) → A'
  10. Translate(E, u) → E'
  11. Segment(A', E') → e'
  12. Translate(E, u) → E'_1
  13. Translate(F, u) → F'
  14. Segment(E'_1, F') → f'
  15. Translate(F, u) → F'_1
  16. Translate(G, u) → G'
  17. Segment(F'_1, G') → g'
  18. Translate(G, u) → G'_1
  19. Translate(H, u) → H'
  20. Segment(G'_1, H') → h'
  21. Translate(J, u) → J'
  22. Translate(B, u) → B'
  23. Segment(J', B') → k'
  24. Translate(H, u) → H'_1
  25. Translate(J, u) → J'_1
  26. Segment(H'_1, J'_1) → i'
  27. Segment(D, I) → j
  28. Segment(I, K) → l
  29. Segment(K, L) → m
  30. Segment(L, M) → n
  31. Segment(M, N) → p
  32. Segment(N, A) → q
  33. Vector(A, B) → v
  34. Translate(A, v) → A'_1
  35. Translate(E, v) → E'_2
  36. Segment(A'_1, E'_2) → e'_1
  37. Translate(A', v) → A''
  38. Translate(E', v) → E''
  39. Segment(A'', E'') → e''
  40. Translate(D, v) → D'
  41. Translate(I, v) → I'
  42. Segment(D', I') → j'
  43. Translate(I, v) → I'_1
  44. Translate(K, v) → K'
  45. Segment(I'_1, K') → l'
  46. Translate(K, v) → K'_1
  47. Translate(L, v) → L'
  48. Segment(K'_1, L') → m'
  49. Translate(L, v) → L'_1
  50. Translate(M, v) → M'
  51. Segment(L'_1, M') → n'
  52. Translate(M, v) → M'_1
  53. Translate(N, v) → N'
  54. Segment(M'_1, N') → p'
  55. Translate(N, v) → N'_1
  56. Translate(A, v) → A'_2
  57. Segment(N'_1, A'_2) → q'

AI Drawing Prompt Reference

Draw a quadrilateral and connect one of its vertices to the opposite vertex with a diagonal. Then, create four segments from this vertex to the other vertices, dividing the quadrilateral into five parts. Next, draw a vector from one vertex to the diagonal endpoint and use this vector to translate the quadrilateral and its divided parts, forming a tessellation pattern. Finally, connect the translated parts with segments to complete the tessellation.
The prompt above was compiled from the original drawing commands and is for reference only.