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Translation Tessellation Step 5

Translation Tessellation Step 5
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2014-03-28 10:07
PolygonVectorGeometric Construction
In collections Translation Tesselation
This example demonstrates the construction of a geometric tessellation pattern through translation operations. Key math concepts include translation transformation, polygon construction, and vector operations. GeoGebra commands and objects used in the construction, as outlined in the summary, are Polygon, Segment, Vector, and Translate. Suitable for high school students learning geometric transformations and spatial geometry, this example illustrates the application of translation in tessellations.

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 geometric tessellation pattern using translation operations. Start by creating a quadrilateral and four connected line segments from one vertex. Then, define a vector for translation and repeatedly move the quadrilateral and initial shape in that direction, connecting corresponding vertices to form a continuous tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.