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Square Tessellation Design

Square Tessellation Design
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2017-06-18 00:35
PolygonTransformationGeometric Construction
This applet designs a square and fills the plane in three different ways to help students identify the transformations in each. It uses commands like Rotate, Mirror, and Translate, suitable for middle school and above students for geometric construction practice.

GeoGebra Commands & Parameters

  1. Rotate(B, 90°, A) → B'
  2. Rotate(A, 90°, B') → A'
  3. Point(Segment[A, B]) → C
  4. LineBisector(A, B) → f
  5. LineBisector(B, A') → g
  6. Mirror(C, f) → C'
  7. Mirror(C', g) → C''
  8. Mirror(C'', f) → C'''
  9. Intersect(f, g) → D
  10. Rotate(C, 90°, D) → E'''
  11. Mirror(E''', g) → E
  12. Mirror(E, f) → E'
  13. Mirror(E', g) → E''
  14. PointIn(Polygon[A, B, A', B']) → F
  15. PointIn(Polygon[A, B, A', B']) → G
  16. Polygon(C, A, E'', G) → poly1, c, a, e'', g_1
  17. Polygon(C, C', F, D) → poly2, c_1, c', f_1, d
  18. Polygon(C, D, C'', G) → poly3, c_2, d_1, c'', g_2
  19. Polygon(E', G, E'') → poly4, e''_1, e', g_3
  20. Polygon(E', B', C''', G) → poly5, e'_1, b', c''', g_4
  21. Polygon(G, C''', C'') → poly6, c''_1, g_5, c'''_1
  22. Polygon(C'', E, A') → poly7, a', c''_2, e
  23. Polygon(E, E''', F, D, C'') → poly8, e_1, e''', f_2, d_2, c''_3
  24. Polygon(E''', B, C', F) → poly9, e'''_1, b, c'_1, f_3
  25. Vector(A, B) → u
  26. Vector(A, B') → v
  27. Sequence(Sequence[Translate[list2, Vector[(i * u) + (j * v)]], i, (-N), N], j, (-N), N) → list4
  28. Sequence(Sequence[Translate[list1, Vector[(i * u) + (j * v)]], i, (-N), N], j, (-N), N) → list5
  29. Sequence(Sequence[Translate[list3, Vector[(i * u) + (j * v)]], i, (-N), N], j, (-N), N) → list6
  30. Midpoint(A, B) → H
  31. Midpoint(A', B) → I
  32. Rotate(list1, 180°, I) → list1'
  33. Rotate(list1, 180°, H) → list1'_1
  34. Midpoint(A', B) → J
  35. Rotate(H, 90°, B) → H'
  36. Rotate(list1'_1, 180°, H') → list7
  37. Rotate(list2, 180°, I) → list2'
  38. Rotate(list2, 180°, H) → list2'_1
  39. Rotate(list2'_1, 180°, H') → list8
  40. Rotate(list3, 180°, I) → list3'
  41. Rotate(list3, 180°, H) → list3'_1
  42. Rotate(list3'_1, 180°, H') → list9
  43. Sequence(Sequence[Translate[{list2, list2', list2'_1, list8}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list10
  44. Sequence(Sequence[Translate[{list1, list1', list1'_1, list7}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list11
  45. Sequence(Sequence[Translate[{list3, list3', list3'_1, list9}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list12
  46. Translate(Mirror[list1, f], v) → list13
  47. Translate(Mirror[list2, f], v) → list14
  48. Translate(Mirror[list3, f], v) → list15
  49. Translate(Mirror[list1, g], u) → list16
  50. Translate(Mirror[list2, g], u) → list17
  51. Translate(Mirror[list3, g], u) → list18
  52. Translate(Mirror[list16, Translate[f, u]], v) → list19
  53. Translate(Mirror[list17, Translate[f, u]], v) → list20
  54. Translate(Mirror[list18, Translate[f, u]], v) → list21
  55. Sequence(Sequence[Translate[{list3, list18, list15, list21}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list22
  56. Sequence(Sequence[Translate[{list2, list17, list14, list20}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list23
  57. Sequence(Sequence[Translate[{list1, list16, list13, list19}, Vector[((2 * i) * u) + ((2 * j) * v)]], i, (-N), N], j, (-N), N) → list24

AI Drawing Prompt Reference

Draw a square and fill the plane using three different methods: rotation by 90 degrees, reflection, and translation. Start by rotating one side's midpoint by 90 degrees to create a new point, then reflect this point over the perpendicular bisector of the side and translate it to generate multiple squares. Arrange these squares in different sequences to form three distinct tessellation patterns.
The prompt above was compiled from the original drawing commands and is for reference only.