MathPlotAI Logo MathPlotAI

Rotate a Triangle to Create Tessellations by mallorina1 (2)

Rotate a Triangle to Create Tessellations by mallorina1 (2)
Loading the math board and drawing, please wait…
2014-04-04 05:10
TrianglePolygonTransformationGeometric Construction
In collections Create a Rotation Tessellation using a Triangle
This example demonstrates how to rotate a triangle to create a tessellation pattern. It involves core mathematical concepts such as rotation, polygon construction, and geometric transformations. Key GeoGebra commands used include Polygon, Segment, Rotate, Midpoint, and PointIn to construct the triangle and perform rotations. Suitable for middle school and above students learning geometric transformations and tessellation principles, it can be used for math education and geometric construction practice.

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
  47. Rotate(F, -60*°, B) → F'_2
  48. Rotate(E, -60*°, B) → E'_2
  49. Rotate(D, -60*°, B) → D'_2
  50. Rotate(A, -60*°, B) → A'_2
  51. Rotate(J', -60*°, B) → J''
  52. Rotate(K', -60*°, B) → K''
  53. Rotate(I, -60*°, B) → I'_1
  54. Rotate(K, -60*°, B) → K'_2
  55. Rotate(J, -60*°, B) → J'_2
  56. Rotate(C, -60*°, B) → C'_1
  57. Rotate(D', -60*°, B) → D''
  58. Rotate(E', -60*°, B) → E''
  59. Rotate(F', -60*°, B) → F''
  60. Rotate(G', -60*°, B) → G''
  61. Rotate(H', -60*°, B) → H''
  62. Rotate(B, -60*°, B) → B'_2
  63. Rotate(H, -60*°, B) → H'_2
  64. Rotate(G, -60*°, B) → G'_2
  65. Polygon(F'_2, E'_2, D'', E'', F'', G'', H'', B'_2, H'_2, G'_2, D'_2, A'_2, J'', K'', I'_1, K'_2, J'_2, C'_1) → poly2', f'_2, c'_1, d'', e'', f'', g'', h'', b'_2, h'_2, g'_2, e'_2, d'_2, a'_2, j'', k'', i'_1, k'_2, j'_2
  66. Rotate(A, -60*°, B) → A'_3
  67. Rotate(D, -60*°, B) → D'_3
  68. Segment(A'_3, D'_3) → d'_3
  69. Rotate(D, -60*°, B) → D'_4
  70. Rotate(E, -60*°, B) → E'_3
  71. Segment(D'_4, E'_3) → e'_3
  72. Rotate(E, -60*°, B) → E'_4
  73. Rotate(F, -60*°, B) → F'_3
  74. Segment(E'_4, F'_3) → f'_3
  75. Rotate(F, -60*°, B) → F'_4
  76. Rotate(G, -60*°, B) → G'_3
  77. Segment(F'_4, G'_3) → g'_3
  78. Rotate(G, -60*°, B) → G'_4
  79. Rotate(H, -60*°, B) → H'_3
  80. Segment(G'_4, H'_3) → h'_3
  81. Rotate(H, -60*°, B) → H'_4
  82. Rotate(B, -60*°, B) → B'_3
  83. Segment(H'_4, B'_3) → i'_2
  84. Rotate(A'_1, -60*°, B) → O
  85. Rotate(D', -60*°, B) → D''_1
  86. Segment(O, D''_1) → d''_1
  87. Rotate(D'_1, -60*°, B) → P
  88. Rotate(E', -60*°, B) → E''_1
  89. Segment(P, E''_1) → e''_1
  90. Rotate(E'_1, -60*°, B) → Q
  91. Rotate(F', -60*°, B) → F''_1
  92. Segment(Q, F''_1) → f''_1
  93. Rotate(F'_1, -60*°, B) → R
  94. Rotate(G', -60*°, B) → G''_1
  95. Segment(R, G''_1) → g''_1
  96. Rotate(G'_1, -60*°, B) → S
  97. Rotate(H', -60*°, B) → H''_1
  98. Segment(S, H''_1) → h''_1
  99. Rotate(H'_1, -60*°, B) → T
  100. Rotate(B'_1, -60*°, B) → U
  101. Segment(T, U) → i''
  102. Rotate(C, -60*°, B) → C'_2
  103. Rotate(J, -60*°, B) → J'_3
  104. Segment(C'_2, J'_3) → j'_3
  105. Rotate(J, -60*°, B) → J'_4
  106. Rotate(K, -60*°, B) → K'_3
  107. Segment(J'_4, K'_3) → k'_3
  108. Rotate(K, -60*°, B) → K'_4
  109. Rotate(I, -60*°, B) → I'_2
  110. Segment(K'_4, I'_2) → l'_1
  111. Rotate(C', -60*°, B) → C''
  112. Rotate(J', -60*°, B) → J''_1
  113. Segment(C'', J''_1) → j''_1
  114. Rotate(J'_1, -60*°, B) → V
  115. Rotate(K', -60*°, B) → K''_1
  116. Segment(V, K''_1) → k''_1
  117. Rotate(K'_1, -60*°, B) → W
  118. Rotate(I', -60*°, B) → I''
  119. Segment(W, I'') → l''
  120. Rotate(A', -60*°, B) → A''_1
  121. Rotate(B', -60*°, B) → B''
  122. Rotate(L, -60*°, B) → L'
  123. Rotate(A'', -60*°, B) → A'''
  124. Rotate(M, -60*°, B) → M'
  125. Rotate(N, -60*°, B) → N'

AI Drawing Prompt Reference

Draw a triangle and then rotate it 60 degrees around one of its vertices, repeating this process multiple times to create a repeating hexagonal pattern. Start by drawing a triangle, then rotate its vertices to generate new triangles, and continue this process until a complete hexagonal pattern is formed.
The prompt above was compiled from the original drawing commands and is for reference only.