MathPlotAI Logo MathPlotAI

Step Five: Creating a Tessellation

Step Five: Creating a Tessellation
Loading the math board and drawing, please wait…
2014-03-29 05:38
PolygonTransformationGeometric Construction
In collections How to create a Tessellation (Rectangle)
This example demonstrates how to create a tessellation using rectangles and transformations. Key math concepts include translation, vectors, and polygon construction. It uses commands like Segment, OrthogonalLine, Point, Intersect, Vector, Translate, Polygon. Suitable for middle school students learning geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(c) → D
  5. OrthogonalLine(D, b) → d
  6. Intersect(b, d) → F
  7. Segment(B, C) → e
  8. Segment(C, D) → f
  9. Vector(B, A) → u
  10. Translate(B, u) → B'
  11. Translate(C, u) → C'
  12. Segment(B', C') → e'
  13. Translate(C, u) → C'_1
  14. Translate(D, u) → D'
  15. Segment(C'_1, D') → f'
  16. Segment(F, E) → g
  17. Segment(E, D) → h
  18. Vector(F, A) → v
  19. Translate(F, v) → F'
  20. Translate(E, v) → E'
  21. Segment(F', E') → g'
  22. Translate(E, v) → E'_1
  23. Translate(D, v) → D'_1
  24. Segment(E'_1, D'_1) → h'
  25. Translate(D', v) → D''
  26. Polygon(A, E', B, C, D, E, F, C') → poly1, a_1, e'_1, b_1, c_1, d_1, e_1, f_1, c'
  27. Segment(I, J) → i
  28. Segment(J, K) → j
  29. Segment(K, L) → k
  30. Segment(L, M) → l
  31. Segment(M, N) → m
  32. Segment(N, O) → n
  33. Segment(I, P) → p
  34. Segment(P, Q) → q
  35. Segment(Q, R) → r
  36. Segment(R, S) → s
  37. Segment(S, O) → t
  38. Polygon(R, Q, S, P, I, J, K, L, M, N, O) → poly2, r_1, o, s_1, q_1, p_1, i_1, j_1, k_1, l_1, m_1, n_1
  39. Vector(A, D') → w
  40. Translate(A, w) → A'
  41. Translate(E', w) → E''
  42. Translate(B, w) → B'_1
  43. Translate(C, w) → C'_2
  44. Translate(D, w) → D'_2
  45. Translate(E, w) → E'_2
  46. Translate(F, w) → F'_1
  47. Translate(C', w) → C''
  48. Polygon(A', E'', B'_1, C'_2, D'_2, E'_2, F'_1, C'') → poly1', a', e'', b'_1, c'_2, d'_2, e'_2, f'_1, c''
  49. Translate(R, w) → R'
  50. Translate(Q, w) → Q'
  51. Translate(P, w) → P'
  52. Translate(I, w) → I'
  53. Translate(J, w) → J'
  54. Translate(K, w) → K'
  55. Translate(L, w) → L'
  56. Translate(M, w) → M'
  57. Translate(N, w) → N'
  58. Translate(O, w) → O'
  59. Translate(S, w) → S'
  60. Polygon(R', Q', S', P', I', J', K', L', M', N', O') → poly2', r', o', s', q', p', i', j', k', l', m', n'
  61. Translate(B, w) → B'_2
  62. Translate(C, w) → C'_3
  63. Segment(B'_2, C'_3) → e'_3
  64. Translate(C, w) → C'_4
  65. Translate(D, w) → D'_3
  66. Segment(C'_4, D'_3) → f'_2
  67. Translate(B', w) → B''
  68. Translate(C', w) → C''_1
  69. Segment(B'', C''_1) → e''_1
  70. Translate(C'_1, w) → T
  71. Translate(D', w) → D''_1
  72. Segment(T, D''_1) → f''
  73. Translate(F, w) → F'_2
  74. Translate(E, w) → E'_3
  75. Segment(F'_2, E'_3) → g'_1
  76. Translate(E, w) → E'_4
  77. Translate(D, w) → D'_4
  78. Segment(E'_4, D'_4) → h'_1
  79. Translate(F', w) → F''
  80. Translate(E', w) → E''_1
  81. Segment(F'', E''_1) → g''
  82. Translate(E'_1, w) → U
  83. Translate(D'_1, w) → V
  84. Segment(U, V) → h''
  85. Translate(G, w) → G'
  86. Translate(H, w) → H'
  87. Vector(A, D''_1) → u_1
  88. Translate(A, u_1) → A'_1
  89. Translate(E', u_1) → E''_2
  90. Translate(B, u_1) → B'_3
  91. Translate(C, u_1) → C'_5
  92. Translate(D, u_1) → D'_5
  93. Translate(E, u_1) → E'_5
  94. Translate(F, u_1) → F'_3
  95. Translate(C', u_1) → C''_2
  96. Polygon(A'_1, E''_2, B'_3, C'_5, D'_5, E'_5, F'_3, C''_2) → poly1'_1, a'_1, e''_2, b'_3, c'_5, d'_5, e'_5, f'_3, c''_2
  97. Translate(R, u_1) → R'_1
  98. Translate(Q, u_1) → Q'_1
  99. Translate(P, u_1) → P'_1
  100. Translate(I, u_1) → I'_1
  101. Translate(J, u_1) → J'_1
  102. Translate(K, u_1) → K'_1
  103. Translate(L, u_1) → L'_1
  104. Translate(M, u_1) → M'_1
  105. Translate(N, u_1) → N'_1
  106. Translate(O, u_1) → O'_1
  107. Translate(S, u_1) → S'_1
  108. Polygon(R'_1, Q'_1, S'_1, P'_1, I'_1, J'_1, K'_1, L'_1, M'_1, N'_1, O'_1) → poly2'_1, r'_1, o'_1, s'_1, q'_1, p'_1, i'_1, j'_1, k'_1, l'_1, m'_1, n'_1
  109. Translate(A', u_1) → A''
  110. Translate(E'', u_1) → E'''
  111. Translate(B'_1, u_1) → W
  112. Translate(C'_2, u_1) → Z
  113. Translate(D'_2, u_1) → A_1
  114. Translate(E'_2, u_1) → B_1
  115. Translate(F'_1, u_1) → C_1
  116. Translate(C'', u_1) → C'''
  117. Polygon(A'', E''', W, Z, A_1, B_1, C_1, C''') → poly1'', a'', e''', w_1, z, a_2, b_2, c_2, c'''
  118. Translate(R', u_1) → R''
  119. Translate(Q', u_1) → Q''
  120. Translate(P', u_1) → P''
  121. Translate(I', u_1) → I''
  122. Translate(J', u_1) → J''
  123. Translate(K', u_1) → K''
  124. Translate(L', u_1) → L''
  125. Translate(M', u_1) → M''
  126. Translate(N', u_1) → N''
  127. Translate(O', u_1) → O''
  128. Translate(S', u_1) → S''
  129. Polygon(R'', Q'', S'', P'', I'', J'', K'', L'', M'', N'', O'') → poly2'', r'', o'', s'', q'', p'', i'', j'', k'', l'', m'', n''
  130. Translate(B, u_1) → B'_4
  131. Translate(C, u_1) → C'_6
  132. Segment(B'_4, C'_6) → e'_4
  133. Translate(C, u_1) → C'_7
  134. Translate(D, u_1) → D'_6
  135. Segment(C'_7, D'_6) → f'_4
  136. Translate(B', u_1) → B''_1
  137. Translate(C', u_1) → C''_3
  138. Segment(B''_1, C''_3) → e''_3
  139. Translate(C'_1, u_1) → D_1
  140. Translate(D', u_1) → D''_2
  141. Segment(D_1, D''_2) → f''_1
  142. Translate(F, u_1) → F'_4
  143. Translate(E, u_1) → E'_6
  144. Segment(F'_4, E'_6) → g'_2
  145. Translate(E, u_1) → E'_7
  146. Translate(D, u_1) → D'_7
  147. Segment(E'_7, D'_7) → h'_2
  148. Translate(F', u_1) → F''_1
  149. Translate(E', u_1) → E''_3
  150. Segment(F''_1, E''_3) → g''_1
  151. Translate(E'_1, u_1) → E_1
  152. Translate(D'_1, u_1) → F_1
  153. Segment(E_1, F_1) → h''_1
  154. Translate(B'_2, u_1) → G_1
  155. Translate(C'_3, u_1) → H_1
  156. Segment(G_1, H_1) → g_1
  157. Translate(C'_4, u_1) → I_1
  158. Translate(D'_3, u_1) → J_1
  159. Segment(I_1, J_1) → h_1
  160. Translate(B'', u_1) → B'''
  161. Translate(C''_1, u_1) → K_1
  162. Segment(B''', K_1) → t_1
  163. Translate(T, u_1) → T'
  164. Translate(D''_1, u_1) → L_1
  165. Segment(T', L_1) → f'''
  166. Translate(F'_2, u_1) → M_1
  167. Translate(E'_3, u_1) → N_1
  168. Segment(M_1, N_1) → d_2
  169. Translate(E'_4, u_1) → O_1
  170. Translate(D'_4, u_1) → P_1
  171. Segment(O_1, P_1) → e_2
  172. Translate(F'', u_1) → F'''
  173. Translate(E''_1, u_1) → Q_1
  174. Segment(F''', Q_1) → g'''
  175. Translate(U, u_1) → U'
  176. Translate(V, u_1) → V'
  177. Segment(U', V') → h'''
  178. Translate(w, u_1) → w'
  179. Translate(G, u_1) → G'_1
  180. Translate(H, u_1) → H'_1
  181. Translate(G', u_1) → G''
  182. Translate(H', u_1) → H''

AI Drawing Prompt Reference

Draw a tessellation composed of rectangles and transformations. Start by creating a line segment and draw perpendicular lines at both ends, marking the intersection points. Connect these points to form a rectangle, then use vector translation to generate multiple identical rectangles. Finally, combine these rectangles to create a complete tessellation, demonstrating the application of geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.