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Museo de Onda: Azulejo 4

Museo de Onda: Azulejo 4
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2023-03-22 21:40
VectorSolid GeometryGeometric ConstructionGraphing
In collections geometriadinamica.es
This example demonstrates the geometric construction and transformation of a tile pattern in three-dimensional space. It involves core mathematical concepts such as vectors, 3D geometry, function graphs, and geometric transformations. GeoGebra commands like Line, Point, OrthogonalLine, Intersect, Midpoint, Mirror, Rotate, Vector, and Translate are used in the construction process. It is suitable for high school and above students learning about solid geometry, vector operations, and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Line(G, b) → e
  3. Point(e) → J
  4. OrthogonalLine(J, e) → h
  5. OrthogonalLine(G, e) → f
  6. Point(f) → H
  7. OrthogonalLine(H, f) → g
  8. Intersect(g, h) → E
  9. Midpoint(E, H) → I
  10. Midpoint(I, E) → B_1
  11. Midpoint(G, J) → D
  12. Midpoint(J, E) → F
  13. Midpoint(H, G) → K
  14. Midpoint(D, I) → L
  15. Midpoint(K, L) → M
  16. Midpoint(L, F) → N
  17. Midpoint(F, J) → O
  18. Midpoint(J, D) → P
  19. Midpoint(G, D) → Q
  20. Midpoint(K, G) → R
  21. Midpoint(Q, M) → S
  22. Midpoint(L, D) → T
  23. Midpoint(P, N) → U
  24. Midpoint(F, E) → V
  25. Midpoint(K, H) → W
  26. Midpoint(W, V) → Z
  27. Midpoint(H, I) → A_1
  28. Midpoint(N, B_1) → C_1
  29. Midpoint(Z, W) → D_1
  30. Midpoint(D, U) → E_1
  31. Midpoint(U, J) → F_1
  32. Midpoint(T, Q) → G_1
  33. Midpoint(S, G) → H_1
  34. Midpoint(S, K) → I_1
  35. Midpoint(M, T) → J_1
  36. Midpoint(T, N) → K_1
  37. Midpoint(N, O) → L_1
  38. Midpoint(F, C_1) → M_1
  39. Midpoint(C_1, L) → N_1
  40. Midpoint(L, D_1) → O_1
  41. Midpoint(D_1, K) → P_1
  42. Midpoint(H, D_1) → Q_1
  43. Midpoint(D_1, I) → R_1
  44. Midpoint(I, C_1) → S_1
  45. Midpoint(C_1, E) → T_1
  46. Mirror(F_1, h) → U_1
  47. Mirror(L_1, h) → V_1
  48. Mirror(M_1, h) → W_1
  49. Mirror(T_1, h) → Z_1
  50. Mirror(B_1, h) → A_2
  51. Mirror(L_1, h) → C_2
  52. Line(S, A_1) → t
  53. Line(I, T) → a_1
  54. Line(U, B_1) → b_1
  55. Line(E_1, N_1) → c_1
  56. Line(F_1, M_1) → d_1
  57. Line(G_1, R_1) → e_1
  58. Line(W_1, P_1) → g_1
  59. Line(Q_1, Z_1) → h_1
  60. Point(a_1) → F_2
  61. Point(b) → A1
  62. Min(90, ((a - 1) * 90)) → r1
  63. Rotate(F_2, ((-r1))°, T) → K_{11}
  64. Rotate(T, ((-r1))°, T) → T'_7
  65. Rotate(U, ((-r1))°, T) → U'_3
  66. Rotate(T, ((-r1))°, T) → T'_8
  67. Rotate(T, ((-r1))°, T'_8) → T'_9
  68. Rotate(F_2, ((-r1))°, T) → J_{13}
  69. Rotate(L, ((-r1))°, T) → L'_2
  70. Mirror(U'_3, b_1) → A_{14}
  71. Mirror(T'_8, b_1) → B_{14}
  72. Mirror(T'_9, b_1) → O_{15}
  73. Mirror(K_{11}, b_1) → G_{16}
  74. Mirror(T'_7, b_1) → H_{16}
  75. Mirror(J_{13}, b_1) → J_{17}
  76. Mirror(L'_2, b_1) → K_{17}
  77. Midpoint(C_1, E) → K_{20}
  78. Line(G_1, O_1) → l_1
  79. Point(a_1) → C
  80. Min(180, ((a - 1) * 180)) → r2
  81. Min(270, ((a - 1) * 270)) → r3
  82. Rotate(T, r1°, T) → T'_4
  83. Rotate(F_2, r1°, T) → G_2
  84. Rotate(T, r2°, T) → T'_5
  85. Rotate(F_2, r2°, T) → J_2
  86. Rotate(T, r3°, T) → T'_6
  87. Rotate(F_2, r3°, T) → N_2
  88. Rotate(F_2, r1°, T) → Q_2
  89. Rotate(C, r1°, T) → C'
  90. Rotate(F_2, r2°, T) → Z_2
  91. Rotate(C, r2°, T) → C'_1
  92. Rotate(F_2, r3°, T) → H_3
  93. Rotate(C, r3°, T) → C'_2
  94. Rotate(C, r1°, T) → C'_3
  95. Rotate(L, r1°, T) → L'_1
  96. Rotate(K_1, r1°, T) → Q_3
  97. Rotate(C, r2°, T) → C'_4
  98. Rotate(L, r2°, T) → L'_3
  99. Rotate(K_1, r2°, T) → Z_3
  100. Rotate(C, r3°, T) → C'_5
  101. Rotate(L, r3°, T) → L'_4
  102. Rotate(K_1, r3°, T) → H_4
  103. Mirror(C'_4, a_1) → F_5
  104. Mirror(L'_3, a_1) → G_5
  105. Mirror(Z_3, a_1) → J_5
  106. Mirror(Z_2, a_1) → O_5
  107. Mirror(C'_1, a_1) → P_5
  108. Mirror(T'_5, a_1) → W_5
  109. Mirror(J_2, a_1) → Z_5
  110. Mirror(C, a_1) → C'_6
  111. Mirror(L, a_1) → L'_5
  112. Mirror(K_1, a_1) → R_6
  113. Mirror(F_2, a_1) → T_6
  114. Mirror(C, a_1) → C'_7
  115. Mirror(T, a_1) → T'_{10}
  116. Mirror(F_2, a_1) → W_6
  117. Min(180, ((a - 5.5) * 180)) → r4
  118. Line(S, O) → q
  119. Line(F, M) → r
  120. Line(D_1, V) → s
  121. Mirror(pic1, t) → pic1'
  122. Mirror(pic1', a_1) → pic1''
  123. Mirror(pic1'', b_1) → pic1'''
  124. Mirror(pic1''', h) → pic2
  125. Vector(C_1, V) → u_1
  126. Line(E_1, l_1) → f_1
  127. Line(F_1, f_1) → k_1
  128. Vector(V, F) → u
  129. Translate(pic1, u) → pic1'_1
  130. Translate(pic1', u) → pic1''_1
  131. Translate(pic1'', u) → pic1'''_1
  132. Translate(pic1''', u) → pic3
  133. Translate(pic2, u) → pic2'
  134. Translate(pic2', u) → pic2''
  135. Translate(pic3, u) → pic3'
  136. Translate(pic2'', u) → pic2'''
  137. Translate(pic2''', u) → pic4
  138. Translate(pic3', u) → pic3''
  139. Translate(pic3'', u) → pic3'''
  140. Translate(pic1'''_1, u) → pic5
  141. Translate(pic5, u) → pic5'
  142. Translate(pic5', u) → pic5''
  143. Translate(pic1''_1, u) → pic6
  144. Translate(pic6, u) → pic6'
  145. Translate(pic6', u) → pic6''
  146. Translate(pic1'_1, u) → pic7
  147. Translate(pic7, u) → pic7'
  148. Translate(h, u) → h'
  149. Translate(pic7', u) → pic7''
  150. Vector(C_1, N) → w

AI Drawing Prompt Reference

Draw a tile pattern in three-dimensional space, consisting of multiple points and line segments. Use methods of intersection, midpoint, and mirroring to construct a complex geometric shape. Start by defining two lines b and e, then gradually build a series of points and line segments through these operations, ultimately forming a symmetrical 3D pattern.
The prompt above was compiled from the original drawing commands and is for reference only.