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3.4.1(b) Museo de Onda: Azulejo 1

3.4.1(b) Museo de Onda: Azulejo 1
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2023-03-22 21:29
Coordinate GeometryTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to use GeoGebra to draw 3.4.1(b) Museo de Onda Azulejo 1. The core mathematical concepts involved include linear equations, symmetries, and rational numbers. By using commands such as Line, Point, OrthogonalLine, Intersect, Midpoint, Mirror, Min, Vector, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

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(D_1, I) → R_1
  43. Midpoint(I, C_1) → S_1
  44. Midpoint(C_1, E) → T_1
  45. Mirror(F_1, h) → U_1
  46. Mirror(L_1, h) → V_1
  47. Mirror(M_1, h) → W_1
  48. Mirror(T_1, h) → Z_1
  49. Mirror(B_1, h) → A_2
  50. Line(Q, A_2) → d
  51. Line(F, d) → i
  52. Line(C_1, d) → k
  53. Line(S_1, k) → l
  54. Line(R_1, L_1) → j
  55. Line(D_1, j) → m
  56. Line(M, j) → n
  57. Line(I, j) → p
  58. Line(S, A_1) → t
  59. Line(I, T) → a_1
  60. Line(U, B_1) → b_1
  61. Line(E_1, N_1) → c_1
  62. Line(F_1, M_1) → d_1
  63. Line(G_1, R_1) → e_1
  64. Line(W_1, P_1) → g_1
  65. Point(a_1) → F_2
  66. Mirror(F_2, m) → L_2
  67. Mirror(F_2, m) → M_2
  68. Point(b) → A1
  69. Min(90, ((a - 1) * 90)) → r1
  70. Line(G_1, O_1) → l_1
  71. OrthogonalLine(G_1, l_1) → m_1
  72. OrthogonalLine(J_1, l_1) → q_1
  73. OrthogonalLine(O_1, l_1) → r_1
  74. OrthogonalLine(R_1, l_1) → s_1
  75. OrthogonalLine(E_1, m_1) → t_1
  76. OrthogonalLine(F_1, m_1) → a_2
  77. Point(a_1) → C
  78. OrthogonalLine(F_2, d) → i_1
  79. OrthogonalLine(C, d) → j_1
  80. Min(180, ((a - 1) * 180)) → r2
  81. Min(270, ((a - 1) * 270)) → r3
  82. Min(180, ((a - 5.5) * 180)) → r4
  83. Midpoint(H_1, G_1) → B_2
  84. Midpoint(G_1, E_1) → C_2
  85. Midpoint(E_1, F_1) → D_2
  86. Midpoint(F_1, U_1) → E_2
  87. Midpoint(O, U) → G_2
  88. Midpoint(U, T) → H_2
  89. Midpoint(T, S) → I_2
  90. Midpoint(S, R) → J_2
  91. Midpoint(I_1, J_1) → K_2
  92. Midpoint(J_1, K_1) → N_2
  93. Midpoint(K_1, L_1) → O_2
  94. Midpoint(L_1, V_1) → P_2
  95. Midpoint(F, N) → Q_2
  96. Midpoint(N, L) → R_2
  97. Midpoint(L, M) → S_2
  98. Midpoint(M, K) → T_2
  99. Midpoint(P_1, O_1) → U_2
  100. Midpoint(O_1, N_1) → V_2
  101. Midpoint(N_1, M_1) → W_2
  102. Midpoint(M_1, W_1) → Z_2
  103. Midpoint(V, C_1) → A_3
  104. Midpoint(C_1, Z) → B_3
  105. Midpoint(Z, D_1) → C_3
  106. Midpoint(D_1, W) → D_3
  107. Mirror(pic1, D_3) → pic1'
  108. Mirror(pic1', T_2) → pic1''
  109. Mirror(pic1'', J_2) → pic1'''
  110. Mirror(J_2, H_1) → E_3
  111. Mirror(U_2, D_1) → F_3
  112. Mirror(V_2, Z) → G_3
  113. Mirror(W_2, C_1) → H_3
  114. Mirror(Z_2, V) → I_3
  115. Mirror(pic1''', E_3) → pic2
  116. Mirror(pic1, F_3) → pic1'_1
  117. Mirror(pic1'_1, G_3) → pic3
  118. Mirror(pic3, H_3) → pic3'
  119. Mirror(pic3', I_3) → pic3''
  120. Mirror(pic1'_1, C_3) → pic4
  121. Mirror(pic4, S_2) → pic4'
  122. Mirror(pic4', I_2) → pic4''
  123. Mirror(pic4'', C_2) → pic4'''
  124. Mirror(pic4', N_2) → pic4''_1
  125. Mirror(pic4, V_2) → pic4'_1
  126. Mirror(pic4'_1, W_2) → pic5
  127. Mirror(pic5, Z_2) → pic5'
  128. Mirror(pic4''_1, O_2) → pic6
  129. Mirror(pic6, P_2) → pic6'
  130. Mirror(pic4''', D_2) → pic7
  131. Mirror(pic7, E_2) → pic7'
  132. Mirror(B_2, Q) → J_3
  133. Mirror(pic2, J_3) → pic2'
  134. Mirror(H_2, E_1) → K_3
  135. Mirror(G_2, F_1) → L_3
  136. Mirror(L_3, J) → M_3
  137. Mirror(pic7', M_3) → pic7''
  138. Mirror(pic7, L_3) → pic7'_1
  139. Mirror(pic4''', K_3) → pic8
  140. Midpoint(E_3, K_3) → Q_1
  141. Vector(K_2, V_2) → u
  142. Vector(K_2, C_2) → w

AI Drawing Prompt Reference

Draw a geometric pattern starting with a line segment, then create points on it and construct two perpendicular lines. Find the intersections of these lines and calculate multiple midpoints. Connect these midpoints to form new segments, and use symmetry operations like mirroring to create a complex geometric design. The final image should display a symmetrical structure made of lines and midpoints, illustrating mathematical concepts such as linear equations, symmetry, and rational numbers.
The prompt above was compiled from the original drawing commands and is for reference only.