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21. Mosaico. La Alhambra

21. Mosaico. La Alhambra
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2023-03-20 19:58
PolygonCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric pattern construction of the Alhambra, involving triangles, circles, and polygons. Key mathematical concepts include geometric construction, transformations, and coordinate geometry. Construction involves GeoGebra commands like If, Line, OrthogonalLine, etc. Suitable for middle or high school mathematics courses to learn geometric transformations and graph analysis.

GeoGebra Commands & Parameters

  1. If(paso > 0 ∧ paso < 7, 1, 0) → t_1
  2. If(paso > 1 ∧ paso < 7, 1, 0) → t_2
  3. If(paso > 2 ∧ paso < 7, 1, 0) → t_3
  4. If(paso > 3 ∧ paso < 7, 1, 0) → t_4
  5. If(paso > 4 ∧ paso < 7, 1, 0) → t_5
  6. If(paso > 5 ∧ paso < 7, 1, 0) → t_6
  7. Line(H1, H2) → a
  8. Line(A, a) → b
  9. OrthogonalLine(A, a) → c
  10. Point(b) → B
  11. Dilate(B, pr, A) → Dil
  12. Circle(A, Dil) → d
  13. Intersect(d, c) → D5, C
  14. OrthogonalLine(C, c) → e
  15. OrthogonalLine(B, b) → f
  16. Intersect(f, e) → D
  17. Polygon(A, B, D, C) → P, a_1, b_1, d_1, c_1
  18. OrthogonalLine(B_1, a_1) → g
  19. Line(E, g) → h
  20. Point(h) → F
  21. Point(g) → H
  22. Point(g) → I
  23. Vector(F, H) → u
  24. Vector(F, I) → v
  25. Line(B_2, a_1) → i
  26. Line(M, i) → j
  27. Line(J, i) → k
  28. OrthogonalLine(K, i) → l
  29. OrthogonalLine(L, i) → m
  30. Intersect(l, k) → R1
  31. Intersect(m, k) → R2
  32. Intersect(m, j) → R4
  33. Intersect(l, j) → R3
  34. Intersect(l, i) → R5
  35. Intersect(m, i) → R6
  36. Line(G, i) → n
  37. Line(N, i) → p
  38. Line(O, i) → q
  39. Point(q) → S3
  40. Point(q) → S2
  41. Point(q) → S1
  42. Point(p) → S6
  43. Point(p) → S5
  44. Point(p) → S4
  45. Point(n) → S9
  46. Point(n) → S8
  47. Point(n) → S7
  48. Point(i) → Q
  49. Point(j) → R
  50. Point(k) → S
  51. Point(m) → T
  52. Line(B_3, c_1) → r
  53. Line(T, r) → s
  54. OrthogonalLine(Q, r) → t
  55. OrthogonalLine(R, r) → e_1
  56. OrthogonalLine(S, r) → f_1
  57. OrthogonalLine(B_4, a_1) → g_1
  58. OrthogonalLine(S7, g_1) → h_1
  59. OrthogonalLine(S4, g_1) → i_1
  60. OrthogonalLine(S1, g_1) → j_1
  61. Line(S8, g_1) → k_1
  62. Line(S9, g_1) → l_1
  63. Rotate(g_1, 45°, B_4) → m_1
  64. Intersect(k_1, e_1) → U
  65. Intersect(k_1, f_1) → V
  66. Line(U, m_1) → n_1
  67. Line(V, m_1) → p_1
  68. Intersect(k_1, t) → W
  69. Line(W, m_1) → q_1
  70. OrthogonalLine(W, m_1) → r_1
  71. OrthogonalLine(U, m_1) → s_1
  72. OrthogonalLine(V, m_1) → a_2
  73. Intersect(r, j_1) → Y
  74. OrthogonalLine(Y, m_1) → b_2
  75. OrthogonalLine(B_5, b_1) → c_2
  76. Point(c_2) → Z
  77. Intersect(c_2, s) → C_1
  78. Point(k_1) → D_1
  79. Point(j_1) → E_1
  80. Point(j_1) → F_1
  81. Point(l_1) → G_1
  82. Polygon(C_1, D_1, S2, E_1, R2, F_1, S3, G_1) → P_1, c_3, d_2, s2, e_2, r2, f_2, s3, g_2
  83. Point(c_2) → K_1
  84. OrthogonalLine(B_6, c_1) → h_2
  85. Point(h_2) → M_1
  86. Point(g_1) → H_1
  87. Point(j_1) → J_1
  88. Point(j_1) → L_1
  89. Point(d_2) → N_1
  90. Point(k_1) → O_1
  91. Intersect(h_2, s) → R_1
  92. Point(i_1) → S_1
  93. Point(k_1) → T_1
  94. Point(l_1) → U_1
  95. Point(i_1) → V_1
  96. Polygon(R_1, S_1, S5, T_1, R4, U_1, S6, V_1) → W_1, r_2, s_2, s5, t_7, r4, u_1, s6, v_1
  97. Point(h_2) → Y_1
  98. Point(r) → Z_1
  99. Polygon(Y_1, H_1, S1, J_1, Z_1, L_1, N_1, O_1) → P_2, y_1, h_4, s1_1, j_3, z_1, l_3, n_3, o_2
  100. Point(g_1) → I_1
  101. Point(i_1) → Q_1
  102. Point(i_1) → C_2
  103. Point(s5) → D_2
  104. Point(k_1) → E_2
  105. Polygon(Y_1, I_1, S4, Q_1, R3, C_2, D_2, E_2) → Q_2, y_2, i_2, s4, q_2, r3, c_4, d_3, e_3
  106. Point(h_2) → F_2
  107. Polygon(F_2, I_1, S4, Q_1, R3, C_2, D_2, E_2) → R_2, f_3, i_3, s4_1, q_3, r3_1, c_5, d_4, e_4
  108. Polygon(F_2, H_1, S1, J_1, Z_1, L_1, N_1, O_1) → S_2, f_4, h_3, s1, j_2, z_2, l_2, n_2, o_1

AI Drawing Prompt Reference

Draw a geometric pattern composed of triangles, circles, and polygons. Start by constructing line a through points A and H2, then construct line b through point A and line a, followed by the perpendicular line c to line b and finding point B on line c. Perform a similarity transformation on point B with respect to point A to get point Dil, then construct circle d with radius ADil. Find the intersection points D5 and C of circle d and line c. Construct the perpendicular lines e to point C and f to point B, and find their intersection point D. Use points A, B, D, and C to construct polygon P. Continue by constructing the perpendiculars of polygon P's sides to find new points F, H, and I, and use these points to construct new lines and polygons, ultimately forming a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.