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Constructing American Airlines Logo

Constructing American Airlines Logo
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2020-01-01 01:22
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to construct the American Airlines logo using GeoGebra. Key mathematical concepts include vectors, geometric transformations, and coordinate geometry. Commands such as LineBisector, Line, Vector, etc., are used to create the essential elements of the logo. Suitable for high school geometry and coordinate geometry courses.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Line(A, B) → s
  3. OrthogonalLine(A, s) → b
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(F, b) → r
  7. OrthogonalLine(I, b) → h
  8. Intersect(h, m) → S
  9. Midpoint(C, A) → J
  10. OrthogonalLine(N, b) → j
  11. LineBisector(A, C) → d
  12. Mirror(h, d) → h'_1
  13. OrthogonalLine(M, d) → i
  14. Intersect(i, h'_1) → G
  15. Segment(G, S) → k
  16. Intersect(r, k) → S_1
  17. Intersect(k, j) → R
  18. Vector(R, G) → a
  19. Intersect(i, h) → L
  20. Mirror(L, m) → L'_2
  21. Segment(K, L'_2) → l
  22. Intersect(r, l) → G_1
  23. Mirror(h, d) → h'
  24. Intersect(m, d) → E
  25. OrthogonalLine(C, v, xOyPlane) → f
  26. Intersect(f, m) → U
  27. Mirror(i, m) → i'
  28. OrthogonalLine(B, u, xOyPlane) → g
  29. Intersect(g, f) → D
  30. Mirror(M, m) → M'
  31. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  32. Translate(B, Vector[(-2.804024317353038, -0.08247130345155984)]) → B'
  33. OrthogonalLine(Q, b) → n
  34. Intersect(l, j) → T
  35. Vector(T, K) → w
  36. LineBisector(Z, V) → p
  37. LineBisector(B_1, A_1) → q
  38. Intersect(p, k) → C_1
  39. Intersect(q, l) → D_1
  40. Polygon(G, Z, V, T, A_1, B_1) → poly1, g_1, z_1, v_1, t, a_1, b_1
  41. Intersect(n, q) → E_1
  42. Vector(D_1, E_1) → u_1
  43. CircleArc(F_1, B_1, A_1) → e
  44. LineBisector(I_1, J_1) → f_1
  45. Intersect(f_1, r) → K_1
  46. CircleArc(K_1, I_1, J_1) → c_1
  47. Intersect(k, n) → M_1
  48. Intersect(d, l) → N_1
  49. LineBisector(M_1, N_1) → h_1
  50. Intersect(n, h_1) → O_1
  51. CircleArc(O_1, N_1, M_1) → d_1
  52. Polygon(M_1, I_1, J_1, L'_2, N_1) → poly2, m_1, i_1, j_1, l'_2, n_1
  53. CircleArc(C_1, V, Z) → c
  54. CurveCartesian(((1 - t)^(4) * M_1) + (((4 * (1 - t)^(3)) * t) * P_1) + (((6 * (1 - t)^(2)) * t^(2)) * Q_1) + (((4 * (1 - t)) * t^(3)) * H_1) + (t^(4) * L_1), t, 0, 1) → e_1
  55. Line(M_1, L_1) → k_1
  56. Intersect(k_1, l) → R_1
  57. Polygon(R_1, L_1, N_1) → t1, l_1, r_1, p_1
  58. CircleArc(O_1, N_1, M_1) → q_1
  59. Polygon(L'_2, G_1, S_1, I_1, J_1) → poly3, h_2, i_2, j_2, k_2, l_2
  60. Polygon(T, A_1, B_1, D_1) → q1, t_1, s_1, f_2, g_2
  61. Polygon(N_1, R_1, M_1) → t2, m_2, n_2, p_2
  62. OrthogonalLine(T_1, d) → q_2
  63. Mirror(q_2, m) → r_2
  64. OrthogonalLine(U_1, d) → s_2
  65. Mirror(s_2, m) → t_2
  66. LineBisector(T_1, U_1) → a_2
  67. Intersect(a_2, d) → V_1
  68. Intersect(q_2, h) → Z_1
  69. Line(Z_1, W_1) → c_2
  70. Line(A_2, c_2) → e_2
  71. Mirror(c_2, a_2) → f_3
  72. Mirror(e_2, a_2) → g_3
  73. Line(B_2, r) → h_3
  74. Intersect(r, e_2) → C_2
  75. Intersect(e_2, h_3) → F_2
  76. Intersect(e_2, g_3) → G_2
  77. Intersect(a_2, h_3) → H_2
  78. Intersect(a_2, r) → I_2
  79. Polygon(Z_1, A_2, C_2, I_2, H_2, F_2, G_2, V_1, W_1) → poly4, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, w_1
  80. Mirror(Z_1, a_2) → J_2
  81. Mirror(A_2, a_2) → K_2
  82. Mirror(C_2, a_2) → L_2
  83. Mirror(I_2, a_2) → M_2
  84. Mirror(H_2, a_2) → N_2
  85. Mirror(F_2, a_2) → O_2
  86. Mirror(G_2, a_2) → P_2
  87. Mirror(V_1, a_2) → Q_2
  88. Mirror(W_1, a_2) → R_2
  89. Polygon(J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2) → poly4', r_3, s_3, t_3, b_3, d_3, o_2, e_3, f_4, g_4
  90. Intersect(t_2, d) → S_2
  91. Vector(Z_1, S_2) → u_2
  92. Translate(Z_1, u_2) → T_2
  93. Translate(A_2, u_2) → U_2
  94. Translate(C_2, u_2) → V_2
  95. Translate(I_2, u_2) → W_2
  96. Translate(H_2, u_2) → Z_2
  97. Translate(F_2, u_2) → A_3
  98. Translate(G_2, u_2) → B_3
  99. Translate(V_1, u_2) → C_3
  100. Translate(W_1, u_2) → D_3
  101. Polygon(T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3) → poly4'_1, h_4, i_4, v_2, w_2, z_2, j_4, k_4, l_4, m_4
  102. Translate(J_2, u_2) → E_3
  103. Translate(K_2, u_2) → F_3
  104. Translate(L_2, u_2) → H_3
  105. Translate(M_2, u_2) → I_3
  106. Translate(N_2, u_2) → J_3
  107. Translate(O_2, u_2) → K_3
  108. Translate(P_2, u_2) → L_3
  109. Translate(Q_2, u_2) → M_3
  110. Translate(R_2, u_2) → N_3
  111. Polygon(E_3, F_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3) → poly4'', n_4, p_4, q_4, r_4, s_4, t_4, a_4, b_4, c_4

AI Drawing Prompt Reference

Draw the American Airlines logo by first constructing a line segment between points A and B, then creating the perpendicular bisector and perpendicular line of this segment. Use vectors and perpendicular lines to construct other key points and segments, gradually building each part of the logo, and finally complete the overall construction through transformations like mirroring and rotating.
The prompt above was compiled from the original drawing commands and is for reference only.