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FedEx Logo Geometric Construction

FedEx Logo Geometric Construction
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2019-06-26 04:55
CircleVectorGeometric Construction
This example demonstrates how to construct the FedEx Logo geometrically using GeoGebra. It involves core mathematical concepts such as vectors, midpoints, angles, triangles, circles, and polygons. Key construction steps include using commands like Vector, OrthogonalVector, Midpoint, LineBisector, Line, OrthogonalLine, Intersect, Mirror, Circle, Polygon, Semicircle, CircleArc, Segment, and CurveCartesian. Suitable for high school students and geometry enthusiasts for learning and exploration.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Midpoint(C, A) → S
  4. Midpoint(G, F) → J
  5. LineBisector(I, K) → l
  6. Line(A, B) → f
  7. OrthogonalLine(F, f) → i
  8. OrthogonalLine(J, f) → k
  9. OrthogonalLine(B, f) → h
  10. OrthogonalLine(S, h) → j
  11. Intersect(j, k) → V
  12. Line(H_1, f) → p
  13. Mirror(L, p) → L'
  14. Intersect(i, p) → F_2
  15. Mirror(I, j) → I'
  16. OrthogonalLine(I', l) → n
  17. OrthogonalLine(A_2, n) → g_1
  18. Intersect(p, g_1) → E_2
  19. Midpoint(U, V) → W
  20. Circle(E_1, W, K) → c
  21. Intersect(c, p) → I_1, J_1
  22. OrthogonalLine(A_1, l) → m
  23. Intersect(m, l) → C_1
  24. OrthogonalLine(A, f) → g
  25. Mirror(H, j) → H'
  26. Intersect(l, n) → D_1
  27. Polygon(H', H, I, U, W, B_1, Z, A_1, C_1, D_1) → poly1, h', d_1, h_1, i_1, u_1, w, b_1, z_1, a_1, c_1
  28. Mirror(F_1, k) → G_1
  29. OrthogonalLine(F_1, p) → q
  30. Mirror(K_1, k) → O_1
  31. Semicircle(K_1, O_1) → e
  32. Line(M_1, f) → r
  33. Intersect(c, r) → L_1, N_1
  34. Intersect(e, r) → P_1, Q_1
  35. Polygon(J_1, K_1, Q_1, N_1) → q1, j_1, k_1, q_1, n_1
  36. Mirror(R_1, k) → S_1
  37. Mirror(U_1, k) → V_1
  38. CircleArc(T_1, V_1, U_1) → d
  39. Segment(U_1, V_1) → t
  40. Segment(I_1, J_1) → a
  41. Line(Z, f) → b
  42. Intersect(b, i) → W_1
  43. CurveCartesian(((1 - t)^(3) * A_2) + (((3 * (1 - t)^(2)) * t) * A_4) + (((3 * (1 - t)) * t^(2)) * B_4) + (t^(3) * J_1), t, 0, 1) → e_1
  44. Mirror(e_1, p) → f_1
  45. Mirror(A_2, p) → D_2
  46. CurveCartesian(((1 - t)^(3) * F_2) + (((3 * (1 - t)^(2)) * t) * B_2) + (((3 * (1 - t)) * t^(2)) * C_2) + (t^(3) * E_2), t, 0, 1) → l_1
  47. Mirror(l_1, p) → m_1
  48. Mirror(M, j) → M'
  49. Mirror(N, j) → N'
  50. Polygon(M', N', N, M) → q2, m', n', n_2, m_2
  51. Polygon(J_1, L, F_2) → t1, f_2, p_1, l_2
  52. Mirror(J_1, p) → I_2
  53. Mirror(F_2, p) → J_2
  54. Polygon(I_2, L', J_2) → t1', j_2, i_2, l'
  55. LineBisector(K_2, E_2) → r_1
  56. Intersect(r_1, i) → L_2
  57. Intersect(r_1, p) → M_2
  58. Polygon(E_2, A_2, K_2) → t2, k_2, e_2, a_2
  59. Mirror(A_2, p) → N_2
  60. Mirror(K_2, p) → O_2
  61. Segment(N_2, O_2) → t_1
  62. Mirror(E_2, p) → P_2
  63. Mirror(A_2, p) → Q_2
  64. Segment(P_2, Q_2) → g_2
  65. Mirror(E_2, p) → R_2
  66. Mirror(A_2, p) → S_2
  67. Segment(R_2, S_2) → h_2
  68. Mirror(E_2, p) → T_2
  69. Mirror(A_2, p) → U_2
  70. Mirror(K_2, p) → V_2
  71. Polygon(T_2, U_2, V_2) → t2', v_2, t_2, u_2
  72. OrthogonalLine(P, f) → p_2
  73. Polygon(E_2, A_2, L') → t3, s, s_1, q_2
  74. Mirror(l_1, p) → v_1
  75. Mirror(E_2, p) → W_2
  76. Mirror(A_2, p) → Z_2
  77. Mirror(L', p) → L''
  78. Polygon(W_2, Z_2, L'') → t3', l'', w_2, z_2
  79. Mirror(l_6, p) → o_1
  80. Line(A_3, p_2) → r_2
  81. Intersect(p_2, n) → B_3
  82. Intersect(p_2, m) → C_3
  83. Intersect(r_2, m) → D_3
  84. Mirror(m, j) → m'_1
  85. Intersect(m'_1, p_2) → I_3
  86. Intersect(r_2, m'_1) → J_3
  87. Intersect(r_1, p_2) → G_3
  88. Intersect(r_2, r_1) → H_3
  89. Polygon(N', B_3, P, N, C_3, D_3, F_3, E_3, G_3, H_3, J_3, I_3) → poly2, s_2, i_3, p_3, n_3, b_3, c_3, d_3, f_3, e_3, g_3, h_3, j_3
  90. OrthogonalLine(O, f) → b_2
  91. LineBisector(H_3, J_3) → c_2
  92. Line(M_3, Q) → d_2
  93. Line(K, A_3) → k_3
  94. LineBisector(Q, R) → l_3
  95. Intersect(d_2, c_2) → O_3
  96. Polygon(N_3, O_3, P, Q, P_3, Q_3, M_3) → poly3, m_3, o_3, p_4, q_3, r_3, s_3, t_3
  97. Mirror(N_3, l_3) → R_3
  98. Mirror(O_3, l_3) → S_3
  99. Mirror(P, l_3) → P'
  100. Mirror(Q, l_3) → Q'
  101. Mirror(P_3, l_3) → T_3
  102. Mirror(Q_3, l_3) → U_3
  103. Mirror(M_3, l_3) → V_3
  104. Polygon(R_3, S_3, P', Q', T_3, U_3, V_3) → poly3', a_3, f_4, p', q', g_4, u_3, v_3
  105. Intersect(i, m'_1) → G_2
  106. Intersect(m'_1, o_1) → H_2, W_3, Z_3
  107. Polygon(G_2, H_2, J_2) → t4, h_4, i_4, j_4
  108. Mirror(J_2, c_2) → E_4
  109. Polygon(C_4, D_4, E_4) → t5, e_4, c_4, d_4
  110. CircleArc(H_1, M_1, I_2) → k_4