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Geometric Construction of a Logistics Company Logo

Geometric Construction of a Logistics Company Logo
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2019-07-15 04:27
CirclePolygonVectorTransformationGeometric Construction
This example demonstrates how to construct a complex company logo using geometric principles. It involves core mathematical concepts such as angles, circles, polygons, vectors, and transformations. Key GeoGebra commands and objects used in the construction include Rotate, Vector, Line, Translate, Intersect, Angle, Polygon, OrthogonalLine, Circle, LineBisector, CircleArc, CurveCartesian, Segment, Midpoint, and Mirror. Suitable for high school students and educators, this example is ideal for learning geometric constructions and visualizing mathematical concepts.

GeoGebra Commands & Parameters

  1. Rotate(A, 18°, B) → A'
  2. Vector(B, A') → w
  3. OrthogonalVector(w) → u
  4. Line(R, T) → h
  5. Line(B_1, h) → k
  6. Translate(w, u) → w'
  7. Translate(G_1, u) → E
  8. Translate(E, Vector[(0.2 * w')]) → E'
  9. Line(D_1, k) → l
  10. Line(G_1, l) → e
  11. Line(R_3, e) → k_4
  12. Line(S_3, k_4) → p_4
  13. Line(Q_3, e) → l_4
  14. Line(T_3, l_4) → q_4
  15. Line(A', B) → f
  16. Line(E_1, f) → m
  17. Intersect(l, m) → I_1
  18. Translate(I_1, u) → C_2
  19. Translate(C_2, Vector[(0.2 * w')]) → H_3
  20. Line(F_1, m) → b
  21. Intersect(l, b) → P_1
  22. Translate(P_1, u) → F_2
  23. Translate(F_2, Vector[(0.2 * w')]) → K_3
  24. Intersect(k, b) → H_1
  25. Translate(H_1, u) → B_2
  26. Translate(B_2, Vector[(0.2 * w')]) → G_3
  27. Line(G_3, K_3) → m_4
  28. Intersect(l_4, m_4) → H_4
  29. Intersect(p_4, m_4) → U_3
  30. Intersect(q_4, m_4) → V_3
  31. Line(H_3, m_4) → n_4
  32. Intersect(q_4, n_4) → G_4
  33. Intersect(p_4, n_4) → C_4
  34. Line(W_3, n_4) → r_4
  35. Intersect(p_4, r_4) → A_4
  36. Intersect(k_4, r_4) → Z_3
  37. Intersect(n_4, l_4) → B_4
  38. Intersect(e, m) → D
  39. Intersect(e, b) → M_1
  40. Line(M, m) → n
  41. Intersect(l, n) → Q_1
  42. Intersect(e, n) → O_1
  43. Angle(A, B, A') → α
  44. Line(O, S) → g
  45. Polygon(S, U, V, T, R, P, Q, I, H, O) → poly1, s, o_1, u_1, v, t, r, p, q, i, h_1
  46. OrthogonalLine(B, f) → j
  47. Circle(Z, A_1) → d
  48. Intersect(e, m) → J_1
  49. Polygon(G_1, D_1, O_1, B_1, H_1, I_1, D, K_1, N_1, P_1, Q_1) → poly2, f_1, a_1, b_1, g_1, i_1, j_1, k_1, l_1, n_1, p_1, q_1
  50. LineBisector(H_1, I_1) → m_1
  51. LineBisector(D_1, B_1) → r_1
  52. Intersect(m_1, n) → R_1
  53. Intersect(r_1, n) → T_1
  54. CircleArc(T_1, B_1, D_1) → e_1
  55. Intersect(r_1, m_1) → S_1
  56. Vector(R_1, S_1) → v_1
  57. CircleArc(U_1, I_1, H_1) → c_1
  58. CurveCartesian(((1 - t)^(3) * A) + (((3 * (1 - t)^(2)) * t) * V_1) + (((3 * (1 - t)) * t^(2)) * W_1) + (t^(3) * B), t, 0, 1) → a
  59. CurveCartesian(((1 - t)^(3) * A) + (((3 * (1 - t)^(2)) * t) * A_2) + (((3 * (1 - t)) * t^(2)) * Z_1) + (t^(3) * B), t, 0, 1) → c
  60. Polygon(C, O_1, G_1) → t1, s_1, c_2, t_1
  61. Segment(A, B) → d_1
  62. Segment(I_1, N_1) → f_2
  63. Segment(D_1, G_1) → g_2
  64. Translate(A, u) → A'_1
  65. Translate(B, u) → B'
  66. Translate(a, u) → a'
  67. Translate(c, u) → c'
  68. Translate(d, u) → d'
  69. Translate(A, u) → A'_2
  70. Translate(B, u) → B'_1
  71. Segment(A'_2, B'_1) → h_2
  72. Translate(S, u) → S'
  73. Translate(P, u) → P'
  74. Translate(Q, u) → Q'
  75. Translate(O, u) → O'
  76. Translate(D_1, u) → F
  77. Translate(B_1, u) → G
  78. Translate(D, u) → D'
  79. Translate(K_1, u) → D_2
  80. Translate(N_1, u) → E_2
  81. Translate(Q_1, u) → G_2
  82. Translate(O_1, u) → H_2
  83. Translate(C, u) → C'
  84. Translate(O_1, u) → I_2
  85. Translate(H_2, Vector[(0.2599999999999998, -1.0000000000000009)]) → J_2
  86. Translate(C, u) → C'_1
  87. Translate(O_1, u) → K_2
  88. Translate(G_1, u) → L_2
  89. Translate(c_1, u) → c_3
  90. Translate(e_1, u) → d_3
  91. Translate(L, u) → L'
  92. Translate(O', Vector[(0.2 * w)]) → O''
  93. Translate(S', Vector[(0.2 * w)]) → S''
  94. Translate(U', Vector[(0.2 * w)]) → U''
  95. Midpoint(S'', R_2) → S_2
  96. Mirror(T_2, S_2) → U_2
  97. Translate(f, u) → f'
  98. Line(M_2, h) → s_2
  99. Line(U_2, h) → t_2
  100. Line(N_2, f') → a_2
  101. Intersect(a_2, t_2) → Z_2
  102. Line(S'', g) → h_3
  103. Mirror(h_3, S_2) → i_3
  104. Line(B_3, f') → j_3
  105. Intersect(j_3, h_3) → C_3
  106. Intersect(j_3, i_3) → D_3
  107. Intersect(j_3, s_2) → E_3
  108. Intersect(j_3, t_2) → F_3
  109. Polygon(Q_2, S'', R_2, U', C_3, E_3, W_2, V_2, A_3, Z_2, F_3, D_3) → poly3, k_3, n_3, p_3, u', s'', l_3, e_3, w_2, v_2, a_3, z_2, m_3
  110. Translate(F, Vector[(0.2 * w')]) → F'
  111. Translate(G, Vector[(0.2 * w')]) → G'
  112. Translate(D', Vector[(0.2 * w')]) → D''
  113. Translate(D_2, Vector[(0.2 * w')]) → I_3
  114. Translate(E_2, Vector[(0.2 * w')]) → J_3
  115. Translate(G_2, Vector[(0.2 * w')]) → L_3
  116. Translate(H_2, Vector[(0.2 * w')]) → M_3
  117. Polygon(E', F', M_3, G', G_3, H_3, D'', I_3, J_3, K_3, L_3) → poly2'', e', g_4, h_4, q_3, g', r_3, s_3, d'', t_3, b_3, f_4
  118. Translate(C'_1, Vector[(0.2 * w')]) → N_3
  119. Translate(K_2, Vector[(0.2 * w')]) → O_3
  120. Polygon(E_4, D_4, U_3, Z_3, A_4, C_4, G_4, H_4, F_4, T_3, V_3) → poly4, j_2, d_2, g_3, k_2, l_2, m_2, n_2, p_2, q_2, r_2, b_2
  121. Translate(L_2, Vector[(0.2 * w')]) → P_3
  122. Polygon(N_3, O_3, P_3) → t1'', i_4, j_4, o_3
  123. Translate(c_3, Vector[(0.2 * w')]) → c_4
  124. Translate(d_3, Vector[(0.2 * w')]) → d_4
  125. Translate(A, u) → A'_3
  126. Translate(B, u) → B'_2
  127. Segment(A'_3, B'_2) → i_2
  128. LineBisector(G_4, H_4) → e_2
  129. Intersect(e_2, m_4) → I_4
  130. CircleArc(I_4, H_4, G_4) → f_3
  131. Segment(H_4, G_4) → s_4
  132. Segment(C_4, G_4) → t_4
  133. Segment(H_4, F_4) → a_4
  134. Translate(I_1, u) → J_4
  135. Translate(D, u) → D'_1
  136. Segment(J_4, D'_1) → b_4
  137. Translate(J_4, Vector[(0.2 * w)]) → K_4
  138. Translate(D'_1, Vector[(0.2 * w)]) → L_4
  139. Segment(K_4, L_4) → e_4
  140. Segment(D_1, G_1) → f_5
  141. Translate(G_1, u) → N_4
  142. Translate(D_1, u) → O_4
  143. Segment(N_4, O_4) → g_5

AI Drawing Prompt Reference

Draw a geometric construction of a logistics company logo. Start with a circle and a point on it; rotate this point by 18 degrees around the center, then connect the two points to form a chord. Construct a perpendicular line to this chord, and use it as a reference to translate several key points, creating a set of parallel lines. Intersect these lines with auxiliary lines inside the circle to determine vertices of a decagon, which are then connected in order. Inside the decagon, add a vertical line perpendicular to the base, and mirror some parts across it. Finally, refine the logo with arcs and segments to achieve a symmetric, dynamic geometric design.
The prompt above was compiled from the original drawing commands and is for reference only.