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Drawing the Toyota Aygo Logo in 2D Geometry

Drawing the Toyota Aygo Logo in 2D Geometry
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2019-11-29 03:40
CirclePolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates how to construct the Toyota Aygo logo using 2D geometric shapes and transformations in GeoGebra. Key math concepts include vectors, circles, polygons, geometric transformations (translation, reflection), and coordinate geometry. The construction involves commands and objects such as Line, Vector, OrthogonalLine, OrthogonalVector, Intersect, Midpoint, Mirror, LineBisector, Polygon, Translate, and Segment as detailed in the construction summary. It is suitable for high school students learning analytical geometry, geometric constructions, and transformations, as well as for mathematical education purposes.

GeoGebra Commands & Parameters

  1. Line(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalLine(U_3, m) → f_1
  4. OrthogonalVector(u) → v
  5. Line(H, m) → l
  6. Line(E, m) → f
  7. Intersect(f_1, f) → N
  8. OrthogonalLine(B_1, f) → q
  9. Intersect(q, l) → E_1
  10. Midpoint(E, B) → D
  11. Line(F, m) → h
  12. Mirror(h, D) → h'
  13. Line(D, h') → j
  14. Mirror(l, j) → l'
  15. OrthogonalLine(G, m) → i
  16. Mirror(i, f_1) → i'
  17. Intersect(i, l') → I
  18. Mirror(I, f_1) → I'
  19. Intersect(l, i) → J
  20. Line(P', j) → a
  21. LineBisector(G, U_3) → k
  22. Mirror(k, f_1) → k'
  23. Intersect(k', h) → K_3
  24. Intersect(k, l') → K
  25. Mirror(L, f_1) → L'_1
  26. OrthogonalLine(L'_1, j) → t
  27. Mirror(L, k) → L'
  28. OrthogonalLine(L', j) → p
  29. Intersect(p, l) → D_1
  30. Midpoint(D_1, E_1) → F_1
  31. Line(G_1, l) → m_2
  32. Intersect(t, m_2) → D_2
  33. Intersect(i', m_2) → C_2
  34. LineBisector(C_2, D_2) → n_2
  35. Intersect(n_2, l') → E_2
  36. Intersect(m_2, n_2) → G_2
  37. LineBisector(C_2, I') → q_2
  38. Mirror(L_2, q_2) → M_2
  39. Intersect(i', q_2) → F_2
  40. Midpoint(I', F_2) → H_2
  41. Mirror(H_2, n_2) → I_2
  42. Mirror(I_2, q_2) → J_2
  43. Mirror(J_2, n_2) → K_2
  44. Polygon(E_2, I_2, J_2, G_2, K_2, H_2) → poly3, e_2, r_2, s_2, t_2, b_2, c_2
  45. Line(M_2, e_2) → d_2
  46. Mirror(d_2, n_2) → f_3
  47. Mirror(f_3, q_2) → h_3
  48. OrthogonalLine(N_2, q_2) → i_3
  49. Intersect(i_3, h_3) → P_2
  50. Translate(P_2, Vector[(-0.205 * u)]) → H_3
  51. Line(H_3, k') → i_4
  52. Intersect(i_3, f_3) → O_2
  53. Translate(O_2, Vector[(-0.205 * u)]) → I_3
  54. OrthogonalLine(I_3, i) → b_4
  55. Intersect(k', b_4) → S_3
  56. Midpoint(I, L) → Q
  57. OrthogonalLine(Q, a) → b
  58. Mirror(O, b) → O'
  59. Mirror(S, b) → S'
  60. LineBisector(S', O') → c
  61. Intersect(k', c) → M_3
  62. LineBisector(K_3, M_3) → j_4
  63. Intersect(i_4, j_4) → O_3
  64. Intersect(k', j_4) → P_3
  65. OrthogonalLine(D, m) → p_1
  66. OrthogonalLine(B, f) → g
  67. Intersect(g, f) → C
  68. Segment(A, B) → a_4
  69. Intersect(p_1, l') → M
  70. OrthogonalLine(L, l') → n
  71. Mirror(L', f_1) → L''
  72. OrthogonalLine(L'', j) → s
  73. Intersect(n, a) → R
  74. Mirror(P, b) → P'_1
  75. Polygon(O, P, P', Q, R, P'_1, O', S', T, S) → poly1, o_1, s_1, p_2, p', q_1, r_1, p'_1, o', s', t_1
  76. Intersect(c, o') → U
  77. Line(V, j) → d
  78. OrthogonalLine(W, l) → e
  79. Intersect(e, d) → Z
  80. Intersect(e, c) → A_1
  81. Polygon(U, V, Z, A_1) → q1, u_1, v_1, z_1, a_1
  82. Mirror(B_1, f_1) → C_1
  83. OrthogonalLine(C_1, f) → r
  84. OrthogonalLine(F_1, f) → g_1
  85. Intersect(p, a) → I_1
  86. Intersect(p, d) → K_1
  87. OrthogonalLine(M_1, l) → h_1
  88. Line(N_1, L_1) → i_1
  89. Line(K_1, i_1) → j_1
  90. Line(G_1, j_1) → k_1
  91. Intersect(k_1, h_1) → O_1
  92. Intersect(j_1, h_1) → P_1
  93. Intersect(j, d) → Q_1
  94. Polygon(J_1, L_1, N_1, G_1, O_1, P_1, K_1, I_1) → poly2, l_1, m_1, n_1, b_1, c_1, d_1, e_1, f_2
  95. Mirror(J_1, g_1) → R_1
  96. Mirror(L_1, g_1) → S_1
  97. Mirror(N_1, g_1) → T_1
  98. Mirror(G_1, g_1) → U_1
  99. Mirror(O_1, g_1) → V_1
  100. Mirror(P_1, g_1) → W_1
  101. Mirror(K_1, g_1) → Z_1
  102. Mirror(I_1, g_1) → A_2
  103. Polygon(R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2) → poly2', g_2, h_2, i_2, j_2, k_2, w_1, l_2, a_2
  104. Intersect(k', l) → B_2
  105. Mirror(d_2, q_2) → g_3
  106. Mirror(i_3, n_2) → j_3
  107. Polygon(L_2, P_2, O_2, M_2) → q2, k_3, l_3, o_2, m_3
  108. Mirror(L_2, n_2) → Q_2
  109. Mirror(P_2, n_2) → R_2
  110. Mirror(O_2, n_2) → S_2
  111. Mirror(M_2, n_2) → T_2
  112. Polygon(Q_2, R_2, S_2, T_2) → q2', n_3, p_3, q_3, r_3
  113. Translate(Q_2, Vector[(-0.205 * u)]) → U_2
  114. Translate(R_2, Vector[(-0.205 * u)]) → V_2
  115. Translate(S_2, Vector[(-0.205 * u)]) → W_2
  116. Translate(T_2, Vector[(-0.205 * u)]) → Z_2
  117. Polygon(U_2, V_2, W_2, Z_2) → q2'', u_2, v_2, w_2, z_2
  118. Translate(E_2, Vector[(-0.205 * u)]) → A_3
  119. Translate(I_2, Vector[(-0.205 * u)]) → B_3
  120. Translate(J_2, Vector[(-0.205 * u)]) → C_3
  121. Translate(G_2, Vector[(-0.205 * u)]) → D_3
  122. Translate(K_2, Vector[(-0.205 * u)]) → E_3
  123. Translate(H_2, Vector[(-0.205 * u)]) → F_3
  124. Polygon(A_3, B_3, C_3, D_3, E_3, F_3) → poly3', a_3, b_3, c_3, d_3, e_3, s_3
  125. Translate(L_2, Vector[(-0.205 * u)]) → G_3
  126. Translate(M_2, Vector[(-0.205 * u)]) → J_3
  127. Polygon(G_3, H_3, I_3, J_3) → q2'_1, t_3, f_4, g_4, h_4
  128. Intersect(i_4, h) → L_3
  129. Polygon(Q_3, P_3, S_3, T_3) → q3, k_4, l_4, m_4, s_4
  130. Intersect(i_4, c) → N_3
  131. Polygon(O_3, Q_3, R_3, N_3) → q4, n_4, p_4, q_4, r_4
  132. Intersect(k, f) → V_3
  133. Mirror(V_3, f_1) → W_3

AI Drawing Prompt Reference

Draw a 2D geometric representation resembling the Toyota Aygo logo using circles, polygons, and lines. Start with a base line and create a vector, then draw perpendicular lines. Use midpoints and mirror operations to construct symmetrical shapes, applying reflections and rotations to form the final logo composed of multiple geometric parts.
The prompt above was compiled from the original drawing commands and is for reference only.