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SEAT Logo

SEAT Logo
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2019-11-22 00:57
CircleVectorGeometric Construction
This example demonstrates how to draw the SEAT car logo using GeoGebra. Key mathematical concepts include geometry, vectors, and circles. Construction highlights the use of Vector, OrthogonalVector, Midpoint, Line, Mirror, and other commands. Suitable for high school geometry lessons or student practice in geometric construction.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Midpoint(E, B) → D
  4. Line(A, B) → m
  5. Line(F, m) → h
  6. Mirror(h, D) → h'
  7. Line(D, h') → j
  8. OrthogonalLine(D, j) → k
  9. OrthogonalLine(G, m) → i
  10. Intersect(h, i) → P
  11. Line(R, j) → p
  12. Mirror(p, j) → p'
  13. Mirror(Q, j) → Q'
  14. OrthogonalLine(Q', p') → q
  15. Intersect(j, q) → J
  16. Line(U, q) → r
  17. Mirror(r, k) → r'
  18. Intersect(r', p') → W
  19. Line(H_1, p') → f_1
  20. LineBisector(Z', D_1) → t
  21. Intersect(t, f_1) → V_1
  22. Intersect(q, p) → S
  23. Mirror(S, j) → S'
  24. LineBisector(S', N) → l
  25. Intersect(l, f_1) → U_1
  26. Line(E_1, p) → h_1
  27. Line(E, m) → f
  28. OrthogonalLine(B, f) → g
  29. Intersect(g, f) → C
  30. Intersect(i, h') → I
  31. Polygon(E, C, B, A) → q2, e, c, b, a
  32. Intersect(i, p') → K
  33. Intersect(k, h) → M
  34. OrthogonalLine(V, f) → g_1
  35. Mirror(q, k) → q'
  36. Mirror(S', D) → S''
  37. Intersect(q', h') → O
  38. Mirror(N, D) → N'
  39. Intersect(l, p') → H
  40. CircleArc(U_1, N, S') → d
  41. Mirror(d, D) → d'
  42. CurveCartesian(((1 - t)^(3) * N) + (((3 * (1 - t)^(2)) * t) * L) + (((3 * (1 - t)) * t^(2)) * T) + (t^(3) * O), t, 0, 1) → n
  43. Mirror(n, D) → n'
  44. CurveCartesian(((1 - t)^(3) * Z') + (((3 * (1 - t)^(2)) * t) * F_1) + (((3 * (1 - t)) * t^(2)) * G_1) + (t^(3) * Z), t, 0, 1) → s
  45. Mirror(s, D) → s'
  46. Intersect(l, t) → I_1
  47. CircleArc(V_1, Z', D_1) → c_1
  48. Mirror(c_1, D) → d_1
  49. Mirror(A_1, k) → K_1
  50. Mirror(B_1, k) → L_1
  51. Mirror(E_1, k) → O_1
  52. Polygon(E_1, Q_1, S_1, R_1) → t1, q_1, e_1, j_2, n_2
  53. Mirror(Z, D) → Z'_1
  54. Polygon(H_1, P_1, T_1, J_1) → t2, i_1, j_1, p_1, p_2
  55. Polygon(D_1, L_1, J_1, T_1, P_1, H_1, Z, Z') → poly1, k_1, l_1, m_1, n_1, r_1, q_2, r_2, s_2
  56. Polygon(B_1, M_1, K_1, C_1) → q1, b_1, s_1, t_1, a_1
  57. Mirror(Z', D) → Z''
  58. Polygon(Z'_1, E_1, Q_1, S_1, R_1, A_1, N_1, O_1, Z'') → poly2, f_2, g_2, h_2, i_2, k_2, l_2, m_2, b_2, c_2
  59. Polygon(Q, S', N, O, S'', N') → poly3, q_3, t_2, n_3, o_1, s'', a_2
  60. Semicircle(T_1, P_1) → d_2
  61. Semicircle(S_1, Q_1) → e_2

AI Drawing Prompt Reference

Draw the SEAT car logo, which includes various geometric elements such as vectors, lines, midpoints, and arcs. Start by creating vector u from points A and B, then create a vector v orthogonal to u. Find the midpoint D of line segment AB and use these vectors and points to construct multiple lines and mirror lines. Finally, use intersection and mirror operations to form the logo's components, and complete the details with arcs and curves.
The prompt above was compiled from the original drawing commands and is for reference only.