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Geometric Construction of the Leclerc Logo

Geometric Construction of the Leclerc Logo
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2019-12-19 05:40
PolygonVector
This example demonstrates how to construct the Leclerc brand logo using GeoGebra. The core mathematical concepts involved include vectors, geometric transformations, and polygons. By using commands such as Line, OrthogonalLine, LineBisector, Vector, OrthogonalVector, Intersect, Mirror, Midpoint, and Polygon, the geometric shape of the Leclerc logo can be constructed. Suitable for high school mathematics education and learning geometric construction.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. LineBisector(A, B) → m
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(I, b) → h
  7. Intersect(h, m) → S
  8. OrthogonalLine(Q_1, s) → p_1
  9. OrthogonalLine(P_1, b) → n_1
  10. OrthogonalLine(C_1, b) → f_1
  11. LineBisector(A, C) → d
  12. Mirror(h, d) → h'
  13. Intersect(m, h') → N
  14. Intersect(m, d) → E
  15. OrthogonalLine(C, v, xOyPlane) → f
  16. Intersect(f, m) → U
  17. Midpoint(C, A) → J
  18. OrthogonalLine(M, d) → i
  19. Mirror(i, m) → i'
  20. OrthogonalLine(B, u, xOyPlane) → g
  21. Intersect(g, f) → D
  22. Mirror(M, m) → M'
  23. Midpoint(E, M') → L
  24. Intersect(g, h') → A_1
  25. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  26. Circle(E, N) → c
  27. Circle(E, O) → k
  28. OrthogonalLine(F, b) → j
  29. OrthogonalLine(K, b) → l
  30. OrthogonalLine(P, b) → p
  31. OrthogonalLine(G, b) → n
  32. OrthogonalLine(Q, b) → q
  33. OrthogonalLine(R, b) → r
  34. OrthogonalLine(T, b) → t
  35. OrthogonalLine(V, s) → a
  36. OrthogonalLine(V, a) → e
  37. OrthogonalLine(W, s) → g_1
  38. OrthogonalLine(Z, s) → h_1
  39. OrthogonalLine(B_1, s) → i_1
  40. OrthogonalLine(E_1, s) → j_1
  41. OrthogonalLine(F_1, s) → k_1
  42. OrthogonalLine(G_1, s) → l_1
  43. OrthogonalLine(H_1, s) → m_1
  44. Intersect(a, t) → I_1
  45. Intersect(m, t) → J_1
  46. Intersect(p_1, j) → L_1
  47. Midpoint(I_1, J_1) → M_1
  48. Intersect(p_1, n_1) → K_1
  49. Midpoint(K_1, L_1) → N_1
  50. Circle(M_1, O_1, N_1) → c_1
  51. Intersect(a, r) → R_1
  52. Intersect(a, q) → S_1
  53. Intersect(g_1, n) → T_1
  54. Intersect(a, j) → U_1
  55. Intersect(a, l) → V_1
  56. Intersect(g_1, p) → W_1
  57. Intersect(j, m_1) → Z_1
  58. Intersect(m_1, f_1) → B_2
  59. Intersect(f_1, l_1) → C_2
  60. Intersect(j_1, l) → G_2
  61. Intersect(h_1, l) → H_2
  62. Intersect(h_1, n) → I_2
  63. Intersect(i_1, q) → J_2
  64. Intersect(r, i_1) → K_2
  65. Polygon(R_1, K_2, V_1, W_1, T_1, S_1, J_2, I_2, H_2, G_2, C_2, B_2, Z_1, U_1) → poly1, r_1, u_1, v_1, w_1, t_1, s_1, k_2, j_2, i_2, h_2, g_2, c_2, q_1, z_1
  66. LineBisector(G_2, C_2) → a_1
  67. Intersect(a_1, n_1) → L_2
  68. CircleArc(L_2, G_2, C_2) → d_1
  69. Intersect(m, n) → M_2
  70. OrthogonalLine(N_2, b) → b_1
  71. Intersect(b_1, i_1) → O_2
  72. Intersect(i_1, p) → P_2
  73. Intersect(j_1, p) → Q_2
  74. Intersect(k_1, n_1) → R_2
  75. Polygon(I_1, J_1, B_2, C_2, G_2, H_2, I_2, J_2, K_2, R_1, M_2, O_2, P_2, Q_2, R_2, K_1, L_1, Z_1) → poly2, e_1, s_2, t_2, a_2, e_2, f_3, g_3, h_3, i_3, j_3, f_2, m_2, o_2, p_2, q_2, r_2, l_2, n_2
  76. LineBisector(Q_2, R_2) → k_3
  77. Intersect(k_3, m) → S_2
  78. Vector(Q_2, R_2) → w
  79. OrthogonalVector(w) → u_2
  80. CircleArc(T_2, Q_2, R_2) → d_3
  81. Intersect(c_1, d) → U_2, V_2
  82. Midpoint(V_2, O_1) → W_2
  83. Mirror(M_1, d) → Z_2
  84. CircleArc(W_2, M_1, Z_2) → e_3

AI Drawing Prompt Reference

Draw the Leclerc brand logo by first drawing a line through points A and B, then drawing a perpendicular line to this line through point A, followed by the perpendicular bisector of line segment AB. Next, draw the vector from A to B and its perpendicular line, find the intersection of this perpendicular line and the bisector to get point S. Continue by drawing a perpendicular line through point C to line AB, a perpendicular line through point Q to line AB, a perpendicular line to vector u through point C, a perpendicular line to the bisector m through point M, a perpendicular line to vector u through point B, a perpendicular line to the bisector m through point M, find the midpoint L between points E and M', and find point A1 as the intersection of line G and h'. Finally, draw a quadrilateral through points A, B, D, and C.
The prompt above was compiled from the original drawing commands and is for reference only.