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Logo PAU GASOL Geometric Construction

Logo PAU GASOL Geometric Construction
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2020-06-01 22:47
CirclePolygonVectorTransformationGeometric Construction
This example demonstrates how to construct the PAU GASOL logo using 2D vectors, circles, rectangles, symmetry, and other geometric elements. The core mathematical concepts involved include 2D vector operations, geometric construction of circles and rectangles, symmetry, midpoint calculation, intersection points, and polygon formation. The construction utilizes GeoGebra commands such as Line, OrthogonalLine, Vector, OrthogonalVector, LineBisector, Mirror, Intersect, Midpoint, Polygon, CircleArc, Center, and Segment for precise geometric drawing. It is suitable for high school mathematics students or teachers learning geometric construction, vector applications, and symmetry principles, as well as for mathematical visualization in education.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(F, b) → f
  6. OrthogonalLine(A_1, b) → r
  7. LineBisector(A_1, A) → l
  8. Mirror(f, l) → f'_1
  9. Mirror(f, l) → f'
  10. OrthogonalLine(D, s) → i
  11. Intersect(i, f') → E
  12. LineBisector(A, B) → m
  13. Mirror(i, m) → i'
  14. Intersect(m, f') → S
  15. OrthogonalLine(K_1, f'_1) → n_1
  16. OrthogonalLine(K, r) → h
  17. Intersect(m, l) → L
  18. Midpoint(S, L) → H
  19. OrthogonalLine(H, m) → k
  20. Intersect(h, k) → B_2
  21. OrthogonalLine(C_2, b) → d_2
  22. Intersect(n_1, d_2) → D_2
  23. Intersect(i', k) → H_1
  24. LineBisector(K_1, H_1) → q_1
  25. Intersect(q_1, k) → I_1
  26. LineBisector(E_2, D_2) → j_3
  27. Intersect(j_3, k) → G_2
  28. Intersect(j_3, m) → F_2
  29. Midpoint(G_2, F_2) → H_2
  30. OrthogonalLine(O, k) → j
  31. Intersect(i, l) → P
  32. OrthogonalLine(B, u, xOyPlane) → g
  33. Intersect(g, r) → C
  34. Mirror(F, l) → F'
  35. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  36. OrthogonalLine(J, b) → p
  37. Intersect(i', f') → W
  38. OrthogonalLine(G, b) → t
  39. Intersect(h, t) → F_1
  40. OrthogonalLine(Q, s) → q
  41. Mirror(t, l) → t'
  42. Mirror(q, m) → q'
  43. Intersect(i, f) → R
  44. LineBisector(R, P) → n
  45. Intersect(n, i) → T
  46. Mirror(p, l) → p'
  47. OrthogonalLine(V, b) → a
  48. Intersect(q', t') → B_1
  49. Intersect(j, t') → I
  50. Intersect(q, t) → M
  51. Intersect(n, q) → C_1
  52. Intersect(h, t') → D_1
  53. Polygon(T, C_1, M, E) → q1, t_1, c_1, m_1, e
  54. Intersect(j, f) → U
  55. LineBisector(T, U) → d
  56. Intersect(d, a) → E_1
  57. CircleArc(E_1, T, U) → d_1
  58. Polygon(T, C_1, I, U) → q2, g_1, h_1, i_1, j_1
  59. CircleArc(E_1, C_1, I) → f_1
  60. Intersect(i', f) → G_1
  61. Intersect(q', k) → Z
  62. Polygon(I, B_1, Z, H_1, G_1, U) → poly1, i_2, b_1, z_1, k_1, l_1, u_1
  63. Intersect(t, n_1) → J_1
  64. Polygon(E, K_1, J_1, M) → q3, e_3, c, p_1, m_2
  65. CircleArc(I_1, H_1, K_1) → r_1
  66. CircleArc(I_1, Z, K_1) → s_1
  67. Polygon(H_1, Z, J_1, K_1) → q4, f_2, z_2, g_2, h_2
  68. Intersect(h, p) → N
  69. Intersect(q', p) → L_1
  70. Intersect(p', q') → M_1
  71. Intersect(j, a) → N_1
  72. Intersect(j, p') → P_1
  73. Intersect(j, n) → Q_1
  74. Intersect(n_1, a) → U_1
  75. Intersect(n, n_1) → V_1
  76. Polygon(L_1, N, O_1, R_1, V_1, U_1, T_1, S_1, P_1, M_1) → poly2, j_2, s_2, n_2, o_1, k_2, v_1, l_2, p_2, q_2, r_2
  77. LineBisector(O_1, R_1) → t_2
  78. Intersect(m, t_2) → W_1
  79. Intersect(t_2, n) → Z_1
  80. Midpoint(Z_1, W_1) → A_2
  81. CircleArc(A_2, O_1, R_1) → c_2
  82. Polygon(E_2, B_2, C_2, D_2) → q5, f_3, g_3, h_3, i_3
  83. CircleArc(H_2, D_2, E_2) → d_3
  84. Center(d_3) → I_2
  85. Center(d_3) → J_2
  86. Intersect(q, n) → K_2
  87. Segment(K_2, I) → k_3

AI Drawing Prompt Reference

Draw the PAU GASOL logo using 2D vectors, circles, rectangles, and symmetry. Start by drawing line segments AB and FA, then construct vector u and its orthogonal vector v. Draw orthogonal lines b and f, and use mirroring and intersections to form the key parts of the logo, ultimately creating the outline of the logo.
The prompt above was compiled from the original drawing commands and is for reference only.