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Logo of Rioja Innovation System

Logo of Rioja Innovation System
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2020-01-22 00:53
PolygonVectorTransformation
This GeoGebra example demonstrates the geometric construction of the Rioja Innovation System logo. Key mathematical concepts include vectors, similarity transformations, and polygons. Using commands like LineBisector, Vector, and Polygon, the various parts of the logo can be constructed. Suitable for high school geometry lessons to help students understand geometric construction and transformations.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. Midpoint(A_1, A) → J
  5. OrthogonalLine(J, m) → i
  6. OrthogonalLine(K, i) → l
  7. OrthogonalLine(F, l) → n
  8. Intersect(m, n) → H
  9. Line(A, B) → s
  10. OrthogonalLine(A, s) → b
  11. OrthogonalLine(G, l) → p
  12. Intersect(l, n) → Q
  13. Line(D, b) → f
  14. Intersect(f, i) → H_1
  15. OrthogonalLine(B, u, xOyPlane) → g
  16. Mirror(J, m) → J'
  17. OrthogonalLine(R, s) → j_4
  18. OrthogonalLine(L, i) → t
  19. OrthogonalLine(A_1, b) → r
  20. Intersect(g, r) → C
  21. Polygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2
  22. Intersect(j_4, i) → P
  23. Midpoint(P, R) → S
  24. Mirror(H_1, i) → Z_1
  25. OrthogonalLine(V_1, s) → h
  26. OrthogonalLine(E, i) → j
  27. OrthogonalLine(I, i) → k
  28. OrthogonalLine(N, i) → q
  29. OrthogonalLine(O, n) → a
  30. OrthogonalLine(T, s) → d
  31. OrthogonalLine(M, n) → e
  32. OrthogonalLine(U, i) → f_1
  33. OrthogonalLine(V, i) → g_1
  34. OrthogonalLine(W, n) → h_1
  35. Intersect(e, r) → Z
  36. Intersect(f_1, r) → B_1
  37. Polygon(Z, B_1, 4) → poly1, i_1, j_1, k_1, l_1, C_1, D_1
  38. Mirror(poly1, r) → poly1'
  39. Line(E_1, r) → m_1
  40. Line(F_1, r) → n_1
  41. Line(G_1, r) → p_1
  42. Line(I_1, r) → q_1
  43. Line(J_1, r) → r_1
  44. Line(K_1, r) → s_1
  45. Line(K_1, m_1) → t_1
  46. Line(K_1, m_1) → c_1
  47. OrthogonalLine(L_1, i) → d_1
  48. Intersect(l, s_1) → M_1
  49. Intersect(j_4, s_1) → N_1
  50. Polygon(M_1, N_1, R, Q) → q2, e_1, f_2, r_2, q_2
  51. Intersect(t, r_1) → O_1
  52. Intersect(f, r_1) → P_1
  53. Polygon(O_1, P_1, D, L) → q3, o_1, g_2, d_2, l_2
  54. Intersect(h, q_1) → Q_1
  55. Intersect(j, q_1) → R_1
  56. Polygon(Q_1, R_1, E, V_1) → q4, h_2, i_2, j_2, k_2
  57. Intersect(k, p_1) → S_1
  58. Intersect(q, p_1) → T_1
  59. Polygon(S_1, T_1, N, I) → q5, m_2, n_2, p_2, s_2
  60. Intersect(a, n_1) → U_1
  61. Intersect(d, n_1) → W_1
  62. Polygon(U_1, W_1, T, O) → q6, t_2, b_2, c_2, e_2
  63. Intersect(e, m_1) → A_2
  64. Intersect(m_1, f_1) → B_2
  65. Intersect(g_1, m_1) → C_2
  66. Intersect(h_1, m_1) → D_2
  67. Polygon(A_2, B_2, U, M) → q7, f_3, g_3, h_3, i_3
  68. Polygon(C_2, D_2, W, V) → q8, j_3, k_3, l_3, m_3
  69. Intersect(d_1, m_1) → E_2
  70. Intersect(h_1, r_1) → G_2
  71. Intersect(d_1, q_1) → F_2
  72. CurveCartesian(((1 - t)^(3) * H_2) + (((3 * (1 - t)^(2)) * t) * G_2) + (((3 * (1 - t)) * t^(2)) * K_2) + (t^(3) * F_2), t, 0, 1) → u_1
  73. Intersect(h_1, n_1) → L_2
  74. CurveCartesian(((1 - t)^(3) * G_2) + (((3 * (1 - t)^(2)) * t) * L_2) + (((3 * (1 - t)) * t^(2)) * I_2) + (t^(3) * E_2), t, 0, 1) → w
  75. Polygon(G_2, H_2, J_2, E_2) → q9, n_3, p_3, q_3, r_3
  76. LineBisector(U, V) → s_3
  77. Mirror(m, s_3) → m'
  78. Line(M_2, i) → a_3
  79. Mirror(a_3, i) → t_3
  80. Intersect(m', a_3) → N_2
  81. Intersect(m, a_3) → O_2
  82. Intersect(m, t_3) → P_2
  83. Intersect(m', t_3) → Q_2
  84. Intersect(s_3, a_3) → R_2
  85. Intersect(s_3, t_3) → T_2
  86. OrthogonalLine(S_2, a_3) → b_3
  87. Intersect(b_3, t_3) → U_2
  88. Polygon(S_2, R_2, T_2, U_2) → q10, c_3, d_3, e_3, u_2
  89. Mirror(S_2, s_3) → V_2
  90. Mirror(R_2, s_3) → W_2
  91. Mirror(T_2, s_3) → Z_2
  92. Mirror(U_2, s_3) → A_3
  93. Polygon(V_2, W_2, Z_2, A_3) → q10', v_2, w_2, z_2, f_4
  94. Mirror(V_2, f_4) → B_3
  95. Intersect(m, i) → C_3
  96. OrthogonalLine(D_3, m') → g_4
  97. Intersect(m', g_4) → E_3
  98. Intersect(m', i) → F_3
  99. Polygon(E_3, D_3, C_3, F_3) → q11, h_4, i_4, k_4, l_4
  100. Mirror(E_3, i) → G_3
  101. Mirror(D_3, i) → H_3
  102. Mirror(C_3, i) → I_3
  103. Mirror(F_3, i) → J_3
  104. Polygon(G_3, H_3, I_3, J_3) → q11', m_4, n_4, p_4, q_4

AI Drawing Prompt Reference

Draw the Rioja Innovation System logo by first drawing the perpendicular bisector m of line AB, then drawing vector u, and subsequently drawing the orthogonal vector v. Find point J and draw the orthogonal line i through J, and continue in this manner to construct the various parts of the logo, ultimately forming a polygon composed of multiple orthogonal and perpendicular lines.
The prompt above was compiled from the original drawing commands and is for reference only.