Logo YÌQI

Logo YÌQI
Loading the math board and drawing, please wait…
2020-12-07 02:32
This example demonstrates the geometric construction of a logo named YÌQI. Key mathematical concepts include vectors and geometric construction. Using GeoGebra commands such as Line, OrthogonalLine, Vector, etc., it shows how to construct complex geometric shapes. Suitable for high school mathematics education and learning.

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. LineBisector(A_1, A) → l
  7. Mirror(f, l) → f'_1
  8. Intersect(b, l) → G
  9. Line(H, l) → h
  10. OrthogonalLine(D, s) → i
  11. LineBisector(A, B) → n
  12. Intersect(n, f'_1) → V_1
  13. OrthogonalLine(J_1, f'_1) → g_1
  14. Intersect(n, f) → P
  15. Mirror(i, n) → i'
  16. Intersect(i', f) → N
  17. LineBisector(F_1, D_1) → p
  18. Intersect(p, h) → H_1
  19. CircleArc(H_1, F_1, D_1) → d
  20. Intersect(d, g_1) → B_4,
  21. LineBisector(G_1, E_1) → k
  22. Intersect(k, h) → I_1
  23. CircleArc(I_1, G_1, E_1) → e
  24. Intersect(e, g_1) → M_1,
  25. OrthogonalLine(R_1, b) → g_2
  26. OrthogonalLine(L_1, f'_1) → h_1
  27. Intersect(e, h_1) → O_1,
  28. LineBisector(O_1, E_1) → f_2
  29. Intersect(i, f) → Z
  30. Mirror(f, l) → f'
  31. Intersect(i, f') → E
  32. OrthogonalLine(A_1, b) → r
  33. OrthogonalLine(K, l) → j
  34. OrthogonalLine(B, u, xOyPlane) → g
  35. Intersect(g, r) → C
  36. Mirror(F, l) → F'
  37. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  38. Mirror(E, n) → E'
  39. Intersect(i, h) → J
  40. Intersect(j, l) → L
  41. Polygon(I, L, J, O, M) → poly1, i_1, l_1, j_1, o, m
  42. CurveCartesian(((1 - t)^(3) * P) + (((3 * (1 - t)^(2)) * t) * T) + (((3 * (1 - t)) * t^(2)) * U) + (t^(3) * R), t, 0, 1) → a
  43. LineBisector(V, W) → q
  44. Intersect(q, f) → K_1
  45. CircleArc(K_1, W, V) → t
  46. Polygon(D_1, V, W, E_1) → q1, d_1, v_1, w, f_1
  47. Polygon(F_1, G_1, M_1, B_4) → t1, q_1, r_1, s_1, h_5
  48. Polygon(J_1, N_1, P_1, O_1, M_1) → poly2, k_1, n_1, p_1, o_1, m_1
  49. Intersect(f_2, g_2) → Q_1
  50. Polygon(O_1, D_1, E_1) → t2, t_1, b_1, c_1
  51. CircleArc(Q_1, O_1, E_1) → c_2
  52. Polygon(S_1, T_1, W_1, U_1, Z_1) → poly3, h_2, i_2, w_1, u_1, z_1
  53. OrthogonalLine(A_2, b) → j_2
  54. Intersect(n, j_2) → B_2
  55. Polygon(E_2, F_2, G_2, H_2, D_2) → poly4, k_2, l_2, m_2, n_2, d_2
  56. OrthogonalLine(C_2, b) → p_2
  57. Intersect(p_2, h_1) → I_2
  58. Polygon(M_2, I_2, J_2, K_2, L_2) → poly5, q_2, r_2, s_2, t_2, f_3
  59. Polygon(R, S, Q, P) → q2, r_3, s_3, q_3, p_3
  60. LineBisector(S, G_1) → g_3
  61. Intersect(s, g_3) → N_2
  62. CircleArc(N_2, S, G_1) → d_3
  63. OrthogonalLine(O_2, b) → h_3
  64. OrthogonalLine(Q_2, j_2) → i_3
  65. OrthogonalLine(R_2, j_2) → j_3
  66. OrthogonalLine(S_2, h) → k_3
  67. OrthogonalLine(T_2, j_2) → l_3
  68. OrthogonalLine(U_2, g_1) → m_3
  69. Intersect(i_3, j_2) → V_2
  70. Intersect(k_3, j_2) → Z_2
  71. Polygon(W_2, Z_2, R_2, B_3, A_3, C_3) → poly6, w_2, z_2, n_3, b_3, t_3, e_3
  72. Intersect(l_3, h) → E_3
  73. Polygon(T_2, R_2, D_3, F_3) → q3, f_4, g_4, h_4, i_4
  74. Polygon(G_3, I_3, Q_2, E_3, H_3) → poly7, j_4, k_4, l_4, m_4, n_4
  75. Intersect(i_3, m_3) → J_3
  76. Intersect(k_3, h_3) → K_3
  77. Intersect(h_3, l_3) → L_3
  78. Intersect(j_3, m_3) → N_3
  79. Intersect(k_3, m_3) → P_3
  80. Polygon(Q_2, J_3, K_3, L_3, M_3, O_3, N_3, P_3, S_2) → poly8, p_4, q_4, r_4, s_4, t_4, o_3, a_4, b_4, c_4
  81. LineBisector(J_3, K_3) → d_4
  82. Intersect(d_4, k_3) → R_3
  83. CircleArc(R_3, J_3, K_3) → e_4
  84. LineBisector(L_3, M_3) → f_5
  85. Intersect(f_5, l_3) → S_3
  86. CircleArc(S_3, L_3, M_3) → c_5
  87. CurveCartesian(((1 - t)^(4) * Q_3) + (((4 * (1 - t)^(3)) * t) * U_3) + (((6 * (1 - t)^(2)) * t^(2)) * W_3) + (((4 * (1 - t)) * t^(3)) * T_3) + (t^(4) * O_3), t, 0, 1) → c
  88. Intersect(h_1, l) → V_3
  89. Polygon(V_3, Z_3, A_4) → t3, g_5, v_3, z_3
  90. LineBisector(M_1, G_1) → i_5
  91. Intersect(i_5, g) → C_4
  92. CircleArc(C_4, G_1, M_1, xOyPlane) → d_5

AI Drawing Prompt Reference

Draw a geometric logo named YÌQI, demonstrating vectors and geometric construction. Start with a line segment and create its perpendicular line. Use vector construction and perpendicular lines to generate multiple geometric elements, including line segments, arcs, and intersection points. Combine these elements through mirroring, bisecting, and reflecting to form a complex geometric shape. The final image should include multiple polygons and curves, showcasing the mathematical concepts of vectors and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.