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Gucci Logo Geometric Construction

Gucci Logo Geometric Construction
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2020-05-22 22:57
CirclePolygonVectorFunctionGeometric Construction
This example demonstrates how to construct a geometric figure similar to the Gucci Logo using GeoGebra, involving elements like circles, symmetry, and quadrilaterals. Key math concepts include circles, symmetry, quadrilaterals, tangent functions, orthocenters, functions, and plane figures. The construction utilizes commands and objects such as LineBisector (angle bisector), Vector, OrthogonalVector, Line, OrthogonalLine, Intersect, Mirror, Polygon, Circle, CircleArc, and Segment. It is suitable for high school mathematics education, showcasing the application of geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A_1, A) → l
  5. LineBisector(A_1, A) → n
  6. LineBisector(A_1, A) → h
  7. Line(A, B) → s
  8. OrthogonalLine(D, s) → i
  9. Intersect(i, l) → P
  10. Line(Q, l) → t
  11. Mirror(t, l) → t'
  12. OrthogonalLine(A, s) → b
  13. OrthogonalLine(B, u, xOyPlane) → g
  14. Mirror(i, m) → i'
  15. OrthogonalLine(A_1, b) → r
  16. Intersect(g, r) → C
  17. Intersect(b, l) → O
  18. Intersect(b, t) → H
  19. Mirror(H, l) → H'
  20. Mirror(H, m) → H'_1
  21. Mirror(H', m) → H''
  22. Polygon(H, H'_1, H'', H') → c1, h_1, h'_1, h'', h'
  23. Intersect(m, l) → L
  24. Mirror(N, m) → N'
  25. Circle(N, N') → c
  26. Intersect(c, l) → E, G
  27. Circle(N, I) → e
  28. Intersect(c, t) → J, K
  29. Intersect(e, t) → R, S
  30. CircleArc(N, K, J) → f
  31. CircleArc(N, S, R) → q
  32. Mirror(f, l) → f'
  33. Mirror(q, l) → q'
  34. Mirror(f, m) → f'_1
  35. Mirror(q, m) → q'_1
  36. Mirror(f', m) → f''
  37. Mirror(q', m) → q''
  38. Intersect(f', t') → M, H_2
  39. Intersect(q', t') → T, I_2
  40. CircleArc(N, J, M) → c_1
  41. CircleArc(N, R, T) → d_1
  42. Polygon(J, R, T, M) → c2, j_1, r_1, t_1, m_1
  43. Mirror(c_1, m) → f_1
  44. Mirror(m, m_1) → m'
  45. Mirror(m, m_1) → m'_1
  46. Mirror(M, m) → M'
  47. Mirror(J, m) → J'
  48. Segment(M', J') → i_1
  49. Mirror(T, m) → T'
  50. Mirror(M, m) → M'_1
  51. Segment(T', M'_1) → k_1
  52. Mirror(J, m) → J'_1
  53. Mirror(R, m) → R'
  54. Mirror(T, m) → T'_1
  55. Mirror(M, m) → M'_2
  56. Polygon(J'_1, R', T'_1, M'_2) → c2', j'_1, r', t'_1, m'_2
  57. Intersect(c, q) → U, , ,
  58. Intersect(c, f, 1) → V
  59. Intersect(q'_1, c) → W, , ,
  60. Intersect(e, m) → Z, B_1
  61. CircleArc(N, K, W) → p_1
  62. CircleArc(N, S, W) → q_1
  63. Polygon(B_1, W, K, S) → c3, b_1, w, k_2, s_1
  64. Mirror(p_1, l) → c_2
  65. Mirror(q_1, l) → d_2
  66. Mirror(S, l) → S'
  67. Mirror(B_1, l) → C_1
  68. Segment(S', C_1) → l_1
  69. Mirror(K, l) → K'
  70. Mirror(S, l) → S'_1
  71. Segment(K', S'_1) → n_1
  72. Mirror(W, l) → W'
  73. Mirror(K, l) → K'_1
  74. Segment(W', K'_1) → w'
  75. Mirror(B_1, l) → D_1
  76. Mirror(W, l) → W'_1
  77. Segment(D_1, W'_1) → a_1
  78. Mirror(c_2, l) → f_2
  79. Mirror(B_1, l) → a
  80. Mirror(W, l) → W'_2
  81. Mirror(K, l) → K'_2
  82. Mirror(S, l) → S'_2
  83. Mirror(B_1, l) → F_1
  84. Mirror(W, l) → W'_3
  85. Mirror(K, l) → K'_3
  86. Mirror(S, l) → S'_3
  87. Polygon(F_1, W'_3, K'_3, S'_3) → c3'_1, h_2, w'_3, k'_3, s'_3
  88. Mirror(B_1, m) → G_1
  89. Mirror(W, m) → W'_4
  90. Mirror(K, m) → K'_4
  91. Mirror(S, m) → S'_4
  92. Polygon(G_1, W'_4, K'_4, S'_4) → c3'_2, i_2, w'_4, k'_4, s'_4
  93. Mirror(p_1, m) → p_2
  94. Mirror(q_1, m) → q_2
  95. Mirror(c_2, m) → g_2
  96. Mirror(F_1, m) → E_1
  97. Mirror(W'_3, m) → H_1
  98. Mirror(K'_3, m) → I_1
  99. Mirror(S'_3, m) → J_1
  100. Polygon(E_1, H_1, I_1, J_1) → c4, j_2, l_2, m_2, n_2
  101. Mirror(d_2, m) → r_2
  102. OrthogonalLine(K_1, m'_1) → s_2
  103. Intersect(c, s_2) → L_1, M_1
  104. Intersect(f, h'') → N_1,
  105. Intersect(f, t') → O_1,
  106. Intersect(c, t') → P_1, Q_1
  107. OrthogonalLine(R_1, s_2) → t_2
  108. Intersect(t_2, s_2) → S_1
  109. Polygon(L_1, S_1, R_1, Q_1) → c5, b_2, f_3, g_3, h_3
  110. Mirror(L_1, m) → T_1
  111. Mirror(S_1, m) → U_1
  112. Mirror(R_1, m) → V_1
  113. Mirror(Q_1, m) → W_1
  114. Polygon(T_1, U_1, V_1, W_1) → c5', i_3, u_1, v_1, a_2
  115. Intersect(c, m) → Z_1, A_2
  116. OrthogonalLine(A_2, m'_1) → j_3
  117. Mirror(j_3, l) → k_3
  118. Intersect(b, j_3) → B_2
  119. Intersect(g, j_3) → C_2
  120. Polygon(B_2, C_2, H'_1, H) → c6, l_3, m_3, n_3, h_4
  121. Mirror(c6, l) → c6'
  122. Polygon(B_2, C_2, C, A_1) → c7, p_3, q_3, c_3, r_3
  123. Mirror(c7, l) → c7'
  124. Mirror(d_1, m) → g_1
  125. Mirror(A_1, l) → D_2
  126. Mirror(B_2, l) → E_2
  127. Segment(D_2, E_2) → s_3
  128. Mirror(C, l) → C'
  129. Mirror(A_1, l) → F_2
  130. Segment(C', F_2) → t_3
  131. Mirror(C_2, l) → G_2
  132. Mirror(C, l) → C'_1
  133. Segment(G_2, C'_1) → b_3

AI Drawing Prompt Reference

Draw a geometric figure similar to the Gucci logo, including two intersecting circles and a quadrilateral. Start by drawing two circles, then use their axes of symmetry and tangents to construct the sides of the quadrilateral. Apply mirroring and rotation commands to generate the other half of the figure, and finally connect the key points to complete the design.
The prompt above was compiled from the original drawing commands and is for reference only.