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Xiaomi Logo Geometric Construction: Vectors, Polygons, and Circular Arcs

Xiaomi Logo Geometric Construction: Vectors, Polygons, and Circular Arcs
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2019-07-10 05:14
PolygonAngleVectorTransformationGeometric Construction
This GeoGebra example reconstructs the Xiaomi brand logo using precise geometric construction, demonstrating how vectors, polygons, angle bisectors, and circular arcs combine to form a modern emblem. Core mathematical concepts include 2D vector operations, polygon vertex construction, perpendicular bisectors (LineBisector) for finding intersections, orthogonal vectors (OrthogonalVector) for perpendicular lines, circular arcs (CircleArc) for curved edges, and mirror transformations (Mirror) for symmetry. The construction defines points A, B and vectors u, v, builds a base polygon poly1 via the Polygon command, then uses Midpoint, LineBisector, Intersect to determine key points C, D, E, etc., and finally employs CircleArc and Segment to outline the logo's smooth contours. Suitable for high school or early college students, this example illustrates integrated use of geometric construction and vector tools, and serves as a creative bridge between mathematics and design, inspiring interest in geometric aesthetics.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Midpoint(D, A) → E
  5. LineBisector(G, E) → a
  6. Midpoint(E, A) → I
  7. LineBisector(V, W) → r
  8. Intersect(r, a) → N_1
  9. Midpoint(C, B) → F
  10. Midpoint(F, B) → J
  11. Line(I, J) → k
  12. Intersect(k, r) → E_1
  13. LineBisector(B_1, A_1) → q
  14. Intersect(a, q) → M_1
  15. Intersect(q, k) → J_1
  16. Vector(J_1, M_1) → j
  17. Line(F_1, a) → b
  18. Line(E, F) → l
  19. Polygon(K, L, S, K') → q1, k_1, l_1, s, k'
  20. Polygon(M, N, U, T) → q2, m, n, u_1, t
  21. Polygon(K', S, V, B_1) → q3, p, s_1, v_1, b_1
  22. CircleArc(D_1, A_1, B_1) → c
  23. Intersect(r, l) → G_1
  24. Vector(E_1, N_1) → w
  25. CircleArc(H_1, W, V) → d
  26. Polygon(W, A_1, P, O) → q4, w_1, a_1, p_1, o_1
  27. Polygon(A_1, W, V, B_1) → q5, e, w_2, v_2, f_1
  28. Polygon(R, Q, Z, C_1) → q6, r_1, q_1, z_1, c_1
  29. Segment(A_1, P) → g_1
  30. Segment(I_1, N) → h_1
  31. Intersect(q, r) → K_1
  32. Intersect(poly1, q1) → L_1
  33. Segment(S, V) → i_1
  34. Segment(M, T) → j_1
  35. Segment(S, L) → m_1
  36. Segment(N, U) → n_1
  37. Segment(O, W) → t_1
  38. Segment(V, W) → d_1
  39. LineBisector(D, G) → e_1
  40. LineBisector(E, I) → f_2
  41. Intersect(f_2, g) → O_1
  42. OrthogonalLine(P_1, e_1) → g_2
  43. LineBisector(O_1, F) → h_2
  44. Line(G, H) → i_2
  45. Intersect(g, h_2) → V_1
  46. Midpoint(C, H) → T_1
  47. Intersect(g_2, h_2) → C_2
  48. Intersect(g_2, e_1) → D_2
  49. LineBisector(W_1, P_1) → j_2
  50. Polygon(Z_1, D_2, C_2, B_2, A_2, U_1, P_1, W_1) → poly2, k_2, d_2, l_2, b_2, a_2, m_2, n_2, p_2
  51. Intersect(j_2, e_1) → E_2
  52. Intersect(j_2, i_2) → F_2
  53. Vector(F_2, E_2) → u_2
  54. CircleArc(G_2, P_1, W_1) → c_2
  55. Segment(Z_1, W_1) → q_2
  56. OrthogonalLine(I_2, i_2) → r_2
  57. Polygon(J_2, K_2, I_2, H_2) → q7, s_2, t_2, e_2, f_3
  58. Mirror(J_2, g_2) → L_2
  59. Mirror(K_2, g_2) → M_2
  60. Mirror(I_2, g_2) → N_2
  61. Mirror(H_2, g_2) → O_2
  62. Polygon(L_2, M_2, N_2, O_2) → q7', g_3, h_3, i_3, o_2
  63. OrthogonalLine(R_1, e_1) → j_3
  64. Mirror(P_2, Q_1) → Q_2
  65. OrthogonalLine(Q_2, f_2) → k_3
  66. Polygon(R_2, S_2, Q_2, P_2) → q8, l_3, m_3, n_3, p_3
  67. OrthogonalLine(P_2, k) → q_3
  68. Intersect(q_3, a) → T_2
  69. OrthogonalLine(S_1, f_2) → r_3
  70. Intersect(j_3, a) → V_2
  71. Polygon(T_2, U_2, W_2, V_2) → q9, s_3, t_3, a_3, b_3
  72. Intersect(r_3, a) → Z_2
  73. Polygon(Z_2, V_2, R_1, S_1) → q10, z_2, c_3, d_3, e_3
  74. Intersect(j_3, e_1) → A_3
  75. Intersect(r_3, e_1) → B_3
  76. Polygon(B_3, A_3, W_2, Z_2) → q11, f_4, g_4, h_4, i_4
  77. OrthogonalLine(Q_1, k) → j_4
  78. Intersect(j_4, e_1) → E_3
  79. Polygon(C_3, D_3, E_3, F_3) → q12, k_4, l_4, m_4, n_4
  80. Mirror(C_3, j_3) → G_3
  81. Mirror(D_3, j_3) → H_3
  82. Mirror(E_3, j_3) → I_3
  83. Mirror(F_3, j_3) → J_3
  84. Polygon(G_3, H_3, I_3, J_3) → q12', p_4, q_4, r_4, s_4
  85. Mirror(B_3, j_3) → K_3
  86. Mirror(A_3, j_3) → L_3
  87. Mirror(W_2, j_3) → M_3
  88. Mirror(Z_2, j_3) → N_3
  89. Polygon(K_3, L_3, M_3, N_3) → q11', t_4, a_4, b_4, c_4
  90. Mirror(Z_2, j_3) → O_3
  91. Mirror(V_2, j_3) → P_3
  92. Mirror(R_1, j_3) → Q_3
  93. Mirror(S_1, j_3) → R_3
  94. Polygon(O_3, P_3, Q_3, R_3) → q10', o_3, d_4, e_4, f_5
  95. Mirror(T_2, j_3) → S_3
  96. Mirror(U_2, j_3) → T_3
  97. Mirror(W_2, j_3) → U_3
  98. Mirror(V_2, j_3) → V_3
  99. Polygon(S_3, T_3, U_3, V_3) → q9', g_5, h_5, u_3, v_3
  100. Mirror(R_2, j_3) → W_3
  101. Mirror(S_2, j_3) → Z_3
  102. Mirror(Q_2, j_3) → A_4
  103. Mirror(P_2, j_3) → B_4
  104. Polygon(W_3, Z_3, A_4, B_4) → q8', w_3, z_3, i_5, j_5

AI Drawing Prompt Reference

Draw a symmetric geometric emblem based on a square, composed of multiple polygons and circular arcs. Start with a square, then use its sides to define vectors and construct auxiliary points via midpoints, perpendicular bisectors, and intersections. Connect these points to form several nested or adjacent quadrilaterals, and add circular arcs between selected points to create smooth curved edges. The overall shape is mirror-symmetric, combining straight segments and arcs, resembling a modern minimalist logo.
The prompt above was compiled from the original drawing commands and is for reference only.