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Venus Williams Logo Geometric Construction

Venus Williams Logo Geometric Construction
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2020-07-23 22:59
TrianglePolygonAngleVectorGeometric Construction
This example demonstrates how to geometrically construct the Venus Williams logo. It involves core mathematical concepts such as angles, reflection, equilateral triangles, right triangles, conditional probability, and the Pythagorean theorem. The construction uses GeoGebra commands like LineBisector, Vector, OrthogonalVector, Line, OrthogonalLine, Intersect, Mirror, Midpoint, Polygon, CircleArc, and Segment. Suitable for high school mathematics education or for those interested in geometric constructions.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A_1, A) → l
  5. Line(A, B) → s
  6. OrthogonalLine(D, s) → i
  7. OrthogonalLine(A, s) → b
  8. OrthogonalLine(A_1, b) → r
  9. OrthogonalLine(F, b) → f
  10. Intersect(m, f) → M
  11. Mirror(f, l) → f'
  12. Intersect(i, f') → E
  13. OrthogonalLine(K, r) → h
  14. Midpoint(K, G) → O
  15. Line(O, R) → t
  16. Line(I, t) → a
  17. Line(V, a) → c
  18. Intersect(c, i) → C_1
  19. Line(M, c) → d
  20. Line(Q, d) → g_1
  21. Line(Z, g_1) → h_1
  22. Intersect(i, h_1) → B_1
  23. OrthogonalLine(B_1, b) → i_1
  24. LineBisector(B_1, O_1) → n_2
  25. Intersect(n_2, i) → S_1
  26. LineBisector(S_1, C_1) → j_5
  27. Intersect(n_2, j_5) → Z_2
  28. OrthogonalLine(B, u, xOyPlane) → g
  29. Mirror(i, m) → i'
  30. Intersect(g, r) → C
  31. Mirror(f, l) → f'_1
  32. Mirror(F, l) → F'
  33. Intersect(m, f') → S
  34. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  35. Intersect(i', f') → W
  36. OrthogonalLine(G, f'_1) → k
  37. OrthogonalLine(H, f'_1) → j
  38. OrthogonalLine(N, r) → p
  39. OrthogonalLine(J, f'_1) → q
  40. OrthogonalLine(T, f'_1) → n
  41. Line(T, t) → e
  42. Line(L, a) → f_1
  43. Intersect(n, d) → D_1
  44. Intersect(g_1, n) → E_1
  45. Intersect(p, e) → F_1
  46. Intersect(h, f') → G_1
  47. Intersect(h, f_1) → H_1
  48. Intersect(j, a) → I_1
  49. Intersect(j, f_1) → J_1
  50. Intersect(k, f_1) → K_1
  51. Intersect(j, c) → L_1
  52. Intersect(k, c) → N_1
  53. Polygon(I, I_1, H_1, L, J_1, K_1, N_1, L_1, M_1, C_1, B_1, O_1) → polígono1, i_2, o_1, q_1, l_2, j_1, k_1, l_1, n_1, m_1, p_1, c_1, b_1
  54. OrthogonalLine(F_1, i') → r_1
  55. Polygon(Q_1, Q, F_1, P_1, M, D_1, E_1, L_1, I_1, T, O, R) → polígono2, s_1, r_2, h_2, j_2, q_2, m_2, d_1, t_1, f_2, g_2, t_2, o
  56. LineBisector(L, H_1) → k_2
  57. Intersect(k_2, i) → R_1
  58. CircleArc(R_1, H_1, L) → c_2
  59. LineBisector(E_1, L_1) → p_2
  60. Intersect(p_2, h) → T_1
  61. CircleArc(T_1, E_1, L_1) → s_2
  62. LineBisector(T, I_1) → f_3
  63. Intersect(f_3, i) → U_1
  64. CircleArc(U_1, I_1, T) → d_3
  65. LineBisector(P_1, F_1) → g_3
  66. Intersect(p, g_3) → V_1
  67. CircleArc(V_1, F_1, P_1) → e_3
  68. LineBisector(Q, Q_1) → h_3
  69. Intersect(h_3, i_1) → W_1
  70. CircleArc(W_1, Q_1, Q) → k_3
  71. Intersect(q, h_1) → Z_1
  72. Intersect(q, c) → A_2
  73. Polygon(Z_1, Z, V, A_2) → c1, z_1, z_2, v_1, i_3
  74. Segment(T, I_1) → j_3
  75. Segment(L, H_1) → l_3
  76. Segment(B_1, O_1) → m_3
  77. Segment(Q, Q_1) → n_3
  78. Segment(E_1, L_1) → p_3
  79. Mirror(Z_1, m) → B_2
  80. Mirror(Z, m) → Z'
  81. Mirror(V, m) → V'
  82. Mirror(A_2, m) → C_2
  83. Polygon(B_2, Z', V', C_2) → c1', q_3, z', v', r_3
  84. Mirror(c_2, m) → s_3
  85. CircleArc(Z_2, B_1, O_1) → d_2
  86. Mirror(d_2, m) → t_3
  87. Mirror(d_3, m) → c_4
  88. Mirror(e_3, m) → d_4
  89. Mirror(k_3, m) → e_4
  90. Mirror(s_2, m) → f_4
  91. Mirror(I, m) → I'
  92. Mirror(I_1, m) → D_2
  93. Mirror(J_1, m) → E_2
  94. Mirror(K_1, m) → F_2
  95. Mirror(N_1, m) → G_2
  96. Mirror(L_1, m) → H_2
  97. Mirror(M_1, m) → I_2
  98. Mirror(C_1, m) → J_2
  99. Mirror(B_1, m) → K_2
  100. Mirror(O_1, m) → L_2
  101. Mirror(H_1, m) → M_2
  102. Mirror(L, m) → L'
  103. Polygon(I', D_2, M_2, L', E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2) → polígono1', b_3, p_4, q_4, l', g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4
  104. Mirror(Q_1, m) → N_2
  105. Mirror(Q, m) → Q'
  106. Mirror(M, m) → M'
  107. Mirror(D_1, m) → O_2
  108. Mirror(E_1, m) → P_2
  109. Mirror(L_1, m) → Q_2
  110. Mirror(I_1, m) → R_2
  111. Mirror(T, m) → T'
  112. Mirror(O, m) → O'
  113. Mirror(R, m) → R'
  114. Mirror(F_1, m) → S_2
  115. Mirror(P_1, m) → T_2
  116. Polygon(N_2, Q', S_2, T_2, M', O_2, P_2, Q_2, R_2, T', O', R') → polígono2', r_4, r', b_4, f_5, q', m', o_2, s_4, t_4, a_4, t', o'
  117. Segment(F_2, R_2) → g_5
  118. Segment(R_2, T') → h_5
  119. Polygon(U_2, R, F_1) → t1, i_5, u_2, r_5
  120. Mirror(U_2, m) → V_2
  121. Mirror(R, m) → R'_1
  122. Mirror(F_1, m) → W_2
  123. Polygon(V_2, R'_1, W_2) → t1', w_2, v_2, r'_1
  124. Segment(B_1, O_1) → k_5
  125. Mirror(Q, m) → Q'_1
  126. Mirror(Q_1, m) → A_3
  127. Segment(Q'_1, A_3) → l_5