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BP Logo

BP Logo
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2019-05-09 00:13
PolygonVectorGeometric Construction
This GeoGebra example demonstrates the geometric construction of the BP logo. Key mathematical concepts include vectors, rotation, ellipses, and symmetry. Using commands such as Circle, Vector, Rotate, Line, LineBisector, OrthogonalLine, Intersect, Midpoint, CircleArc, Mirror, Segment, Polygon, Sequence, the geometric shape of the logo is constructed. Suitable for high school geometry lessons or student practice in geometric construction.

GeoGebra Commands & Parameters

  1. Circle(O, A) → c
  2. Vector(O, A) → u
  3. Rotate(E, (-(20°)), O) → E'
  4. Circle(O, E) → d
  5. Rotate(E', (-(20°)), O) → E''
  6. Rotate(E'', (-(20°)), O) → E'''
  7. Rotate(E''', (-(20°)), O) → F
  8. Rotate(F, (-(20°)), O) → F'
  9. Circle(O, D) → p
  10. Line(E, O) → g
  11. Circle(O, B) → r
  12. Circle(O, C) → s
  13. LineBisector(O, E) → l
  14. OrthogonalLine(E'', l) → k
  15. Intersect(k, l) → G
  16. Intersect(p, l) → I, J
  17. Midpoint(I, G) → H
  18. Vector(G, H) → v
  19. CircleArc(K, E, O) → e
  20. Rotate(e, (-(20°)), O) → e'
  21. Rotate(e', (-(20°)), O) → e''
  22. Mirror(e, g) → e'_1
  23. Rotate(e'', (-(20°)), O) → e'''
  24. Rotate(e''', (-(20°)), O) → h
  25. Rotate(h, (-(20°)), O) → h'
  26. Rotate(h', (-(20°)), O) → h''
  27. Rotate(h'', (-(20°)), O) → h'''
  28. Rotate(h''', (-(20°)), O) → f
  29. Rotate(f, (-(20°)), O) → f'
  30. Rotate(f', (-(20°)), O) → f''
  31. Rotate(f'', (-(20°)), O) → f'''
  32. Rotate(f''', (-(20°)), O) → q
  33. Rotate(q, (-(20°)), O) → q'
  34. Rotate(q', (-(20°)), O) → q''
  35. Rotate(q'', (-(20°)), O) → q'''
  36. Rotate(q''', (-(20°)), O) → t
  37. Rotate(e, 20°, O) → e'_2
  38. Rotate(e'_1, 20°, O) → c_1
  39. Rotate(e'_1, (-(20°)), O) → d_1
  40. Intersect(e'_1, e') → L, M, ,
  41. Intersect(e'_1, e'') → N, P, ,
  42. Intersect(c_1, e'') → Q, R, ,
  43. Intersect(e''', e'_1) → S, T, ,
  44. Intersect(c_1, e) → W, Z, ,
  45. CircleArc(K, W, O) → e_1
  46. Rotate(e_1, (-(20°)), O) → f_1
  47. Line(W, O) → i
  48. Mirror(e_1, i) → g_1
  49. Mirror(e_1, g) → h_1
  50. Mirror(K, g) → K'
  51. Line(E', O) → j
  52. Circle(O, T) → s_1
  53. Intersect(s_1, e'') → A_1, , ,
  54. Segment(A_1, T) → m
  55. Mirror(T, m) → T'
  56. Mirror(N, g) → N'_1
  57. Mirror(T, g) → T'_1
  58. CircleArc(K, N'_1, T'_1) → k_1
  59. Mirror(k_1, g) → p_1
  60. Polygon(T, A_1, N) → t1, n, t_1, a_1
  61. Mirror(p_1, j) → q_1
  62. Mirror(T, g) → T'_2
  63. Mirror(T, g) → T'_3
  64. Mirror(A_1, g) → C_1
  65. Mirror(N, g) → N'_2
  66. Polygon(T'_3, C_1, N'_2) → t1', n'_2, t'_3, a
  67. Mirror(q_1, g) → r_1
  68. Mirror(T, m) → T'_4
  69. Mirror(A_1, m) → D_1
  70. Mirror(N, m) → N'_3
  71. Mirror(N, m) → N'_4
  72. Mirror(T, m) → T'_5
  73. Mirror(N, m) → N'_5
  74. Mirror(T, m) → T'_6
  75. Mirror(N, m) → N'
  76. Mirror(T'_4, g) → B_1
  77. Mirror(D_1, g) → E_1
  78. Mirror(N'_3, g) → F_1
  79. Rotate(k_1, (-(20°)), O) → e_2
  80. Mirror(e_2, g) → f_2
  81. Rotate(T'_3, (-(20°)), O) → G_1
  82. Rotate(C_1, (-(20°)), O) → H_1
  83. Rotate(N'_2, (-(20°)), O) → I_1
  84. Polygon(G_1, H_1, I_1) → t1'', n_1, g_2, h_2
  85. Rotate(F_1, (-(20°)), O) → J_1
  86. Rotate(B_1, (-(20°)), O) → K_1
  87. Rotate(B_1, 20°, O) → N_1
  88. Rotate(E_1, 20°, O) → O_1
  89. Rotate(F_1, 20°, O) → P_1
  90. Rotate(B_1, (-(20°)), O) → Q_1
  91. Rotate(E_1, (-(20°)), O) → R_1
  92. Rotate(F_1, (-(20°)), O) → S_1
  93. Rotate(r_1, 20°, O) → c_3
  94. Rotate(k_1, 20°, O) → d_3
  95. Rotate(T'_3, 20°, O) → T_1
  96. Rotate(C_1, 20°, O) → U_1
  97. Rotate(N'_2, 20°, O) → V_1
  98. Polygon(T_1, U_1, V_1) → t1''_1, v_1, a_2, u_1
  99. Rotate(e_1, 20°, O) → e_3
  100. Rotate(g_1, 20°, O) → f_3
  101. Mirror(e_3, g) → g_3
  102. Mirror(f_3, g) → h_3
  103. Mirror(d_3, g) → k_3
  104. Mirror(T_1, g) → W_1
  105. Mirror(U_1, g) → Z_1
  106. Mirror(V_1, g) → A_2
  107. Polygon(W_1, Z_1, A_2) → t3, b_2, w_1, z_1
  108. Mirror(N_1, g) → B_2
  109. Mirror(O_1, g) → C_2
  110. Mirror(P_1, g) → D_2
  111. Rotate(q_1, (-(20°)), O) → q_3
  112. Circle(O, S_1) → s_3
  113. Mirror(e_2, i) → c_2
  114. Sequence(Rotate[d_1, ((20 * λ))°, O], λ, 1, 18) → l1
  115. Sequence(Rotate[h_3, ((20 * β))°, O], β, 1, 16) → l2
  116. Rotate(l2, 20°, O) → l2'
  117. Sequence(Rotate[g_3, ((-((20 * α))))°, O], α, 1, 16) → l3
  118. Sequence(Rotate[q_3, ((-20 * β))°, O], β, 1, 16) → l4
  119. Sequence(Rotate[k_3, ((-20 * β))°, O], β, 1, 16) → l5
  120. Sequence(Polygon[Rotate[W_1, ((-20 * β))°, O], Rotate[Z_1, ((-20 * β))°, O], Rotate[A_2, ((-20 * β))°, O]], β, 1, 16) → l6
  121. LineBisector(S_1, A_1) → b
  122. OrthogonalLine(E''', b) → i_1
  123. Intersect(i_1, b) → U
  124. CircleArc(U, A_1, S_1) → d_2
  125. Mirror(d_2, g) → k_2
  126. Rotate(k_2, (-(20°)), O) → p_2
  127. Sequence(Rotate[k_2, ((-((20 * β))))°, O], β, 1, 19) → l7
  128. Sequence(Rotate[d_2, ((-((20 * β))))°, O], β, 1, 19) → l8
  129. Rotate(S_1, (-(20°)), O) → V
  130. Polygon(A_1, S_1, V) → t2, v_2, j_1, l_1
  131. Sequence(Polygon[Rotate[A_1, ((-((20 * α))))°, O], Rotate[S_1, ((-((20 * α))))°, O], Rotate[V, ((-((20 * α))))°, O]], α, 1, 19) → l9
  132. Segment(E, I_1) → m_1
  133. Sequence(Segment[Rotate[E, ((-((20 * θ))))°, O], Rotate[I_1, ((-((20 * θ))))°, O]], θ, 1, 19) → l10