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Geometric Construction of NBC Logo

Geometric Construction of NBC Logo
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2019-05-20 16:15
CirclePolygonVectorTrigonometryGeometric Construction
This example demonstrates how to construct the NBC logo using GeoGebra. Key mathematical concepts include rotation, translation, and circles. Commands such as Vector, Rotate, Translate, and Circle are used to construct the various parts of the logo. Suitable for high school geometry lessons or math enthusiasts learning geometric construction.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → n
  3. Rotate(A, (-(33.5°)), D) → A'_4
  4. Rotate(D, (-(33.5°)), D) → D'_4
  5. Rotate(A, (-(33.5°)), D) → A'_2
  6. Rotate(A'_2, (-(33.5°)), D) → E
  7. Segment(A'_2, D'_4) → i'
  8. OrthogonalLine(A'_2, i') → j
  9. LineBisector(A, B) → f
  10. Mirror(A'_2, f) → U
  11. Intersect(f, j) → F
  12. Vector(A'_2, F) → v
  13. Vector(A'_2, G) → w
  14. Translate(D'_4, w) → K
  15. Translate(A'_2, w) → J
  16. Translate(E, w) → E'
  17. LineBisector(J, E') → k
  18. Intersect(k, j) → L
  19. Vector(K, L) → b
  20. Vector(K, M) → c
  21. Translate(A'_4, w) → H
  22. Translate(H, c) → H'
  23. Mirror(H', f) → H''_1
  24. Vector(H''_1, U) → v_3
  25. Midpoint(H''_1, U) → O_1
  26. Segment(A, D) → g
  27. Segment(A, D) → i
  28. Polygon(A, D, A'_2) → t1, a'_2, a, d
  29. Rotate(D, (-(33.5°)), D) → D'_5
  30. Translate(D'_5, w) → I
  31. Segment(J, K) → i''
  32. Translate(I, c) → I'
  33. Translate(E', c) → E''
  34. Polygon(H', I', E'') → t1''', e'', l, m
  35. Rotate(H', (-(33.5°)), M) → H''
  36. Rotate(I', (-(33.5°)), M) → I''
  37. Rotate(E'', (-(33.5°)), M) → E'''
  38. OrthogonalLine(E'', l) → p
  39. Intersect(f, p) → N
  40. Vector(E'', N) → q
  41. Vector(E'', O) → r
  42. Translate(H'', r) → H'''
  43. Translate(I'', r) → I'''
  44. Translate(E''', r) → P
  45. LineBisector(O, P) → s
  46. Translate(M, r) → M'
  47. Intersect(s, j) → Q
  48. Vector(M', Q) → t
  49. Vector(M', R) → u_1
  50. Translate(H''', u_1) → S
  51. Translate(I''', u_1) → T
  52. Translate(P, u_1) → P'
  53. Polygon(S, T, P') → t2'', p', s_1, t_1
  54. Semicircle(A, A'_2) → e
  55. Semicircle(H', E'') → h
  56. Semicircle(S, P') → c_1
  57. Mirror(S, f) → S'
  58. Mirror(T, f) → T'
  59. Mirror(P', f) → P''
  60. Polygon(S', T', P'') → t2''', p'', s', t'
  61. Mirror(c_1, f) → d_1
  62. Mirror(I', f) → I''_1
  63. Mirror(E'', f) → E'''_1
  64. Polygon(H''_1, I''_1, E'''_1) → t2, e'''_1, h''_1, i''_1
  65. Mirror(h, f) → h'
  66. Mirror(A, f) → A'
  67. Mirror(D, f) → D'
  68. Polygon(A', D', U) → t1', u_2, a', d'
  69. Mirror(e, f) → e'
  70. Mirror(R, f) → R'
  71. Mirror(M, f) → M'_1
  72. Midpoint(P', P'') → V
  73. Line(A_1, u) → f_1
  74. Mirror(A_1, f) → B_1
  75. Vector(E'''_1, H''_1) → v_1
  76. Semicircle(W, C_1) → g_1
  77. Vector(P'', S') → w_1
  78. Semicircle(P', D_1) → h_1
  79. Polygon(P', P'', R', M'_1, D', D, M, R) → polígono1, i_1, j_1, r', m'_1, k_1, d_2, m_1, r_1
  80. Polygon(B_1, A_1, B, A) → c1, b_1, a_1, b_2, a_2
  81. Polygon(M'_1, R', S', D_1, W, E'''_1) → polígono2, l_1, n_1, p_1, q_1, w_2, f_2
  82. Polygon(M'_1, D', U, C_1, H''_1) → polígono3, g_2, h_2, u_3, i_2, j_2
  83. Line(A'_2, P') → k_2
  84. Line(E_1, k_2) → l_2
  85. Intersect(l_2, j_1) → F_1
  86. LineBisector(F_1, E_1) → m_2
  87. Intersect(m_2, p'') → G_1
  88. CircleArc(G_1, E_1, F_1) → c_2
  89. Polygon(P'', F_1, E_1) → t3, n_2, p_2, q_2
  90. Semicircle(O_1, A_1) → e_1
  91. Mirror(e_1, f) → e_2
  92. Mirror(g_1, f) → r_2
  93. Mirror(h_1, f) → s_2
  94. Mirror(M'_1, f) → H_1
  95. Mirror(R', f) → R''
  96. Mirror(S', f) → S''
  97. Mirror(D_1, f) → I_1
  98. Mirror(W, f) → W'
  99. Mirror(E'''_1, f) → J_1
  100. Polygon(H_1, R'', S'', I_1, W', J_1) → polígono2', t_2, r'', s'', f_3, w', g_3
  101. Mirror(M'_1, f) → K_1
  102. Mirror(D', f) → D''
  103. Mirror(U, f) → U'
  104. Mirror(C_1, f) → L_1
  105. Mirror(H''_1, f) → M_1
  106. Polygon(K_1, D'', U', L_1, M_1) → polígono3', h_3, d'', u', i_3, j_3
  107. Semicircle(E'''_1, H''_1) → c_3
  108. Semicircle(U, B) → d_3
  109. Semicircle(P'', S') → e_3
  110. Semicircle(E'''_1, H''_1) → k_3
  111. Mirror(c_3, f) → p_3
  112. Mirror(e_3, f) → q_3
  113. Mirror(d_3, f) → r_3
  114. Translate(p_3, Vector[(0.04 * b)]) → s_3
  115. Mirror(s_3, f) → t_3
  116. Translate(q_3, Vector[(0.03 * t)]) → c_4
  117. Mirror(c_4, f) → d_4
  118. Polygon(P', P'', F_1) → t4, l_3, m_3, n_3
  119. Segment(F_1, R') → a_3
  120. Midpoint(U, B) → N_1
  121. Vector(D', N_1) → v_2
  122. Translate(d_3, Vector[(0.03 * v_2)]) → e_4
  123. Mirror(e_4, f) → f_4
  124. Semicircle(F_1, P'') → g_4