NBC标志的几何构造

NBC标志的几何构造
几何画板及绘图内容加载中,请稍等……
2019-05-20 16:15
这个范例演示了如何使用GeoGebra构造NBC标志。涉及的核心数学概念包括旋转、平移、向量和圆。通过使用Vector, Rotate, Translate, Circle等命令,可以构造出标志的各个部分。适合高中几何课程或数学爱好者学习几何作图。

GeoGebra 命令及参数

  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