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FCC&C标志的几何构造

FCC&C标志的几何构造
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2020-05-05 16:59
多边形向量几何作图
该范例演示了如何使用GeoGebra构造FCC&C标志。涉及的核心数学概念包括几何变换、多边形和向量。通过使用Line, OrthogonalLine, Vector, LineBisector, Mirror, Intersect, Translate等命令，可以构造标志的各个部分。适合用于高中几何教学。

GeoGebra 命令及参数

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(F, b) → f
  6. LineBisector(A_1, A) → h
  7. Mirror(f, h) → f'
  8. Line(P, f') → l
  9. Line(H, h) → j
  10. Line(U_1, j) → k
  11. OrthogonalLine(D, s) → i
  12. Intersect(i, l) → N_3
  13. Intersect(i, f') → J
  14. LineBisector(M_3, N_3) → i_5
  15. Line(M_3, f') → h_5
  16. Intersect(i, k) → R
  17. OrthogonalLine(U, k) → a
  18. Line(P_1, a) → j_2
  19. Translate(j_2, Vector[(0.21 * u)]) → g_5
  20. Intersect(h_5, g_5) → R_3
  21. Line(T_1, j_2) → k_2
  22. Intersect(k_2, l) → P_3
  23. Midpoint(R_3, P_3) → T_3
  24. Intersect(k_2, h_5) → O_3
  25. Line(O_3, T_3) → d_5
  26. Line(R_3, d_5) → e_5
  27. Line(B_2, k) → l_2
  28. Intersect(a, j) → D_2
  29. Line(N_1, a) → h_2
  30. Intersect(l_2, h_2) → H_2
  31. Line(I_2, l_2) → r_3
  32. Intersect(a, r_3) → J_2
  33. Intersect(h_2, j) → E_2
  34. OrthogonalLine(A_1, b) → r
  35. LineBisector(A, B) → m
  36. Intersect(m, f) → E
  37. OrthogonalLine(B, u, xOyPlane) → g
  38. Intersect(g, r) → C
  39. Mirror(i, m) → i'
  40. Mirror(J, m) → J'
  41. Mirror(J, h) → J'_1
  42. Mirror(J', h) → J''
  43. Line(G, h) → n
  44. Line(O, l) → p
  45. Line(K, p) → q
  46. Line(N, p) → t
  47. Intersect(a, p) → V
  48. OrthogonalLine(Q, f') → d
  49. OrthogonalLine(S, k) → e
  50. Intersect(e, p) → W
  51. Intersect(e, t) → Z
  52. Intersect(e, q) → B_1
  53. Intersect(a, t) → C_1
  54. Intersect(a, q) → D_1
  55. Intersect(i, q) → E_1
  56. Intersect(j, i) → F_1
  57. Intersect(d, j) → G_1
  58. Intersect(n, i) → H_1
  59. Intersect(n, d) → I_1
  60. Intersect(d, q) → J_1
  61. OrthogonalLine(T, k) → f_1
  62. Intersect(f_1, n) → K_1
  63. Polygon(R, Q, G_1, F_1) → q2, r_1, q_1, g_1, h_1
  64. Polygon(H_1, I_1, J_1, E_1) → q3, i_1, j_1, k_1, l_1
  65. Polygon(W, V, C_1, Z) → q4, w, v_1, c_1, z_1
  66. Intersect(e, n) → L_1
  67. Polygon(D_1, K_1, L_1, B_1) → q5, d_1, m_1, n_1, p_1
  68. LineBisector(E_1, W) → s_1
  69. Intersect(s_1, q) → M_1
  70. CircleArc(M_1, W, E_1) → t_1
  71. Polygon(Z, W, E_1, J_1) → q6, z_2, w_1, f_2, g_2
  72. Line(O_1, a) → i_2
  73. Intersect(i_2, p) → Q_1
  74. Intersect(k_2, p) → R_1
  75. Intersect(k_2, t) → S_1
  76. Intersect(i_2, t) → V_1
  77. Intersect(h_2, q) → W_1
  78. Intersect(a, n) → Z_1
  79. Intersect(h_2, n) → A_2
  80. Intersect(k_2, l_2) → C_2
  81. Polygon(S_1, R_1, Q_1, V_1) → q7, m_2, n_2, p_2, q_2
  82. Polygon(V_1, W_1, D_1, Q_1) → q8, r_2, s_2, t_2, b_2
  83. LineBisector(D_1, Q_1) → c_2
  84. Intersect(c_2, q) → F_2
  85. CircleArc(F_2, Q_1, B_1) → d_2
  86. Polygon(D_1, W_1, A_2, Z_1) → q10, i_3, j_3, k_3, l_3
  87. Intersect(l_2, a) → G_2
  88. Polygon(D_2, E_2, I_2, J_2) → q11, m_3, n_3, p_3, q_3
  89. Intersect(l_2, i_2) → K_2
  90. Polygon(C_2, K_2, O_1, P_1) → q12, s_3, t_3, o_1, a_3
  91. Polygon(O_1, J_2, I_2, K_2) → q13, b_3, c_3, d_3, e_3
  92. LineBisector(O_1, J_2) → f_4
  93. Intersect(f_4, r_3) → L_2
  94. CircleArc(L_2, J_2, O_1) → c_4
  95. Translate(S_1, Vector[(0.21 * u)]) → M_2
  96. Translate(R_1, Vector[(0.21 * u)]) → N_2
  97. Translate(Q_1, Vector[(0.21 * u)]) → O_2
  98. Translate(V_1, Vector[(0.21 * u)]) → P_2
  99. Polygon(M_2, N_2, O_2, P_2) → q7', e_6, f_3, o_2, g_3
  100. Translate(V_1, Vector[(0.21 * u)]) → Q_2
  101. Translate(W_1, Vector[(0.21 * u)]) → R_2
  102. Translate(D_1, Vector[(0.21 * u)]) → S_2
  103. Translate(Q_1, Vector[(0.21 * u)]) → T_2
  104. Polygon(Q_2, R_2, S_2, T_2) → q8', h_3, g_4, h_4, i_4
  105. Translate(D_1, Vector[(0.21 * u)]) → U_2
  106. Translate(W_1, Vector[(0.21 * u)]) → V_2
  107. Translate(A_2, Vector[(0.21 * u)]) → W_2
  108. Translate(Z_1, Vector[(0.21 * u)]) → Z_2
  109. Polygon(U_2, V_2, W_2, Z_2) → q10', u_2, v_2, w_2, j_4
  110. Translate(D_2, Vector[(0.21 * u)]) → A_3
  111. Translate(E_2, Vector[(0.21 * u)]) → B_3
  112. Translate(I_2, Vector[(0.21 * u)]) → C_3
  113. Translate(J_2, Vector[(0.21 * u)]) → D_3
  114. Polygon(A_3, B_3, C_3, D_3) → q11', k_4, l_4, m_4, n_4
  115. Translate(C_2, Vector[(0.21 * u)]) → E_3
  116. Translate(K_2, Vector[(0.21 * u)]) → F_3
  117. Translate(O_1, Vector[(0.21 * u)]) → G_3
  118. Translate(P_1, Vector[(0.21 * u)]) → H_3
  119. Polygon(E_3, F_3, G_3, H_3) → q12', p_4, q_4, r_4, s_4
  120. Translate(O_1, Vector[(0.21 * u)]) → I_3
  121. Translate(J_2, Vector[(0.21 * u)]) → J_3
  122. Translate(I_2, Vector[(0.21 * u)]) → K_3
  123. Translate(K_2, Vector[(0.21 * u)]) → L_3
  124. Polygon(I_3, J_3, K_3, L_3) → q13', t_4, a_4, b_4, d_4
  125. Translate(c_4, Vector[(0.21 * u)]) → e_4
  126. Translate(d_2, Vector[(0.21 * u)]) → c_5
  127. Translate(k_2, Vector[(0.21 * u)]) → f_5
  128. Intersect(e_5, i_5) → Q_3
  129. OrthogonalLine(R_3, k) → j_5
  130. Intersect(j_5, l) → S_3
  131. Polygon(O_3, T_3, P_3, S_3, Q_3, R_3) → poly1, o_3, k_5, l_5, m_5, n_5, p_5
  132. Translate(O_3, Vector[(0.2 * u)]) → U_3
  133. Translate(T_3, Vector[(0.2 * u)]) → V_3
  134. Translate(P_3, Vector[(0.2 * u)]) → W_3
  135. Translate(S_3, Vector[(0.2 * u)]) → Z_3
  136. Translate(Q_3, Vector[(0.2 * u)]) → A_4
  137. Translate(R_3, Vector[(0.2 * u)]) → B_4
  138. Polygon(Translate[O_3, Vector[(0.19 * u)]], Translate[T_3, Vector[(0.19 * u)]], Translate[P_3, Vector[(0.19 * u)]], Translate[S_3, Vector[(0.19 * u)]], Translate[Q_3, Vector[(0.19 * u)]], Translate[R_3, Vector[(0.19 * u)]]) → poly1', q_5, r_5, s_5, t_5, a_5, b_5
  139. Line(C_4, f) → f_6
  140. Intersect(i', f_6) → D_4
  141. Intersect(b, f') → E_4
  142. Polygon(C_4, D_4, J', E_4) → q9, g_6, h_6, j', i_6