MathPlotAI Logo MathPlotAI

Geometric Construction of FCC&C Logo

Geometric Construction of FCC&C Logo
Loading the math board and drawing, please wait…
2020-05-05 16:59
PolygonVectorGeometric Construction
This example demonstrates how to construct the FCC&C logo using GeoGebra. Key mathematical concepts include geometric transformations, polygons, and vectors. Commands such as Line, OrthogonalLine, Vector, LineBisector, Mirror, Intersect, and Translate are used to construct the various parts of the logo. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  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