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Brazilian Air Routes

Brazilian Air Routes
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2019-12-17 01:02
PolygonVectorGeometric Construction
This example demonstrates the geometric representation of Brazilian air routes. Key mathematical concepts include geometric transformations, vectors, and polygons. Using GeoGebra commands such as LineBisector, Vector, and Polygon, complex geometric shapes can be constructed. Suitable for high school geometry courses.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A, C) → d
  5. Intersect(m, d) → E
  6. Midpoint(C, A) → J
  7. OrthogonalLine(M, d) → i
  8. Line(A, B) → s
  9. OrthogonalLine(A, s) → b
  10. OrthogonalLine(I, b) → h
  11. Mirror(h, d) → h'
  12. Intersect(m, h') → N
  13. Mirror(F, m) → F'
  14. OrthogonalLine(C, v, xOyPlane) → f
  15. Intersect(f, m) → U
  16. Mirror(i, m) → i'
  17. Intersect(h, m) → S
  18. OrthogonalLine(B, u, xOyPlane) → g
  19. Intersect(g, f) → D
  20. Mirror(M, m) → M'
  21. Intersect(g, h') → A_1
  22. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  23. Mirror(F', E) → F''
  24. Mirror(F', E) → F''_1
  25. LaTeX(q11, true, true) → text1
  26. Line(C, E) → j
  27. Mirror(j, m) → j'
  28. Circle(E, N) → c
  29. Circle(E, K) → e
  30. Circle(E, H) → k
  31. Intersect(e, j') → L, O
  32. Intersect(e, j) → P, R
  33. AngularBisector(j', m) → l, n
  34. Mirror(n, m) → n'
  35. Mirror(l, d) → l'
  36. Intersect(k, n') → T, V
  37. Intersect(k, n) → W, Z
  38. Intersect(k, l') → B_1, C_1
  39. Intersect(k, l) → D_1, E_1
  40. Line(W, L) → p
  41. Mirror(p, m) → p'
  42. Intersect(p, p') → F_1
  43. Polygon(F_1, E, L) → t1, l_1, f_1, e_1
  44. Mirror(F_1, E) → G_1
  45. Mirror(E, E) → E'
  46. Mirror(L, E) → L'
  47. Polygon(G_1, E', L') → t1', q, g_1, e'
  48. Mirror(F_1, m) → H_1
  49. Mirror(E, m) → E'_1
  50. Mirror(L, m) → L'_1
  51. Polygon(H_1, E'_1, L'_1) → t1'_1, l'_1, h_1, e'_1
  52. Mirror(H_1, E) → I_1
  53. Mirror(E'_1, E) → J_1
  54. Mirror(L'_1, E) → K_1
  55. Polygon(I_1, J_1, K_1) → t2, k_1, i_1, j_1
  56. Rotate(F_1, -90°, E) → L_1
  57. Rotate(E, -90°, E) → E'_2
  58. Rotate(L, -90°, E) → L'_2
  59. Polygon(L_1, E'_2, L'_2) → t1'_2, l'_2, r, e'_2
  60. Rotate(F_1, 90°, E) → M_1
  61. Rotate(E, 90°, E) → E'_3
  62. Rotate(L, 90°, E) → L'_3
  63. Polygon(M_1, E'_3, L'_3) → t1'_3, l'_3, m_1, e'_3
  64. Mirror(M_1, E) → N_1
  65. Mirror(E'_3, E) → O_1
  66. Mirror(L'_3, E) → P_1
  67. Rotate(I_1, 90°, E) → Q_1
  68. Rotate(J_1, 90°, E) → R_1
  69. Rotate(K_1, 90°, E) → S_1
  70. Polygon(Q_1, R_1, S_1) → t2', s_1, q_1, r_1
  71. Mirror(Q_1, E) → T_1
  72. Mirror(R_1, E) → U_1
  73. Mirror(S_1, E) → V_1
  74. Polygon(T_1, U_1, V_1) → t2'', v_1, t_1, u_1
  75. Intersect(c, j') → W_1, Z_1
  76. Intersect(c, j) → A_2, B_2
  77. Polygon(W, W_1, S_1) → t4, t, w, w_1
  78. Mirror(W, U_1) → W'
  79. Mirror(W_1, U_1) → C_2
  80. Mirror(S_1, U_1) → F_2
  81. Polygon(W', C_2, F_2) → t4', f_2, w', c_2
  82. Rotate(W, -90°, U_1) → W'_1
  83. Rotate(W_1, -90°, U_1) → G_2
  84. Rotate(S_1, -90°, U_1) → H_2
  85. Polygon(W'_1, G_2, H_2) → t4'_1, h_2, w'_1, g_2
  86. Mirror(W'_1, E) → I_2
  87. Mirror(G_2, E) → J_2
  88. Mirror(H_2, E) → K_2
  89. Polygon(I_2, J_2, K_2) → t5, k_2, i_2, j_2
  90. Polygon(S_1, B_1, W_1) → t6, a, a_1, b_1
  91. Mirror(S_1, E) → L_2
  92. Mirror(B_1, E) → M_2
  93. Mirror(W_1, E) → N_2
  94. Polygon(L_2, M_2, N_2) → t6', n_2, l_2, m_2
  95. Rotate(S_1, 90°, E) → O_2
  96. Rotate(B_1, 90°, E) → P_2
  97. Rotate(W_1, 90°, E) → Q_2
  98. Polygon(O_2, P_2, Q_2) → t6'_1, q_2, o_2, p_2
  99. Mirror(O_2, E) → R_2
  100. Mirror(P_2, E) → S_2
  101. Mirror(Q_2, E) → T_2
  102. Polygon(R_2, S_2, T_2) → t7, t_2, r_2, s_2
  103. Rotate(M, 9°, U_1) → M'_1
  104. Rotate(M'_1, 9°, U_1) → U_2
  105. Rotate(U_2, 9°, U_1) → V_2
  106. Rotate(V_2, 9°, E) → W_2
  107. Rotate(Z_2, 9°, U_1) → A_3
  108. Rotate(Z_2, 18°, U_1) → B_3
  109. Rotate(A_3, 18°, E) → C_3
  110. Rotate(B_3, 18°, U_1) → D_3
  111. Segment(M'_1, A_3) → n_1
  112. Segment(U_2, B_3) → p_1
  113. Segment(V_2, C_3) → c_1
  114. Segment(W_2, D_3) → d_1
  115. Mirror(M'_1, d) → E_3
  116. Mirror(A_3, d) → F_3
  117. Segment(E_3, F_3) → a_2
  118. Mirror(U_2, d) → G_3
  119. Mirror(B_3, d) → H_3
  120. Segment(G_3, H_3) → e_2
  121. Mirror(V_2, d) → I_3
  122. Mirror(C_3, d) → J_3
  123. Segment(I_3, J_3) → f_3
  124. Mirror(W_2, d) → K_3
  125. Mirror(D_3, d) → L_3
  126. Segment(K_3, L_3) → g_3
  127. Mirror(M'_1, m) → M_3
  128. Mirror(A_3, m) → N_3
  129. Segment(M_3, N_3) → h_3
  130. Mirror(U_2, m) → O_3
  131. Mirror(B_3, m) → P_3
  132. Segment(O_3, P_3) → i_3
  133. Mirror(V_2, m) → Q_3
  134. Mirror(C_3, m) → R_3
  135. Segment(Q_3, R_3) → j_3
  136. Mirror(W_2, m) → S_3
  137. Mirror(D_3, m) → T_3
  138. Segment(S_3, T_3) → k_3
  139. Mirror(E_3, m) → U_3
  140. Mirror(F_3, m) → V_3
  141. Segment(U_3, V_3) → l_3
  142. Mirror(G_3, m) → W_3
  143. Mirror(H_3, m) → Z_3
  144. Segment(W_3, Z_3) → m_3
  145. Mirror(I_3, m) → A_4
  146. Mirror(J_3, m) → B_4
  147. Segment(A_4, B_4) → n_3
  148. Mirror(K_3, m) → C_4
  149. Mirror(L_3, m) → D_4
  150. Segment(C_4, D_4) → p_3
  151. Mirror(M'_1, j') → E_4
  152. Mirror(A_3, j') → F_4
  153. Segment(E_4, F_4) → q_3
  154. Mirror(U_2, j') → G_4
  155. Mirror(B_3, j') → H_4
  156. Segment(G_4, H_4) → r_3
  157. Mirror(V_2, j') → I_4
  158. Mirror(C_3, j') → J_4
  159. Segment(I_4, J_4) → s_3
  160. Mirror(W_2, j') → K_4
  161. Mirror(D_3, j') → L_4
  162. Segment(K_4, L_4) → t_3
  163. Mirror(E_4, m) → M_4
  164. Mirror(F_4, m) → N_4
  165. Segment(M_4, N_4) → b_3
  166. Mirror(G_4, m) → O_4
  167. Mirror(H_4, m) → P_4
  168. Segment(O_4, P_4) → d_3
  169. Mirror(I_4, m) → Q_4
  170. Mirror(J_4, m) → R_4
  171. Segment(Q_4, R_4) → e_3
  172. Mirror(K_4, m) → S_4
  173. Mirror(L_4, m) → T_4
  174. Segment(S_4, T_4) → f_4
  175. Mirror(E_4, d) → U_4
  176. Mirror(F_4, d) → V_4
  177. Segment(U_4, V_4) → g_4
  178. Mirror(G_4, d) → W_4
  179. Mirror(H_4, d) → Z_4
  180. Segment(W_4, Z_4) → h_4
  181. Mirror(I_4, d) → A_5
  182. Mirror(J_4, d) → B_5
  183. Segment(A_5, B_5) → i_4
  184. Mirror(K_4, d) → C_5
  185. Mirror(L_4, d) → D_5
  186. Segment(C_5, D_5) → j_4
  187. Mirror(M_4, d) → E_5
  188. Mirror(N_4, d) → F_5
  189. Segment(E_5, F_5) → k_4
  190. Mirror(O_4, d) → G_5
  191. Mirror(P_4, d) → H_5
  192. Segment(G_5, H_5) → l_4
  193. Mirror(Q_4, d) → I_5
  194. Mirror(R_4, d) → J_5
  195. Segment(I_5, J_5) → m_4
  196. Mirror(S_4, d) → K_5
  197. Mirror(T_4, d) → L_5
  198. Segment(K_5, L_5) → n_4

AI Drawing Prompt Reference

Draw a geometric representation of Brazilian air routes, showcasing geometric transformations, vectors, and polygons. Start by constructing the perpendicular bisector of segment AB and vector AB, then create a orthogonal vector. Use midpoint, orthogonal lines, and mirror operations to form complex shapes, including polygons and circles. The final image features multiple polygons and circles, highlighting the details and aesthetics of geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.