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Logo SPIUK Geometric Construction Example

Logo SPIUK Geometric Construction Example
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2019-10-14 19:43
CirclePolygonVectorTransformationGeometric Construction
This example demonstrates how to construct the Logo SPIUK geometric figure using GeoGebra. It involves core mathematical concepts such as vectors, angles, circles, polygons, and geometric transformations. Key construction steps include using commands like Vector, LineBisector, OrthogonalVector, Midpoint, Line, Mirror, OrthogonalLine, Intersect, Translate, Polygon, Semicircle, Circle, and Segment. It is suitable for high school students and teachers for learning geometric constructions and spatial reasoning.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. LineBisector(M, O) → a_2
  3. OrthogonalVector(u) → v
  4. Midpoint(E, B) → D
  5. Line(A, B) → m
  6. Line(F, m) → h
  7. Mirror(h, D) → h'
  8. Line(D, h') → j
  9. Line(J, j) → l_1
  10. OrthogonalLine(W_2, l_1) → e_4
  11. Intersect(e_4, l_1) → Z_2
  12. Midpoint(Z_2, W_2) → A_3
  13. Intersect(a_2, j) → L_1
  14. Translate(M_1, Vector[(0.05 * u)]) → V_1
  15. Mirror(V_1, D) → B_2
  16. Translate(B_2, Vector[(0.05 * u)]) → J_2
  17. Mirror(M_1, j) → O_1
  18. Translate(O_1, Vector[(0.05 * u)]) → S_1
  19. Mirror(S_1, D) → W_1
  20. Translate(W_1, Vector[(0.05 * u)]) → G_2
  21. Mirror(M_1, a_2) → N_1
  22. Translate(N_1, Vector[(0.05 * u)]) → U_1
  23. Mirror(U_1, D) → A_2
  24. Translate(A_2, Vector[(0.05 * u)]) → I_2
  25. Mirror(N_1, j) → P_1
  26. Translate(P_1, Vector[(0.05 * u)]) → T_1
  27. Mirror(T_1, D) → Z_1
  28. Translate(Z_1, Vector[(0.05 * u)]) → H_2
  29. Polygon(G_2, H_2, I_2, J_2) → q6''', i_4, j_4, k_4, l_4
  30. Mirror(G_2, i_4) → O_2
  31. Semicircle(N_1, M_1) → c_3
  32. Translate(c_3, Vector[(0.05 * u)]) → k_3
  33. OrthogonalLine(O, j) → n
  34. Intersect(k_3, n) → C_2,
  35. OrthogonalLine(K, j) → k
  36. Intersect(k, h) → N
  37. Line(H, N) → s
  38. OrthogonalLine(M, j) → l
  39. Intersect(l, j) → D_1
  40. Mirror(E_1, D_1) → F_1
  41. Line(F_1, s) → b_2
  42. Line(E_1, b_2) → e_2
  43. Intersect(k, l_1) → G_1
  44. OrthogonalLine(I_1, l_1) → m_1
  45. Intersect(b_2, m_1) → J_1
  46. OrthogonalLine(H_1, l_1) → p_1
  47. Intersect(e_2, p_1) → K_1
  48. Line(E, m) → f
  49. Intersect(k, f) → A_1
  50. OrthogonalLine(B, f) → g
  51. Intersect(g, f) → C_4
  52. OrthogonalLine(G, m) → i
  53. Polygon(E, C_4, B, A) → q2, e, c, b, a
  54. OrthogonalLine(L, j) → p
  55. Intersect(k, j) → Q
  56. Intersect(i, f) → S
  57. LineBisector(U, T) → q
  58. Intersect(k, q) → P
  59. LineBisector(Q, N) → r
  60. Line(J, s) → t
  61. Intersect(t, r) → R
  62. Line(V, i) → d
  63. Intersect(d, q) → I
  64. Line(U, W) → f_1
  65. Line(I, f_1) → g_1
  66. OrthogonalLine(W, g_1) → h_1
  67. Intersect(h_1, g_1) → Z
  68. Semicircle(W, Z) → c_1
  69. Semicircle(Q, N) → d_1
  70. Semicircle(H, J) → e_1
  71. Semicircle(T, U) → k_1
  72. Polygon(W, Z, I, U) → q1, w, z_1, i_1, u_1
  73. Polygon(I, U, T, R, Q) → poly1, i_2, u_2, t_1, r_1, q_1
  74. Polygon(J, R, Q, N, H) → poly2, j_1, r_2, q_2, n_1, h_2
  75. Semicircle(B_1, C_1) → s_1
  76. Semicircle(E_1, F_1) → c_2
  77. Semicircle(I_1, H_1) → d_2
  78. Polygon(C_1, E_1, F_1, B_1) → q3, a_1, b_1, f_2, g_2
  79. Polygon(E_1, K_1, J_1, F_1) → q4, j_2, k_2, l_2, m_2
  80. Polygon(J_1, K_1, H_1, I_1) → q5, n_2, p_2, s_2, t_2
  81. Mirror(c_3, j) → d_3
  82. Polygon(O_1, P_1, N_1, M_1) → q6, o_1, f_3, g_3, h_3
  83. Circle(Q_1, R_1) → e_3
  84. Polygon(S_1, T_1, U_1, V_1) → q6', i_3, j_3, l_3, v_1
  85. Mirror(k_3, j) → p_3
  86. Mirror(k_3, D) → q_3
  87. Polygon(W_1, Z_1, A_2, B_2) → q6'', w_1, m_3, n_3, r_3
  88. Mirror(q_3, j) → s_3
  89. Intersect(r, j_3) → D_2
  90. Line(C_2, E_2) → t_3
  91. Line(D_2, t_3) → a_3
  92. Intersect(a_3, m_3) → F_2
  93. Polygon(D_2, F_2, E_2, C_2) → q7, b_3, f_4, g_4, h_4
  94. Translate(s_3, Vector[(0.05 * u)]) → c_4
  95. Mirror(G_2, h') → K_2
  96. Mirror(H_2, h') → L_2
  97. Mirror(I_2, h') → M_2
  98. Mirror(J_2, h') → N_2
  99. Polygon(K_2, L_2, M_2, N_2) → q8, m_4, n_4, p_4, q_4
  100. Mirror(c_4, h') → d_4
  101. Mirror(H_2, i_4) → P_2
  102. Intersect(j, q6''') → Q_2, R_2
  103. Line(Q_2, a_3) → r_4
  104. Intersect(r_4, q6''') → S_2, T_2
  105. Line(U_2, Q_2) → s_4
  106. OrthogonalLine(U_2, s_4) → t_4
  107. Line(V_2, s_4) → a_4
  108. LineBisector(T_2, O_2) → b_4
  109. Segment(D_3, A_3) → f_5
  110. OrthogonalLine(A_3, f_5) → g_5
  111. Intersect(g_5, b_4) → B_3
  112. Vector(A_3, B_3) → v_2
  113. Line(C_3, f_5) → h_5
  114. Semicircle(U_2, V_2) → c_5
  115. Semicircle(C_3, A_3) → d_5
  116. Intersect(a_4, h_5) → E_3
  117. Polygon(V_2, E_3, T_2, U_2) → q9, i_5, j_5, k_5, l_5
  118. Polygon(C_3, A_3, D_3, E_3) → q10, m_5, n_5, p_5, q_5
  119. Polygon(E_3, T_2, D_3) → t1, r_5, s_5, t_5
  120. OrthogonalLine(B_4, b) → a_5
  121. Intersect(a_5, f) → F_3
  122. OrthogonalLine(G_3, f) → e_5
  123. Intersect(e_5, f) → H_3
  124. Polygon(F_3, H_3, G_3, B_4) → c1, b_5, f_6, g_6, h_6
  125. Translate(F_3, Vector[(0.07 * u)]) → I_3
  126. Translate(H_3, Vector[(0.07 * u)]) → J_3
  127. Translate(G_3, Vector[(0.07 * u)]) → K_3
  128. Translate(B_4, Vector[(0.07 * u)]) → L_3
  129. Polygon(I_3, J_3, K_3, L_3) → c1', i_6, j_6, k_6, l_6