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Logo DIA Geometric Construction

Logo DIA Geometric Construction
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2019-06-22 04:28
PolygonAngleVectorGeometric Construction
This example demonstrates how to construct the Logo DIA using GeoGebra, involving core math concepts like 2D vectors, angles, area, geometry, sine, vector addition, right triangles, midpoints, rotation, etc. Key GeoGebra commands and objects used include Vector, OrthogonalVector, Polygon, Line, OrthogonalLine, Mirror, Intersect, Rotate, Angle, CircleArc, Circle, PolyLine, Midpoint, Semicircle, etc. Suitable for high school mathematics teaching, illustrating geometric transformations and vector applications.

GeoGebra Commands & Parameters

  1. Vector(A, B) → w
  2. OrthogonalVector(w) → u_1
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Vector(A, C) → u
  5. Line(A, C) → j
  6. OrthogonalLine(B, j) → k
  7. Mirror(M, k) → M'
  8. Line(M', f) → n
  9. Line(M, n) → q
  10. Intersect(k, j) → F
  11. OrthogonalLine(F, q) → t_1
  12. Mirror(W, t_1) → W'
  13. Mirror(B_2, S) → C_2
  14. Mirror(E, k) → E'
  15. Rotate(E', 6°, F) → E''_2
  16. Line(E''_2, F) → m
  17. Intersect(h, m) → K
  18. Mirror(K, k) → K'_1
  19. Mirror(K, j) → K'
  20. Mirror(K', k) → K''
  21. Rotate(E', 90°, F) → E''
  22. Rotate(E'', 12°, F) → E'''
  23. Line(F, E''') → b
  24. Intersect(b, i) → R
  25. Mirror(R, j) → R'_1
  26. Mirror(R, k) → R'
  27. Mirror(R', j) → R''
  28. OrthogonalVector(u) → v
  29. Rotate(E', (-(90°)), F) → E''_1
  30. Polygon(E, E''_1, E', E'') → q1, e, e''_1, e', e''
  31. Angle(E'', F, E''') → α
  32. Line(E''', F) → l
  33. Intersect(l, e'') → H
  34. Mirror(H, k) → H'
  35. CircleArc(J, H', H) → d
  36. Angle(E', F, E''_2) → β
  37. CircleArc(L, K', K) → p
  38. Mirror(N, F) → N'
  39. Polygon(M, N, M', N') → q2, m_1, n_1, m', n'
  40. OrthogonalLine(M, q) → r
  41. Line(O, n) → s
  42. Intersect(r, s) → P
  43. Circle(O, P) → t
  44. CircleArc(I, R', R) → c
  45. Mirror(c, j) → c'
  46. Mirror(d, j) → d'
  47. Mirror(p, k) → p'
  48. Mirror(t, j) → t'
  49. Mirror(E''', j) → Q
  50. Polygon(K, R', R, K'_1, K'', R'_1, R'', K') → poly2, f_1, g_1, i_1, j_1, k_1, l_1, p_1, q_1
  51. Mirror(H, j) → H'_1
  52. Mirror(H', j) → H''
  53. Polygon(E', H', H, E, H'_1, H'') → poly3, a, h', h_1, e_1, h'_1, h''
  54. Mirror(d_4, j) → c_1
  55. Mirror(H', k) → H''_1
  56. Mirror(L, k) → L'
  57. Mirror(H'', k) → H'''
  58. PolyLine(H, E, H'_1) → s_1
  59. Mirror(H, k) → H'_2
  60. Mirror(E, k) → E'_1
  61. Mirror(H'_1, k) → G
  62. PolyLine(H'_2, E'_1, G) → r_1
  63. OrthogonalLine(S, t_1) → a_1
  64. Mirror(T, t_1) → T'
  65. Polygon(U, V, T', T) → q3, u_2, v_1, b_1, t_2
  66. Midpoint(Z, W) → A_1
  67. OrthogonalLine(A_1, r) → d_1
  68. Mirror(C_1, d_1) → D_1
  69. Mirror(E_1, d_1) → F_1
  70. Semicircle(D_1, D_1) → c_2
  71. Semicircle(C_1, D_1) → d_2
  72. Mirror(G_1, d_1) → H_1
  73. Semicircle(G_1, H_1) → e_2
  74. Polygon(Z, A_1, B_1, E_1, G_1, C_1) → poly4, z_1, g_2, h_2, i_2, j_2, k_2
  75. Mirror(Z, d_1) → Z'
  76. Mirror(A_1, d_1) → I_1
  77. Mirror(B_1, d_1) → J_1
  78. Mirror(E_1, d_1) → K_1
  79. Mirror(G_1, d_1) → L_1
  80. Mirror(C_1, d_1) → M_1
  81. Polygon(Z', I_1, J_1, K_1, L_1, M_1) → poly4', z', l_2, m_2, n_2, p_2, q_2
  82. OrthogonalLine(W', d_1) → f_2
  83. Intersect(e_2, f_2) → N_1,
  84. Polygon(E_1, G_1, H_1, F_1) → q4, r_2, s_2, a_2, b_2
  85. OrthogonalLine(V, f_2) → f_3
  86. Intersect(f_2, f_3) → P_1
  87. Midpoint(P_1, W') → Q_1
  88. Line(Q_1, a_1) → g_3
  89. Circle(O_1, Q_1) → c_3
  90. Rotate(Q_1, 60°, W') → R_1
  91. Angle(Q_1, W', R_1) → γ
  92. Line(W', R_1) → h_3
  93. Intersect(c_3, h_3) → S_1, T_1
  94. Circle(O_1, U_1) → d_3
  95. Polygon(Q_1, W', S_1) → t1, i_3, j_3, w'
  96. Polygon(G_1, V_1, C_1) → t2, k_3, l_3, m_3
  97. Mirror(G_1, d_1) → W_1
  98. Mirror(V_1, d_1) → Z_1
  99. Mirror(C_1, d_1) → A_2
  100. Polygon(W_1, Z_1, A_2) → t2', n_3, w_1, p_3
  101. Polygon(E_2, D_2, F_2, G_2) → q5, q_3, r_3, s_3, t_3