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Levi's Logo Geometric Construction

Levi's Logo Geometric Construction
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2019-10-26 23:40
CircleVectorGeometric Construction
This example demonstrates how to construct the Levi's Logo geometrically using GeoGebra. It involves core mathematical concepts like vectors, midpoints, line segments, circles, reflections, and geometric constructions. Key GeoGebra commands and objects used include Vector, OrthogonalVector, Midpoint, Line, OrthogonalLine, Intersect, Mirror, LineBisector, Segment, CurveCartesian, Polygon, Semicircle, CircleArc, Circle. Suitable for high school mathematics education to showcase geometric construction techniques and applications of spatial geometric relationships.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. Midpoint(E, B) → D
  4. Line(A, B) → m
  5. OrthogonalLine(G, m) → i
  6. Line(F, m) → h
  7. Intersect(i, h) → H
  8. Mirror(h, D) → h'
  9. Line(D, h') → j
  10. Line(Q, j) → k
  11. Mirror(k, j) → k'
  12. OrthogonalLine(D, m) → p_1
  13. OrthogonalLine(W', k') → r
  14. Intersect(r, j) → T_2
  15. Intersect(r, h') → W_2
  16. Mirror(S, p_1) → S'
  17. LineBisector(V_1, W') → l_3
  18. Intersect(l_3, h') → M
  19. Mirror(M, r) → T
  20. Mirror(Z_2, r) → A_3
  21. Mirror(A_3, T_2) → E_3
  22. Mirror(M_3, T_2) → N_3
  23. Mirror(M, T_2) → M'
  24. Segment(U_2, E_3) → t_3
  25. Mirror(U_2, T_2) → V_2
  26. CurveCartesian(((1 - t)^(4) * A_3) + (((4 * (1 - t)^(3)) * t) * D_3) + (((6 * (1 - t)^(2)) * t^(2)) * T_2) + (((4 * (1 - t)) * t^(3)) * Z_2) + (t^(4) * V_2), t, 0, 1) → w
  27. Mirror(w, T_2) → w'
  28. Intersect(t_3, w') → F_3, G_3, H_3, I_3
  29. Mirror(H_3, T_2) → O_3
  30. OrthogonalLine(S', k') → q
  31. Line(V_1, q) → c_1
  32. Intersect(c_1, k) → K_2
  33. Midpoint(M_2, N_2) → R_2
  34. LineBisector(M_2, N_2) → f_3
  35. Polygon(M_2, N_2, 4) → poly3, r_2, s_2, t_2, a_2, O_2, P_2
  36. Polygon(P_2, O_2, N_2, Q_2, R_2, M_2) → polígono1, g_3, o_2, h_3, i_3, j_3, k_3
  37. OrthogonalLine(S, h) → p
  38. Intersect(p, j) → C_1
  39. OrthogonalLine(W, j) → n
  40. Intersect(n, j) → B_1
  41. LineBisector(B_1, C_1) → t
  42. Mirror(D_1, t) → F_1
  43. Intersect(p, k) → P_1
  44. Intersect(n, k) → O_1
  45. Mirror(F_2, p_1) → G_2
  46. Line(E, m) → f
  47. OrthogonalLine(B, f) → g
  48. Intersect(g, f) → C
  49. Mirror(i, D) → i'
  50. Intersect(i, h') → I
  51. Polygon(F_2, G_2, B, A) → q2, a, b, c, e
  52. Intersect(l_3, k) → S_1
  53. Intersect(j, i') → U_1
  54. OrthogonalLine(R, h') → l
  55. Intersect(l, k') → V
  56. Mirror(D_1, j) → G_1
  57. Mirror(F_1, j) → H_1
  58. Intersect(l, k) → L_1
  59. Intersect(k', i) → M_1
  60. Intersect(l, h) → N_1
  61. Polygon(Q, L_1, N_1, Z, A_1, M_1) → poly1, q_1, l_1, n_1, z_1, a_1, m_1
  62. CurveCartesian(((1 - t)^(4) * D_1) + (((4 * (1 - t)^(3)) * t) * O_1) + (((6 * (1 - t)^(2)) * t^(2)) * I_1) + (((4 * (1 - t)) * t^(3)) * P_1) + (t^(4) * F_1), t, 0, 1) → s
  63. Mirror(s, j) → s'
  64. Mirror(K_1, t) → Q_1
  65. Semicircle(K_1, Q_1) → d_1
  66. OrthogonalLine(K_1, j) → f_1
  67. Intersect(f_1, j) → R_1
  68. Semicircle(Z_1, R_1) → e_1
  69. Polygon(D_1, F_1, C_1, B_1) → q1, g_1, h_1, i_1, b_1
  70. Line(G_1, k') → j_1
  71. Intersect(e_1, j_1) → A_2, B_2
  72. Polygon(B_1, R_1, B_2, G_1) → q3, k_1, r_1, b_2, s_1
  73. Line(P_1, D_2) → t_1
  74. Line(H_2, t_1) → f_2
  75. OrthogonalLine(I_2, j_1) → g_2
  76. Mirror(f_2, g_2) → h_2
  77. Line(C_2, h_2) → i_2
  78. Intersect(h_2, k) → E_2
  79. Intersect(i_2, k) → J_2
  80. Polygon(P_1, H_2, I_2, E_2, J_2, C_2, D_2) → poly2, j_2, k_2, l_2, e_2, m_2, c_2, d_2
  81. Intersect(q, k) → P
  82. Intersect(q, k') → W_1
  83. Intersect(k', c_1) → L_2
  84. Polygon(P, K_2, L_2, W_1) → q4, p_2, n_2, q_2, w_1
  85. Mirror(S_1, r) → S_2
  86. CurveCartesian(((1 - t)^(4) * M) + (((4 * (1 - t)^(3)) * t) * S_1) + (((6 * (1 - t)^(2)) * t^(2)) * T_1) + (((4 * (1 - t)) * t^(3)) * S_2) + (t^(4) * T), t, 0, 1) → d
  87. Mirror(T, T_2) → T'
  88. Mirror(d, j) → d'
  89. CircleArc(B_3, Z_2, A_3) → c_3
  90. Mirror(Z_2, T_2) → C_3
  91. Polygon(M, A_3, N_3, O_3, V_2, M', E_3, M_3, H_3, U_2) → poly4, m_3, j_4, n_3, p_3, q_3, r_3, s_3, e_3, h_4, i_4
  92. Mirror(c_3, j) → d_3
  93. LineBisector(H_3, E_3) → a_3
  94. Intersect(a_3, k') → J_3
  95. Intersect(a_3, h) → K_3
  96. LineBisector(M, U_2) → b_3
  97. CircleArc(L_3, M, U_2) → d_4
  98. Mirror(d_4, T_2) → e_4
  99. Segment(A_3, V_2) → f_4
  100. Polygon(H_3, E_3, M_3) → t1, k_4, l_4, m_4
  101. Mirror(H_3, T_2) → P_3
  102. Mirror(E_3, T_2) → Q_3
  103. Mirror(M_3, T_2) → R_3
  104. Polygon(P_3, Q_3, R_3) → t1', g_4, n_4, p_4
  105. Segment(H_3, M_3) → q_4
  106. Mirror(H_3, T_2) → S_3
  107. Mirror(M_3, T_2) → T_3
  108. Segment(S_3, T_3) → r_4
  109. Midpoint(A, B) → U_3
  110. LineBisector(A, U_3) → s_4
  111. Intersect(s_4, c) → V_3
  112. CircleArc(W_3, U_3, A) → c_4
  113. Mirror(c_4, p_1) → t_4
  114. Segment(A, B) → a_4
  115. Segment(Z_2, A_3) → b_4
  116. Mirror(Z_2, j) → Z_3
  117. Mirror(A_3, j) → A_4
  118. Segment(Z_3, A_4) → f_5
  119. Intersect(k, i') → B_4
  120. Midpoint(C_4, B_4) → D_4
  121. Circle(D_4, B_4) → c_5
  122. Circle(D_4, E_4) → d_5
  123. Mirror(F_4, k) → G_4
  124. Segment(G_4, F_4) → g_5
  125. Midpoint(G_4, F_4) → H_4
  126. OrthogonalLine(D_4, k) → h_5
  127. Mirror(F_4, h_5) → I_4
  128. Segment(D_4, I_4) → i_5
  129. CurveCartesian(((1 - t)^(3) * G_4) + (((3 * (1 - t)^(2)) * t) * J_4) + (((3 * (1 - t)) * t^(2)) * K_4) + (t^(3) * H_4), t, 0, 1) → o_1
  130. Segment(P_3, A_3) → j_5
  131. Segment(E_3, H_3) → k_5