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Levi's Logo 几何构造

Levi's Logo 几何构造
几何画板及绘图内容加载中，请稍等……
2019-10-26 23:40
圆向量几何作图
①本范例演示如何使用 GeoGebra 构造 Levi's Logo 的几何图形；②涉及的核心数学概念包括向量、中点、线段、圆、反射、几何作图等；③作图要点提炼自构造摘要，使用了 Vector, OrthogonalVector, Midpoint, Line, OrthogonalLine, Intersect, Mirror, LineBisector, Segment, CurveCartesian, Polygon, Semicircle, CircleArc, Circle 等命令和对象；④适合高中数学教学，用于展示几何作图技巧和空间几何关系的应用。

GeoGebra 命令及参数

  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