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Logo SPIUK 几何作图范例

Logo SPIUK 几何作图范例
几何画板及绘图内容加载中，请稍等……
2019-10-14 19:43
圆多边形向量变换几何作图
①本范例演示了如何通过 GeoGebra 构造 Logo SPIUK 的几何图形；②涉及的核心数学概念包括向量、角度、圆、多边形、几何变换等；③作图要点：使用了 Vector（向量）、LineBisector（角平分线）、OrthogonalVector（正交向量）、Midpoint（中点）、Line（直线）、Mirror（镜像）、OrthogonalLine（正交线）、Intersect（交点）、Translate（平移）、Polygon（多边形）、Semicircle（半圆）、Circle（圆）、Segment（线段）等命令和对象；④适合高中阶段学生学习和教师教学演示，可用于几何作图和空间想象能力的培养。

GeoGebra 命令及参数

  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