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BP标志

BP标志
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2019-05-09 00:13
多边形向量几何作图
这个GeoGebra范例演示了BP标志的几何构造。涉及的核心数学概念包括向量、旋转、椭圆和对称性。通过使用Circle, Vector, Rotate, Line, LineBisector, OrthogonalLine, Intersect, Midpoint, CircleArc, Mirror, Segment, Polygon, Sequence等命令，构造了标志的几何形状。适合用于高中几何教学或学生练习几何作图。

GeoGebra 命令及参数

  1. Circle(O, A) → c
  2. Vector(O, A) → u
  3. Rotate(E, (-(20°)), O) → E'
  4. Circle(O, E) → d
  5. Rotate(E', (-(20°)), O) → E''
  6. Rotate(E'', (-(20°)), O) → E'''
  7. Rotate(E''', (-(20°)), O) → F
  8. Rotate(F, (-(20°)), O) → F'
  9. Circle(O, D) → p
  10. Line(E, O) → g
  11. Circle(O, B) → r
  12. Circle(O, C) → s
  13. LineBisector(O, E) → l
  14. OrthogonalLine(E'', l) → k
  15. Intersect(k, l) → G
  16. Intersect(p, l) → I, J
  17. Midpoint(I, G) → H
  18. Vector(G, H) → v
  19. CircleArc(K, E, O) → e
  20. Rotate(e, (-(20°)), O) → e'
  21. Rotate(e', (-(20°)), O) → e''
  22. Mirror(e, g) → e'_1
  23. Rotate(e'', (-(20°)), O) → e'''
  24. Rotate(e''', (-(20°)), O) → h
  25. Rotate(h, (-(20°)), O) → h'
  26. Rotate(h', (-(20°)), O) → h''
  27. Rotate(h'', (-(20°)), O) → h'''
  28. Rotate(h''', (-(20°)), O) → f
  29. Rotate(f, (-(20°)), O) → f'
  30. Rotate(f', (-(20°)), O) → f''
  31. Rotate(f'', (-(20°)), O) → f'''
  32. Rotate(f''', (-(20°)), O) → q
  33. Rotate(q, (-(20°)), O) → q'
  34. Rotate(q', (-(20°)), O) → q''
  35. Rotate(q'', (-(20°)), O) → q'''
  36. Rotate(q''', (-(20°)), O) → t
  37. Rotate(e, 20°, O) → e'_2
  38. Rotate(e'_1, 20°, O) → c_1
  39. Rotate(e'_1, (-(20°)), O) → d_1
  40. Intersect(e'_1, e') → L, M, ,
  41. Intersect(e'_1, e'') → N, P, ,
  42. Intersect(c_1, e'') → Q, R, ,
  43. Intersect(e''', e'_1) → S, T, ,
  44. Intersect(c_1, e) → W, Z, ,
  45. CircleArc(K, W, O) → e_1
  46. Rotate(e_1, (-(20°)), O) → f_1
  47. Line(W, O) → i
  48. Mirror(e_1, i) → g_1
  49. Mirror(e_1, g) → h_1
  50. Mirror(K, g) → K'
  51. Line(E', O) → j
  52. Circle(O, T) → s_1
  53. Intersect(s_1, e'') → A_1, , ,
  54. Segment(A_1, T) → m
  55. Mirror(T, m) → T'
  56. Mirror(N, g) → N'_1
  57. Mirror(T, g) → T'_1
  58. CircleArc(K, N'_1, T'_1) → k_1
  59. Mirror(k_1, g) → p_1
  60. Polygon(T, A_1, N) → t1, n, t_1, a_1
  61. Mirror(p_1, j) → q_1
  62. Mirror(T, g) → T'_2
  63. Mirror(T, g) → T'_3
  64. Mirror(A_1, g) → C_1
  65. Mirror(N, g) → N'_2
  66. Polygon(T'_3, C_1, N'_2) → t1', n'_2, t'_3, a
  67. Mirror(q_1, g) → r_1
  68. Mirror(T, m) → T'_4
  69. Mirror(A_1, m) → D_1
  70. Mirror(N, m) → N'_3
  71. Mirror(N, m) → N'_4
  72. Mirror(T, m) → T'_5
  73. Mirror(N, m) → N'_5
  74. Mirror(T, m) → T'_6
  75. Mirror(N, m) → N'
  76. Mirror(T'_4, g) → B_1
  77. Mirror(D_1, g) → E_1
  78. Mirror(N'_3, g) → F_1
  79. Rotate(k_1, (-(20°)), O) → e_2
  80. Mirror(e_2, g) → f_2
  81. Rotate(T'_3, (-(20°)), O) → G_1
  82. Rotate(C_1, (-(20°)), O) → H_1
  83. Rotate(N'_2, (-(20°)), O) → I_1
  84. Polygon(G_1, H_1, I_1) → t1'', n_1, g_2, h_2
  85. Rotate(F_1, (-(20°)), O) → J_1
  86. Rotate(B_1, (-(20°)), O) → K_1
  87. Rotate(B_1, 20°, O) → N_1
  88. Rotate(E_1, 20°, O) → O_1
  89. Rotate(F_1, 20°, O) → P_1
  90. Rotate(B_1, (-(20°)), O) → Q_1
  91. Rotate(E_1, (-(20°)), O) → R_1
  92. Rotate(F_1, (-(20°)), O) → S_1
  93. Rotate(r_1, 20°, O) → c_3
  94. Rotate(k_1, 20°, O) → d_3
  95. Rotate(T'_3, 20°, O) → T_1
  96. Rotate(C_1, 20°, O) → U_1
  97. Rotate(N'_2, 20°, O) → V_1
  98. Polygon(T_1, U_1, V_1) → t1''_1, v_1, a_2, u_1
  99. Rotate(e_1, 20°, O) → e_3
  100. Rotate(g_1, 20°, O) → f_3
  101. Mirror(e_3, g) → g_3
  102. Mirror(f_3, g) → h_3
  103. Mirror(d_3, g) → k_3
  104. Mirror(T_1, g) → W_1
  105. Mirror(U_1, g) → Z_1
  106. Mirror(V_1, g) → A_2
  107. Polygon(W_1, Z_1, A_2) → t3, b_2, w_1, z_1
  108. Mirror(N_1, g) → B_2
  109. Mirror(O_1, g) → C_2
  110. Mirror(P_1, g) → D_2
  111. Rotate(q_1, (-(20°)), O) → q_3
  112. Circle(O, S_1) → s_3
  113. Mirror(e_2, i) → c_2
  114. Sequence(Rotate[d_1, ((20 * λ))°, O], λ, 1, 18) → l1
  115. Sequence(Rotate[h_3, ((20 * β))°, O], β, 1, 16) → l2
  116. Rotate(l2, 20°, O) → l2'
  117. Sequence(Rotate[g_3, ((-((20 * α))))°, O], α, 1, 16) → l3
  118. Sequence(Rotate[q_3, ((-20 * β))°, O], β, 1, 16) → l4
  119. Sequence(Rotate[k_3, ((-20 * β))°, O], β, 1, 16) → l5
  120. Sequence(Polygon[Rotate[W_1, ((-20 * β))°, O], Rotate[Z_1, ((-20 * β))°, O], Rotate[A_2, ((-20 * β))°, O]], β, 1, 16) → l6
  121. LineBisector(S_1, A_1) → b
  122. OrthogonalLine(E''', b) → i_1
  123. Intersect(i_1, b) → U
  124. CircleArc(U, A_1, S_1) → d_2
  125. Mirror(d_2, g) → k_2
  126. Rotate(k_2, (-(20°)), O) → p_2
  127. Sequence(Rotate[k_2, ((-((20 * β))))°, O], β, 1, 19) → l7
  128. Sequence(Rotate[d_2, ((-((20 * β))))°, O], β, 1, 19) → l8
  129. Rotate(S_1, (-(20°)), O) → V
  130. Polygon(A_1, S_1, V) → t2, v_2, j_1, l_1
  131. Sequence(Polygon[Rotate[A_1, ((-((20 * α))))°, O], Rotate[S_1, ((-((20 * α))))°, O], Rotate[V, ((-((20 * α))))°, O]], α, 1, 19) → l9
  132. Segment(E, I_1) → m_1
  133. Sequence(Segment[Rotate[E, ((-((20 * θ))))°, O], Rotate[I_1, ((-((20 * θ))))°, O]], θ, 1, 19) → l10