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MAHOU标志

MAHOU标志
几何画板及绘图内容加载中，请稍等……
2020-10-18 04:06
圆向量变换
这个GeoGebra范例演示了一个MAHOU标志的几何构造。涉及的核心数学概念包括向量、角度、圆和变换。通过使用Vector、OrthogonalVector、LineBisector等命令，可以构造出标志中的关键元素。适合高中学生或数学爱好者学习几何作图和变换。

GeoGebra 命令及参数

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. LineBisector(A_1, A) → l
  4. Line(A, B) → s
  5. OrthogonalLine(D, s) → i
  6. OrthogonalLine(A, s) → b
  7. OrthogonalLine(I, b) → h
  8. OrthogonalLine(F, b) → f
  9. Mirror(f, l) → f'
  10. Intersect(i, f') → E
  11. Mirror(f, l) → f'_1
  12. OrthogonalLine(Q, f'_1) → n
  13. Intersect(n, h) → Z
  14. Translate(Z, Vector[(0.232 * u)]) → Z'
  15. Translate(Z', Vector[(0.24 * u)]) → Z''_2
  16. OrthogonalLine(L, f'_1) → k
  17. OrthogonalLine(R, b) → q
  18. Intersect(k, q) → S
  19. LineBisector(M, S) → t
  20. Intersect(t, i) → T
  21. LineBisector(A, B) → m
  22. OrthogonalLine(B, u, xOyPlane) → g
  23. Mirror(i, m) → i'
  24. Intersect(m, f) → G
  25. Intersect(i', f') → P
  26. OrthogonalLine(A_1, b) → r
  27. Intersect(m, l) → K
  28. Intersect(i, l) → J
  29. Intersect(g, r) → C
  30. Mirror(F, l) → F'
  31. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  32. Intersect(i', f) → J_1
  33. Mirror(E, l) → E'
  34. OrthogonalLine(H, b) → j
  35. OrthogonalLine(M, b) → p
  36. CircleArc(T, S, M) → c
  37. Intersect(k, h) → W
  38. Polygon(W, Z, V, O, N, M, S) → poly1, w, z_1, v_1, o, n_1, m_1, s_1
  39. LineBisector(O, V) → a
  40. Intersect(a, p) → U
  41. Intersect(m, a) → B_1
  42. Vector(U, B_1) → e
  43. CircleArc(C_1, V, O) → d
  44. Translate(W, Vector[(0.232 * u)]) → W'
  45. Translate(V, Vector[(0.232 * u)]) → V'
  46. Translate(O, Vector[(0.232 * u)]) → O'
  47. Translate(N, Vector[(0.232 * u)]) → N'
  48. Translate(M, Vector[(0.232 * u)]) → M'
  49. Translate(S, Vector[(0.232 * u)]) → S'
  50. Polygon(Translate[W, Vector[(0.24 * u)]], Translate[Z, Vector[(0.24 * u)]], Translate[V, Vector[(0.24 * u)]], Translate[O, Vector[(0.24 * u)]], Translate[N, Vector[(0.24 * u)]], Translate[M, Vector[(0.24 * u)]], Translate[S, Vector[(0.24 * u)]]) → poly1', j_2, k_2, l_2, m_2, n_2, p_2, q_2
  51. Translate(d, Vector[(0.234 * u)]) → d'
  52. Translate(c, Vector[(0.23 * u)]) → c'
  53. Translate(W', Vector[(0.24 * u)]) → W''_2
  54. Translate(V', Vector[(0.24 * u)]) → V''_2
  55. Translate(O', Vector[(0.24 * u)]) → O''_2
  56. Translate(N', Vector[(0.24 * u)]) → N''_2
  57. Translate(M', Vector[(0.24 * u)]) → M''
  58. Translate(S', Vector[(0.24 * u)]) → S''
  59. Polygon(W''_2, Z''_2, V''_2, O''_2, N''_2, M'', S'') → poly1'', w''_2, z''_2, v''_2, o''_2, n''_2, m'', s''
  60. Translate(d', Vector[(0.24 * u)]) → d''
  61. Translate(c', Vector[(0.24 * u)]) → c''
  62. Polygon(G_1, F_1, E_1, D_1) → q1, g_1, f_1, h_1, d_1
  63. LineBisector(F_1, E_1) → i_1
  64. Intersect(i_1, g_1) → I_1
  65. LineBisector(N_1, D_1) → j_1
  66. Intersect(j_1, l) → H_1
  67. Polygon(F_1, W''_2, E_1) → t1, l_1, p_1, q_1
  68. Line(E_1, D_1) → r_1
  69. Line(V''_2, Z''_2) → t_1
  70. Intersect(r_1, t_1) → K_1
  71. Polygon(Z''_2, K_1, E_1) → t2, b_1, f_2, g_2
  72. Intersect(i_1, j) → L_1
  73. Vector(I_1, L_1) → u_1
  74. CircleArc(M_1, F_1, E_1) → c_1
  75. Intersect(j_1, f) → O_1
  76. Vector(H_1, O_1) → w_1
  77. CircleSector(P_1, N_1, D_1) → k_1
  78. Intersect(n, q) → Q_1
  79. LineBisector(F, H) → r_2
  80. Circle(R_1, S_1) → c_2
  81. Rotate(S_1, 72°, R_1) → T_1
  82. Angle(S_1, R_1, T_1) → α
  83. Rotate(T_1, 72°, R_1) → U_1
  84. Angle(T_1, R_1, U_1) → β
  85. Rotate(U_1, 72°, R_1) → W_1
  86. Angle(U_1, R_1, W_1) → γ
  87. Rotate(W_1, 72°, R_1) → Z_1
  88. Angle(W_1, R_1, Z_1) → δ
  89. Polygon(Z_1, T_1, W_1, S_1, U_1) → poly2, s_2, t_2, d_2, f_3, g_3
  90. Intersect(s_2, poly2) → A_2, B_2, C_2, D_2
  91. Intersect(t_2, poly2) → E_2, F_2, G_2, H_2
  92. Intersect(g_3, poly2) → I_2, J_2, K_2, L_2
  93. Polygon(B_2, C_2, F_2, G_2, K_2) → poly3, h_3, i_3, j_3, k_3, l_3
  94. Translate(Z_1, Vector[(0.18 * u)]) → M_2
  95. Translate(T_1, Vector[(0.18 * u)]) → N_2
  96. Translate(W_1, Vector[(0.18 * u)]) → O_2
  97. Translate(S_1, Vector[(0.18 * u)]) → P_2
  98. Translate(U_1, Vector[(0.18 * u)]) → Q_2
  99. Translate(Z_1, Vector[(0.2 * u)]) → R_2
  100. Translate(T_1, Vector[(0.2 * u)]) → S_2
  101. Translate(W_1, Vector[(0.2 * u)]) → T_2
  102. Translate(S_1, Vector[(0.2 * u)]) → U_2
  103. Translate(U_1, Vector[(0.2 * u)]) → V_2
  104. Polygon(Translate[Z_1, Vector[(0.18 * u)]], Translate[T_1, Vector[(0.18 * u)]], Translate[W_1, Vector[(0.18 * u)]], Translate[S_1, Vector[(0.18 * u)]], Translate[U_1, Vector[(0.18 * u)]]) → poly2', m_3, n_3, p_3, q_3, i_5
  105. Translate(B_2, Vector[(0.2 * u)]) → W_2
  106. Translate(C_2, Vector[(0.2 * u)]) → Z_2
  107. Translate(F_2, Vector[(0.2 * u)]) → A_3
  108. Translate(G_2, Vector[(0.2 * u)]) → B_3
  109. Translate(K_2, Vector[(0.2 * u)]) → C_3
  110. Polygon(Translate[B_2, Vector[(0.18 * u)]], Translate[C_2, Vector[(0.18 * u)]], Translate[F_2, Vector[(0.18 * u)]], Translate[G_2, Vector[(0.18 * u)]], Translate[K_2, Vector[(0.18 * u)]]) → poly3', r_3, s_3, b_3, j_5, k_5
  111. Translate(R_2, Vector[(0.2 * u)]) → D_3
  112. Translate(S_2, Vector[(0.2 * u)]) → E_3
  113. Translate(T_2, Vector[(0.2 * u)]) → F_3
  114. Translate(U_2, Vector[(0.2 * u)]) → G_3
  115. Translate(V_2, Vector[(0.2 * u)]) → H_3
  116. Translate(poly2', Vector[(0.18 * u)]) → poly2''
  117. Translate(W_2, Vector[(0.2 * u)]) → I_3
  118. Translate(Z_2, Vector[(0.2 * u)]) → J_3
  119. Translate(A_3, Vector[(0.2 * u)]) → K_3
  120. Translate(B_3, Vector[(0.2 * u)]) → L_3
  121. Translate(C_3, Vector[(0.2 * u)]) → M_3
  122. Translate(poly3', Vector[(0.18 * u)]) → poly3''
  123. Translate(D_3, Vector[(0.2 * u)]) → N_3
  124. Translate(E_3, Vector[(0.2 * u)]) → O_3
  125. Translate(F_3, Vector[(0.2 * u)]) → P_3
  126. Translate(G_3, Vector[(0.2 * u)]) → Q_3
  127. Translate(H_3, Vector[(0.2 * u)]) → R_3
  128. Translate(poly2'', Vector[(0.18 * u)]) → poly2'''
  129. Translate(I_3, Vector[(0.2 * u)]) → S_3
  130. Translate(J_3, Vector[(0.2 * u)]) → T_3
  131. Translate(K_3, Vector[(0.2 * u)]) → U_3
  132. Translate(L_3, Vector[(0.2 * u)]) → V_3
  133. Translate(M_3, Vector[(0.2 * u)]) → W_3
  134. Translate(poly3'', Vector[(0.18 * u)]) → poly3'''
  135. Translate(O_3, Vector[(0.18 * u)]) → A_4
  136. Translate(P_3, Vector[(0.18 * u)]) → B_4
  137. Translate(Q_3, Vector[(0.18 * u)]) → C_4
  138. Translate(R_3, Vector[(0.18 * u)]) → D_4
  139. Translate(poly2''', Vector[(0.18 * u)]) → poly4
  140. Translate(S_3, Vector[(0.18 * u)]) → E_4
  141. Translate(T_3, Vector[(0.18 * u)]) → F_4
  142. Translate(U_3, Vector[(0.18 * u)]) → G_4
  143. Translate(V_3, Vector[(0.18 * u)]) → H_4
  144. Translate(W_3, Vector[(0.18 * u)]) → I_4
  145. Translate(poly3''', Vector[(0.18 * u)]) → poly5
  146. LineBisector(V, O) → t_3
  147. Intersect(n, q) → J_4
  148. Polygon(V, U, J_4) → t4, j_4, v_2, u_2

AI 绘图提示语参考

绘制一个由几何变换构成的标志图形。先画一条线段作为基准，并取其垂直方向。构造该线段的垂直平分线，以及过端点与基准线垂直的直线。利用对称与平移，在基准线两侧生成一系列平行线，并求交点以确定关键点。连接这些点形成两个多边形：一个四边形和一个七边形。再以某些点为圆心，绘制两段圆弧，使它们与多边形的边相切或相交。整体图形呈现对称与旋转的组合，体现矢量与圆形的几何美感。
以上提示语为根据原始绘图命令整理而来，仅供参考。