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数学与艺术的结合

数学与艺术的结合
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2016-05-09 04:43
多边形变换几何作图
这个范例展示了数学与艺术的完美结合。它通过几何图形和变换展示了数学中的几何作图和变换概念。使用了Line, Point, Polygon, Intersect, LineBisector, Mirror, Rotate, Circle, Segment, Dilate, Midpoint等GeoGebra命令。适合高中学生和数学爱好者学习和探索几何变换和图形构造。

GeoGebra 命令及参数

  1. Line(A, B) → l
  2. Point(l) → G
  3. Polygon(A, G, 8) → poly1, f, D, E, F, H, I, g, h, i, j, k, m, n, C
  4. Line(A, E) → p
  5. Line(D, I) → q
  6. Line(G, F) → r
  7. Intersect(p, q) → J
  8. Line(C, H) → s
  9. LineBisector(A, I) → t
  10. LineBisector(A, G) → a
  11. LineBisector(G, C) → b
  12. LineBisector(C, D) → c
  13. Polygon(I, G, 4) → poly2, d, e, f_1, g_1, K, L
  14. Polygon(A, C, 4) → poly3, h_1, i_1, j_1, k_1, M, N
  15. Intersect(t, d) → O
  16. Polygon(I, O, 4) → poly4, l_1, m_1, n_1, p_1, P, Q
  17. Intersect(a, d) → R
  18. Polygon(R, G, 4) → poly5, q_1, r_1, s_1, t_1, S, T
  19. Intersect(t, f_1) → U
  20. Polygon(D, U, 4) → poly6, a_1, b_1, c_1, d_1, V, W
  21. Intersect(a, f_1) → Z
  22. Polygon(Z, F, 4) → poly7, e_1, f_2, g_2, h_2, A_1, B_1
  23. Intersect(p, d) → C_1
  24. Mirror(C_1, A) → D_1
  25. Rotate(D_1, 60°, A) → E_1
  26. Mirror(E_1, p) → F_1
  27. Polygon(D_1, E_1, 6) → poly8, i_2, J_1, j_2, k_2, l_2, m_2, n_2, G_1, H_1, I_1
  28. LineBisector(T, R) → p_2
  29. Intersect(p, p_2) → K_1
  30. Intersect(a, p_2) → L_1
  31. Polygon(C_1, L_1, 4) → poly9, q_2, r_2, s_2, t_2, M_1, N_1
  32. Mirror(poly9, a) → poly9'
  33. Mirror(poly9', b) → poly9''
  34. Mirror(poly9'', c) → poly9'''
  35. Mirror(poly9''', t) → poly10
  36. Mirror(poly10, a) → poly10'
  37. Mirror(poly10', b) → poly10''
  38. Mirror(poly10'', c) → poly10'''
  39. Mirror(poly8, a) → poly8'
  40. Mirror(poly8', b) → poly8''
  41. Mirror(poly8'', c) → poly8'''
  42. Mirror(poly8''', t) → poly11
  43. Mirror(poly11, a) → poly11'
  44. Mirror(poly11', b) → poly11''
  45. Mirror(poly11'', c) → poly11'''
  46. Mirror(M_1, t) → O_1
  47. Mirror(O_1, c) → P_1
  48. Mirror(P_1, b) → Q_1
  49. Mirror(Q_1, a) → R_1
  50. Mirror(R_1, t) → S_1
  51. Mirror(S_1, c) → T_1
  52. Mirror(T_1, b) → U_1
  53. Mirror(U_1, a) → V_1
  54. Line(P_1, O_1) → a_2
  55. Intersect(t, a_2) → W_1
  56. Polygon(W_1, M_1, 4) → poly12, b_2, c_2, d_2, e_2, Z_1, A_2
  57. Mirror(poly12, a) → poly12'
  58. Mirror(poly12', r) → poly12''
  59. Mirror(poly12', s) → poly12''_1
  60. Mirror(poly12''_1, q) → poly13
  61. Mirror(poly13, p) → poly13'
  62. Mirror(poly13', r) → poly13''
  63. Mirror(poly13'', s) → poly13'''
  64. Circle(J, D_1) → c_3
  65. Line(J, L_1) → f_3
  66. Mirror(B, f_3) → B'
  67. LineBisector(G_1, E_1) → g_3
  68. Intersect(f_3, g_3) → B_2
  69. Mirror(G_1, f_3) → C_2
  70. Mirror(E_1, f_3) → D_2
  71. Line(N_1, O) → h_3
  72. Intersect(c_3, h_3, 2) → E_2
  73. Segment(F_1, E_2) → i_3
  74. Mirror(F_1, h_3) → F_2
  75. Mirror(E_2, h_3) → G_2
  76. Segment(F_2, G_2) → j_3
  77. Mirror(I_1, h_3) → H_2
  78. Point(g_3) → I_2
  79. Line(I_2, j_3) → k_3
  80. Intersect(h_3, k_3) → J_2
  81. Mirror(I_2, h_3) → K_2
  82. Line(K_2, m_2) → l_3
  83. Line(I_1, H_2) → m_3
  84. Intersect(l_3, m_3) → L_2
  85. Line(L_2, l_2) → n_3
  86. Point(n_3) → M_2
  87. Line(M_2, t_2) → p_3
  88. Intersect(p_3, h_3) → N_2
  89. Mirror(C_1, h_3) → O_2
  90. Line(N_1, O_2) → q_3
  91. Mirror(p_3, h_3) → r_3
  92. Mirror(n_3, h_3) → s_3
  93. Intersect(m_3, s_3) → P_2
  94. Line(N_1, J_2) → t_3
  95. Mirror(M_2, t_3) → Q_2
  96. Polygon(M_2, N_2, Q_2, P_2, I_2, J_2, K_2, L_2) → poly14, m_4, n_4, q_4, p_4, i_4, j_4, k_4, l_4
  97. Mirror(M_2, p) → R_2
  98. Mirror(N_2, p) → S_2
  99. Mirror(Q_2, p) → T_2
  100. Mirror(P_2, p) → U_2
  101. Mirror(I_2, p) → V_2
  102. Mirror(J_2, p) → W_2
  103. Mirror(K_2, p) → Z_2
  104. Mirror(L_2, p) → A_3
  105. Polygon(R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3) → poly14', r_4, s_4, t_4, u_2, v_2, w_2, z_2, a_3
  106. Mirror(R_2, r) → B_3
  107. Mirror(S_2, r) → C_3
  108. Mirror(T_2, r) → D_3
  109. Mirror(U_2, r) → E_3
  110. Mirror(V_2, r) → F_3
  111. Mirror(W_2, r) → G_3
  112. Mirror(Z_2, r) → H_3
  113. Mirror(A_3, r) → I_3
  114. Polygon(B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3) → poly14'', b_3, c_4, d_3, e_3, f_4, g_4, h_4, i_5
  115. Mirror(B_3, s) → J_3
  116. Mirror(C_3, s) → K_3
  117. Mirror(D_3, s) → L_3
  118. Mirror(E_3, s) → M_3
  119. Mirror(F_3, s) → N_3
  120. Mirror(G_3, s) → O_3
  121. Mirror(H_3, s) → P_3
  122. Mirror(I_3, s) → Q_3
  123. Polygon(J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3) → poly14''', j_5, k_5, l_5, m_5, n_5, o_3, p_5, q_5
  124. Mirror(J_3, q) → R_3
  125. Mirror(K_3, q) → S_3
  126. Mirror(L_3, q) → T_3
  127. Mirror(M_3, q) → U_3
  128. Mirror(N_3, q) → V_3
  129. Mirror(O_3, q) → W_3
  130. Mirror(P_3, q) → Z_3
  131. Mirror(Q_3, q) → A_4
  132. Polygon(R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4) → poly15, r_5, s_5, t_5, u_3, v_3, w_3, z_3, a_4
  133. Mirror(R_3, p) → B_4
  134. Mirror(S_3, p) → C_4
  135. Mirror(T_3, p) → D_4
  136. Mirror(U_3, p) → E_4
  137. Mirror(V_3, p) → F_4
  138. Mirror(W_3, p) → G_4
  139. Mirror(Z_3, p) → H_4
  140. Mirror(A_4, p) → I_4
  141. Polygon(B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4) → poly15', b_4, c_5, d_4, e_4, f_5, g_5, h_5, i_6
  142. Mirror(B_4, r) → J_4
  143. Mirror(C_4, r) → K_4
  144. Mirror(D_4, r) → L_4
  145. Mirror(E_4, r) → M_4
  146. Mirror(F_4, r) → N_4
  147. Mirror(G_4, r) → O_4
  148. Mirror(H_4, r) → P_4
  149. Mirror(I_4, r) → Q_4
  150. Polygon(J_4, K_4, L_4, M_4, N_4, O_4, P_4, Q_4) → poly15'', j_6, k_6, l_6, m_6, n_6, o_4, p_6, q_6
  151. Mirror(J_4, s) → R_4
  152. Mirror(K_4, s) → S_4
  153. Mirror(L_4, s) → T_4
  154. Mirror(M_4, s) → U_4
  155. Mirror(N_4, s) → V_4
  156. Mirror(O_4, s) → W_4
  157. Mirror(P_4, s) → Z_4
  158. Mirror(Q_4, s) → A_5
  159. Polygon(R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5) → poly15''', r_6, s_6, t_6, u_4, v_4, w_4, z_4, a_5
  160. Mirror(F_2, q) → B_5
  161. Mirror(G_2, q) → C_5
  162. Segment(B_5, C_5) → b_5
  163. Mirror(B_5, c) → D_5
  164. Mirror(C_5, c) → E_5
  165. Segment(D_5, E_5) → d_5
  166. Mirror(Z_4, s) → F_5
  167. Mirror(D_5, s) → G_5
  168. Mirror(E_5, s) → H_5
  169. Segment(G_5, H_5) → e_5
  170. Mirror(G_5, b) → I_5
  171. Mirror(H_5, b) → J_5
  172. Segment(I_5, J_5) → f_6
  173. Mirror(I_5, r) → K_5
  174. Mirror(J_5, r) → L_5
  175. Segment(K_5, L_5) → g_6
  176. Mirror(K_5, f_3) → M_5
  177. Mirror(L_5, f_3) → N_5
  178. Segment(M_5, N_5) → h_6
  179. Mirror(M_5, p) → O_5
  180. Mirror(N_5, p) → P_5
  181. Segment(O_5, P_5) → a_6
  182. Mirror(O_5, t_3) → Q_5
  183. Mirror(P_5, t_3) → R_5
  184. Segment(Q_5, R_5) → b_6
  185. Mirror(Q_5, q) → S_5
  186. Mirror(R_5, q) → T_5
  187. Segment(S_5, T_5) → c_6
  188. Mirror(S_5, c) → U_5
  189. Mirror(T_5, c) → V_5
  190. Segment(U_5, V_5) → d_6
  191. Mirror(U_5, s) → W_5
  192. Mirror(V_5, s) → Z_5
  193. Segment(W_5, Z_5) → e_6
  194. Mirror(W_5, b) → A_6
  195. Mirror(Z_5, b) → B_6
  196. Segment(A_6, B_6) → f_7
  197. Mirror(A_6, r) → C_6
  198. Mirror(B_6, r) → D_6
  199. Segment(C_6, D_6) → g_7
  200. Mirror(C_6, f_3) → E_6
  201. Mirror(D_6, f_3) → F_6
  202. Segment(E_6, F_6) → h_7
  203. Dilate(poly11''', 0.85, I) → poly16
  204. Dilate(poly11'', 0.85, H) → poly11'''_1
  205. Dilate(poly11', 0.85, F) → poly11''_1
  206. Dilate(poly11, 0.85, E) → poly11'_1
  207. Dilate(poly8''', 0.85, D) → poly17
  208. Dilate(poly8'', 0.85, C) → poly8'''_1
  209. Midpoint(U_1, Q_1) → G_6
  210. Mirror(poly11''_1, G_6) → poly18
  211. Mirror(poly11'_1, G_6) → poly19

AI 绘图提示语参考

从一条线段出发，在线段上取一点，构造一个八边形，并连接其对角线形成多条辅助线。利用这些辅助线的交点，依次构造多个正方形和六边形，并通过角平分线和中垂线确定对称轴。将部分多边形沿这些对称轴进行镜像和旋转，最终形成一幅由几何变换构成的对称图案，融合数学与艺术美感。
以上提示语为根据原始绘图命令整理而来，仅供参考。