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十二边形之间的几何变换

十二边形之间的几何变换
几何画板及绘图内容加载中，请稍等……
2023-03-13 17:58
多边形角向量变换几何作图
所属专题 geometriadinamica.es
本范例演示多个十二边形在平面上的排列与分布关系。核心数学概念包括多边形性质、旋转变换、平移变换及向量应用。作图要点：使用Polygon命令绘制十二边形，通过Rotate命令实现绕定点的旋转，运用Translate命令进行平移，借助Vector定义向量关系，用Intersect求取交点，以及使用Circle、Segment完善图形结构。本范例适合中学高年级学生理解多边形性质及几何变换，也可作为大学先修几何的入门素材。

GeoGebra 命令及参数

  1. Rotate(B, 29.999999999999996°, A) → C
  2. Rotate(C, 29.999999999999996°, A) → D
  3. Rotate(D, 29.999999999999996°, A) → E
  4. Rotate(E, 29.999999999999996°, A) → F
  5. Rotate(F, 29.999999999999996°, A) → G
  6. Rotate(G, 29.999999999999996°, A) → H
  7. Rotate(H, 29.999999999999996°, A) → I
  8. Rotate(I, 29.999999999999996°, A) → J
  9. Rotate(J, 29.999999999999996°, A) → K
  10. Rotate(K, 29.999999999999996°, A) → L
  11. Rotate(L, 29.999999999999996°, A) → M
  12. Polygon(B, C, L, M, D, E, F, G, H, I, J, K) → P, b, k, l, m, c, d, e, f, g, h, i, j
  13. Segment(C, A) → a
  14. Circle(C, n) → p
  15. Intersect(p, a, 1) → N
  16. Rotate(C, 210°, N) → O
  17. Rotate(N, 210°, O) → Q
  18. Rotate(O, 210°, Q) → R
  19. Rotate(N, 329.99999999999994°, A) → S
  20. Polygon(B, C, N, O, Q, R, S) → T, b_1, c_1, n_1, o, q, r, s
  21. Rotate(S, 329.99999999999994°, A) → U
  22. Polygon(B, S, R, U, M) → V, b_2, s_1, r_1, u, m_1
  23. Rotate(R, 210°, Q) → W
  24. Rotate(Q, 210°, W) → Y
  25. Rotate(M, 210°, U) → Z
  26. Rotate(U, 119.99999999999999°, Z) → A_1
  27. Polygon(A, A_1, Z, U, R, Q, W, Y) → P_1, a_1, a_2, z, u_1, r_2, q_1, w, y
  28. Rotate(U, 210°, Z) → B_1
  29. Rotate(Z, 59.99999999999999°, B_1) → C_1
  30. Rotate(Y, 300.00000000000006°, A) → D_1
  31. Polygon(D_1, C_1, B_1, Z, A_1) → Q_1, d_1, c_2, b_3, z_1, a_3
  32. Rotate(B, (t * 210°), B) → B'
  33. Rotate(S, (t * 210°), B) → S'
  34. Rotate(R, (t * 210°), B) → R'
  35. Rotate(U, (t * 210°), B) → U'
  36. Rotate(M, (t * 210°), B) → M'
  37. Polygon(B', S', R', U', M') → V', b', s', r', u', m'
  38. Rotate(B', 59.99999999999999°, A) → B''
  39. Rotate(S', 59.99999999999999°, A) → S''
  40. Rotate(R', 59.99999999999999°, A) → R''
  41. Rotate(U', 59.99999999999999°, A) → U''
  42. Rotate(M', 59.99999999999999°, A) → M''
  43. Polygon(B'', S'', R'', U'', M'') → V'', b'', s'', r'', u'', m''
  44. Rotate(A, (t * 240°), U) → A'
  45. Rotate(A_1, (t * 240°), U) → A_1'
  46. Rotate(Z, (t * 240°), U) → Z'
  47. Rotate(U, (t * 240°), U) → U'_1
  48. Rotate(R, (t * 240°), U) → R'_1
  49. Rotate(Q, (t * 240°), U) → Q'
  50. Rotate(W, (t * 240°), U) → W'
  51. Rotate(Y, (t * 240°), U) → Y'
  52. Polygon(A', A_1', Z', U'_1, R'_1, Q', W', Y') → P_1', a', a_1', z', u'_1, r'_1, q', w', y'
  53. Vector(U'_1, R) → v
  54. Translate(A', v_1) → A''
  55. Translate(A_1', v_1) → A_1''
  56. Translate(Z', v_1) → Z''
  57. Translate(U'_1, v_1) → U'_1'
  58. Translate(R'_1, v_1) → R'_1'
  59. Translate(Q', v_1) → Q''
  60. Translate(W', v_1) → W''
  61. Translate(Y', v_1) → Y''
  62. Polygon(A'', A_1'', Z'', U'_1', R'_1', Q'', W'', Y'') → P_1'', a'', a_1'', z'', u'_1', r'_1', q'', w'', y''
  63. Vector(B_1, S') → w_1
  64. Translate(D_1, e_1) → D_1'
  65. Translate(C_1, e_1) → C_1'
  66. Translate(B_1, e_1) → B_1'
  67. Translate(Z, e_1) → Z'_1
  68. Translate(A_1, e_1) → A_2
  69. Polygon(D_1', C_1', B_1', Z'_1, A_2) → Q_1', d_1', c_1', b_1', z'_1, a_4
  70. Rotate(B'', 59.99999999999999°, A) → B'''
  71. Rotate(S'', 59.99999999999999°, A) → S'''
  72. Rotate(R'', 59.99999999999999°, A) → R'''
  73. Rotate(U'', 59.99999999999999°, A) → U'''
  74. Rotate(M'', 59.99999999999999°, A) → M'''
  75. Polygon(B''', S''', R''', U''', M''') → V''', b''', s''', r''', u''', m'''
  76. Rotate(B''', 59.99999999999999°, A) → B''''
  77. Rotate(S''', 59.99999999999999°, A) → S''''
  78. Rotate(R''', 59.99999999999999°, A) → R''''
  79. Rotate(U''', 59.99999999999999°, A) → U''''
  80. Rotate(M''', 59.99999999999999°, A) → M''''
  81. Polygon(B'''', S'''', R'''', U'''', M'''') → V'''', b'''', s'''', r'''', u'''', m''''
  82. Rotate(B'''', 59.99999999999999°, A) → B'''''
  83. Rotate(S'''', 59.99999999999999°, A) → S'''''
  84. Rotate(R'''', 59.99999999999999°, A) → R'''''
  85. Rotate(U'''', 59.99999999999999°, A) → U'''''
  86. Rotate(M'''', 59.99999999999999°, A) → M'''''
  87. Polygon(B''''', S''''', R''''', U''''', M''''') → V''''', b''''', s''''', r''''', u''''', m'''''
  88. Rotate(B''''', 59.99999999999999°, A) → B''''''
  89. Rotate(S''''', 59.99999999999999°, A) → S''''''
  90. Rotate(R''''', 59.99999999999999°, A) → R''''''
  91. Rotate(U''''', 59.99999999999999°, A) → U''''''
  92. Rotate(M''''', 59.99999999999999°, A) → M''''''
  93. Polygon(B'''''', S'''''', R'''''', U'''''', M'''''') → V'''''', b'''''', s'''''', r'''''', u'''''', m''''''
  94. Rotate(B, 59.99999999999999°, A) → B'_1
  95. Rotate(C, 59.99999999999999°, A) → C'
  96. Rotate(N, 59.99999999999999°, A) → N'
  97. Rotate(O, 59.99999999999999°, A) → O'
  98. Rotate(Q, 59.99999999999999°, A) → Q'_1
  99. Rotate(R, 59.99999999999999°, A) → R'_2
  100. Rotate(S, 59.99999999999999°, A) → S'_1
  101. Polygon(B'_1, C', N', O', Q'_1, R'_2, S'_1) → T', b'_1, c', n', o', q'_1, r'_2, s'_1
  102. Rotate(B'_1, 59.99999999999999°, A) → B'_1'
  103. Rotate(C', 59.99999999999999°, A) → C''
  104. Rotate(N', 59.99999999999999°, A) → N''
  105. Rotate(O', 59.99999999999999°, A) → O''
  106. Rotate(Q'_1, 59.99999999999999°, A) → Q'_1'
  107. Rotate(R'_2, 59.99999999999999°, A) → R'_2'
  108. Rotate(S'_1, 59.99999999999999°, A) → S'_1'
  109. Polygon(B'_1', C'', N'', O'', Q'_1', R'_2', S'_1') → T'', b'_1', c'', n'', o'', q'_1', r'_2', s'_1'
  110. Rotate(B'_1', 59.99999999999999°, A) → B'_1''
  111. Rotate(C'', 59.99999999999999°, A) → C'''
  112. Rotate(N'', 59.99999999999999°, A) → N'''
  113. Rotate(O'', 59.99999999999999°, A) → O'''
  114. Rotate(Q'_1', 59.99999999999999°, A) → Q'_1''
  115. Rotate(R'_2', 59.99999999999999°, A) → R'_2''
  116. Rotate(S'_1', 59.99999999999999°, A) → S'_1''
  117. Polygon(B'_1'', C''', N''', O''', Q'_1'', R'_2'', S'_1'') → T''', b'_1'', c''', n''', o''', q'_1'', r'_2'', s'_1''
  118. Rotate(B'_1'', 59.99999999999999°, A) → B'_1'''
  119. Rotate(C''', 59.99999999999999°, A) → C''''
  120. Rotate(N''', 59.99999999999999°, A) → N''''
  121. Rotate(O''', 59.99999999999999°, A) → O''''
  122. Rotate(Q'_1'', 59.99999999999999°, A) → Q'_1'''
  123. Rotate(R'_2'', 59.99999999999999°, A) → R'_2'''
  124. Rotate(S'_1'', 59.99999999999999°, A) → S'_1'''
  125. Polygon(B'_1''', C'''', N'''', O'''', Q'_1''', R'_2''', S'_1''') → T'''', b'_1''', c'''', n'''', o'''', q'_1''', r'_2''', s'_1'''
  126. Rotate(B'_1''', 59.99999999999999°, A) → B'_1''''
  127. Rotate(C'''', 59.99999999999999°, A) → C'''''
  128. Rotate(N'''', 59.99999999999999°, A) → N'''''
  129. Rotate(O'''', 59.99999999999999°, A) → O'''''
  130. Rotate(Q'_1''', 59.99999999999999°, A) → Q'_1''''
  131. Rotate(R'_2''', 59.99999999999999°, A) → R'_2''''
  132. Rotate(S'_1''', 59.99999999999999°, A) → S'_1''''
  133. Polygon(B'_1'''', C''''', N''''', O''''', Q'_1'''', R'_2'''', S'_1'''') → T''''', b'_1'''', c''''', n''''', o''''', q'_1'''', r'_2'''', s'_1''''
  134. Rotate(A'', 59.99999999999999°, A) → A'''
  135. Rotate(A_1'', 59.99999999999999°, A) → A_1'''
  136. Rotate(Z'', 59.99999999999999°, A) → Z'''
  137. Rotate(U'_1', 59.99999999999999°, A) → U'_1''
  138. Rotate(R'_1', 59.99999999999999°, A) → R'_1''
  139. Rotate(Q'', 59.99999999999999°, A) → Q'''
  140. Rotate(W'', 59.99999999999999°, A) → W'''
  141. Rotate(Y'', 59.99999999999999°, A) → Y'''
  142. Polygon(A''', A_1''', Z''', U'_1'', R'_1'', Q''', W''', Y''') → P_1''', a''', a_1''', z''', u'_1'', r'_1'', q''', w''', y'''
  143. Rotate(A''', 59.99999999999999°, A) → A''''
  144. Rotate(A_1''', 59.99999999999999°, A) → A_1''''
  145. Rotate(Z''', 59.99999999999999°, A) → Z''''
  146. Rotate(U'_1'', 59.99999999999999°, A) → U'_1'''
  147. Rotate(R'_1'', 59.99999999999999°, A) → R'_1'''
  148. Rotate(Q''', 59.99999999999999°, A) → Q''''
  149. Rotate(W''', 59.99999999999999°, A) → W''''
  150. Rotate(Y''', 59.99999999999999°, A) → Y''''
  151. Polygon(A'''', A_1'''', Z'''', U'_1''', R'_1''', Q'''', W'''', Y'''') → P_1'''', a'''', a_1'''', z'''', u'_1''', r'_1''', q'''', w'''', y''''
  152. Rotate(A'''', 59.99999999999999°, A) → A'''''
  153. Rotate(A_1'''', 59.99999999999999°, A) → A_1'''''
  154. Rotate(Z'''', 59.99999999999999°, A) → Z'''''
  155. Rotate(U'_1''', 59.99999999999999°, A) → U'_1''''
  156. Rotate(R'_1''', 59.99999999999999°, A) → R'_1''''
  157. Rotate(Q'''', 59.99999999999999°, A) → Q'''''
  158. Rotate(W'''', 59.99999999999999°, A) → W'''''
  159. Rotate(Y'''', 59.99999999999999°, A) → Y'''''
  160. Polygon(A''''', A_1''''', Z''''', U'_1'''', R'_1'''', Q''''', W''''', Y''''') → P_1''''', a''''', a_1''''', z''''', u'_1'''', r'_1'''', q''''', w''''', y'''''
  161. Rotate(A''''', 59.99999999999999°, A) → A''''''
  162. Rotate(A_1''''', 59.99999999999999°, A) → A_1''''''
  163. Rotate(Z''''', 59.99999999999999°, A) → Z''''''
  164. Rotate(U'_1'''', 59.99999999999999°, A) → U'_1'''''
  165. Rotate(R'_1'''', 59.99999999999999°, A) → R'_1'''''
  166. Rotate(Q''''', 59.99999999999999°, A) → Q''''''
  167. Rotate(W''''', 59.99999999999999°, A) → W''''''
  168. Rotate(Y''''', 59.99999999999999°, A) → Y''''''
  169. Polygon(A'''''', A_1'''''', Z'''''', U'_1''''', R'_1''''', Q'''''', W'''''', Y'''''') → P_1'''''', a'''''', a_1'''''', z'''''', u'_1''''', r'_1''''', q'''''', w'''''', y''''''
  170. Rotate(A'''''', 59.99999999999999°, A) → A'''''''
  171. Rotate(A_1'''''', 59.99999999999999°, A) → A_1'''''''
  172. Rotate(Z'''''', 59.99999999999999°, A) → Z'''''''
  173. Rotate(U'_1''''', 59.99999999999999°, A) → U'_1''''''
  174. Rotate(R'_1''''', 59.99999999999999°, A) → R'_1''''''
  175. Rotate(Q'''''', 59.99999999999999°, A) → Q'''''''
  176. Rotate(W'''''', 59.99999999999999°, A) → W'''''''
  177. Rotate(Y'''''', 59.99999999999999°, A) → Y'''''''
  178. Polygon(A''''''', A_1''''''', Z''''''', U'_1'''''', R'_1'''''', Q''''''', W''''''', Y''''''') → P_1''''''', a''''''', a_1''''''', z''''''', u'_1'''''', r'_1'''''', q''''''', w''''''', y'''''''
  179. Rotate(D_1', 59.99999999999999°, A) → D_1''
  180. Rotate(C_1', 59.99999999999999°, A) → C_1''
  181. Rotate(B_1', 59.99999999999999°, A) → B_1''
  182. Rotate(Z'_1, 59.99999999999999°, A) → Z'_1'
  183. Rotate(A_2, 59.99999999999999°, A) → A_2'
  184. Polygon(D_1'', C_1'', B_1'', Z'_1', A_2') → Q_1'', d_1'', c_1'', b_1'', z'_1', a_2'
  185. Rotate(D_1'', 59.99999999999999°, A) → D_1'''
  186. Rotate(C_1'', 59.99999999999999°, A) → C_1'''
  187. Rotate(B_1'', 59.99999999999999°, A) → B_1'''
  188. Rotate(Z'_1', 59.99999999999999°, A) → Z'_1''
  189. Rotate(A_2', 59.99999999999999°, A) → A_2''
  190. Polygon(D_1''', C_1''', B_1''', Z'_1'', A_2'') → Q_1''', d_1''', c_1''', b_1''', z'_1'', a_2''
  191. Rotate(D_1''', 59.99999999999999°, A) → D_1''''
  192. Rotate(C_1''', 59.99999999999999°, A) → C_1''''
  193. Rotate(B_1''', 59.99999999999999°, A) → B_1''''
  194. Rotate(Z'_1'', 59.99999999999999°, A) → Z'_1'''
  195. Rotate(A_2'', 59.99999999999999°, A) → A_2'''
  196. Polygon(D_1'''', C_1'''', B_1'''', Z'_1''', A_2''') → Q_1'''', d_1'''', c_1'''', b_1'''', z'_1''', a_2'''
  197. Rotate(D_1'''', 59.99999999999999°, A) → D_1'''''
  198. Rotate(C_1'''', 59.99999999999999°, A) → C_1'''''
  199. Rotate(B_1'''', 59.99999999999999°, A) → B_1'''''
  200. Rotate(Z'_1''', 59.99999999999999°, A) → Z'_1''''
  201. Rotate(A_2''', 59.99999999999999°, A) → A_2''''
  202. Polygon(D_1''''', C_1''''', B_1''''', Z'_1'''', A_2'''') → Q_1''''', d_1''''', c_1''''', b_1''''', z'_1'''', a_2''''
  203. Rotate(D_1''''', 59.99999999999999°, A) → D_1''''''
  204. Rotate(C_1''''', 59.99999999999999°, A) → C_1''''''
  205. Rotate(B_1''''', 59.99999999999999°, A) → B_1''''''
  206. Rotate(Z'_1'''', 59.99999999999999°, A) → Z'_1'''''
  207. Rotate(A_2'''', 59.99999999999999°, A) → A_2'''''
  208. Polygon(D_1'''''', C_1'''''', B_1'''''', Z'_1''''', A_2''''') → Q_1'''''', d_1'''''', c_1'''''', b_1'''''', z'_1''''', a_2'''''

AI 绘图提示语参考

画一个包含多个十二边形的图形，十二边形之间有旋转和平移的关系。图形中包含多个十二边形、圆、线段和交点。请先画出一个十二边形，然后通过旋转和平移将其复制多次，形成一个复杂的图形。最后，画出连接这些十二边形的线段和圆，包括交点和圆心。
以上提示语为根据原始绘图命令整理而来，仅供参考。