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相态E：七边形构造

相态E：七边形构造
几何画板及绘图内容加载中，请稍等……
2023-01-09 22:40
多边形角向量几何作图
所属专题 Polygon Angles: Interactive Exploration
本范例演示了如何通过GeoGebra构造七边形，并展示其几何特性。核心数学概念包括多边形、角度、向量和变换。作图要点涉及使用Ray、Circle、Intersect、Polygon等命令，以及Point、Midpoint等对象。适合初中及以上学生用于学习几何作图和参数方程。

GeoGebra 命令及参数

  1. Ray(N_1, D) → l_4
  2. Circle(D, 3) → k
  3. Intersect(k, l_4) → W_1, Z_1
  4. Ray(D, A_1) → a_3
  5. Intersect(k, a_3, 1) → D_1
  6. Segment(C, A_1) → i_3
  7. Circle(C, 3) → h
  8. Intersect(h, i_3) → L,
  9. Ray(C, D) → c
  10. Intersect(h, c, 1) → P
  11. Ray(A, B) → a
  12. Ray(B, C) → b
  13. Ray(E, A) → e
  14. Circle(A, 3) → f
  15. Circle(B, 3) → g
  16. Circle(E, 3) → p
  17. Segment(C, A) → i
  18. Segment(C, E) → j
  19. Intersect(f, a, 1) → F
  20. Intersect(f, i, 1) → G
  21. Intersect(f, e, 1) → H
  22. Intersect(f, e, 2) → I
  23. Intersect(p, e) → J,
  24. Intersect(p, j) → K,
  25. Intersect(k, c, 2) → O
  26. Intersect(h, j, 1) → Q
  27. Intersect(h, i, 1) → R
  28. Intersect(h, b, 1) → S
  29. Intersect(g, a, 2) → T
  30. Intersect(g, b, 1) → U
  31. Intersect(g, a, 1) → V
  32. CircleSector(A, F, G) → q
  33. CircleSector(A, G, H) → r
  34. CircleSector(B, U, V) → s
  35. CircleSector(C, Q, R) → c_1
  36. CircleSector(C, R, S) → d_1
  37. Intersect(k, c, 1) → W
  38. CircleSector(E, J, K) → h_1
  39. CircleSector(A, I, F) → p_1
  40. CircleSector(B, T, U) → q_1
  41. Intersect(h, b, 2) → Z
  42. Vector(A, B) → u
  43. Vector(C, B) → v
  44. Vector(E, D) → w
  45. Vector(C, D) → u_1
  46. Vector(C, E) → v_1
  47. Vector(A, E) → w_1
  48. Translate(d_1, v) → s_1
  49. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  50. Dilate(C, If[0 < l ≤ 1, 1 - l, 0], B) → C'
  51. Dilate(A, If[1 < l ≤ 2, 2 - l, 0], E) → A'_1
  52. Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1
  53. Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2
  54. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'
  55. Vector(A, B) → a_1
  56. Vector(C, C') → b_1
  57. Vector(A, A'_1) → i_1
  58. Vector(E, E') → j_1
  59. Vector(C, C'_2) → l_1
  60. Vector(C, C'_1) → m_1
  61. Translate(d_1, b_1) → c_2
  62. Translate(r, i_1) → r'_1
  63. Translate(r, w_1) → r'_2
  64. Translate(c_1, v_1) → f_2
  65. Translate(c_1, m_1) → g_2
  66. CircleSector(C, P, L) → t
  67. Translate(t, u_1) → t'
  68. Translate(t, l_1) → t'_1
  69. Translate(q, a_1) → r'
  70. Translate(d_1, b_1) → h_2
  71. Vector(A, A') → n_1
  72. Ray(C, E) → i_2
  73. Vector(D, C) → u_2
  74. Vector(E, C) → v_2
  75. Vector(A, C) → w_2
  76. Vector(B, C) → l_2
  77. Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'
  78. Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2
  79. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1
  80. Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'
  81. Vector(B, B') → m_2
  82. Vector(A, A'_2) → n_2
  83. Vector(E, E'_1) → s_2
  84. Vector(D, D') → t_2
  85. Translate(q_1, m_2) → c_3
  86. Translate(q_1, l_2) → d_3
  87. Translate(p_1, w_2) → e_3
  88. If(1 < o < 2, Translate[p_1, n_2]) → h_3
  89. Ray(A_1, E) → b_3
  90. Circle(A_1, 3) → q_3
  91. Intersect(q_3, i_3) → M,
  92. Intersect(q_3, b_3, 1) → N
  93. Intersect(q_3, a_3, 2) → B_1
  94. Intersect(k, c, 2) → C_1
  95. Intersect(k, c, 1) → E_1
  96. CircleSector(C, L, Q) → d
  97. Intersect(p, b_3, 1) → F_1
  98. Intersect(p, i_2) → G_1, H_2
  99. CircleSector(E, G_1, N) → e_1
  100. Dilate(E, If[2 < l < 3, 3 - l, 0], A_1) → E'_2
  101. Dilate(C, If[2 < l < 3, 3 - l, 0], A_1) → C'_3
  102. Dilate(C, If[3 < l < 4, 4 - l, 0], D) → C'_4
  103. Dilate(A_1, If[3 < l < 4, 4 - l, 0], D) → H_1
  104. Vector(E, A_1) → f_1
  105. Vector(C, A_1) → g_1
  106. Translate(e_1, f_1) → k_1
  107. Translate(d, g_1) → d'
  108. Vector(E, E'_2) → a_2
  109. Vector(C, C'_3) → b_2
  110. Translate(e_1, a_2) → d_2
  111. Translate(d, b_2) → d'_1
  112. CircleSector(A_1, N, M) → f_3
  113. Intersect(q_3, a_3, 1) → I_1
  114. CircleSector(A_1, M, I_1) → g_3
  115. CircleSector(D, D_1, E_1) → k_3
  116. Vector(C, D) → j_2
  117. Vector(A_1, D) → u_3
  118. Translate(g_3, u_3) → p_3
  119. Translate(t, j_2) → t'_2
  120. Vector(A_1, H_1) → v_3
  121. Vector(C, C'_4) → w_3
  122. Translate(g_3, v_3) → s_3
  123. Translate(t, w_3) → t'_3
  124. Intersect(p, b_3, 2) → J_1
  125. Polygon(A, B, C) → poly1, c_4, a_4, b_4
  126. Polygon(A, C, E) → poly2, e_4, a_5, c_5
  127. Polygon(E, C, A_1) → poly3, a_6, e_5, c_6
  128. Polygon(A_1, C, D) → poly4, d_4, a_7, c_7
  129. Intersect(p, e, 1) → L_1
  130. CircleSector(E, J_1, L_1) → f_4
  131. CircleSector(A_1, B_1, N) → g_4
  132. Vector(E, C) → j_3
  133. Vector(A_1, C) → l_3
  134. Vector(D, C) → m_3
  135. Translate(f_4, j_3) → k_4
  136. Translate(g_4, l_3) → p_4
  137. CircleSector(D, Z_1, D_1) → h_4
  138. Translate(h_4, m_3) → q_4
  139. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_3
  140. Dilate(A_1, If[3 < o < 4, 4 - o, 0], C) → M_1
  141. Dilate(D, If[4 < o < 5, 5 - o, 0], C) → D'_1
  142. Vector(E, E'_3) → n_3
  143. Vector(A_1, M_1) → u_4
  144. Vector(D, D'_1) → v_4
  145. If(2 < o < 3, Translate[f_4, n_3]) → r_4
  146. If(3 < o < 4, Translate[g_4, u_4]) → s_4
  147. If(4 < o < 5, Translate[h_4, v_4]) → t_4
  148. Ray(C, N_1) → i_4
  149. Circle(N_1, 3) → d_5
  150. Intersect(d_5, i_4, 2) → K_1
  151. Intersect(d_5, l_4, 1) → O_1
  152. Intersect(d_5, i_4, 1) → P_1
  153. Intersect(h, i_4, 1) → Q_1
  154. CircleSector(C, Q_1, P) → f_5
  155. CircleSector(N_1, O_1, P_1) → g_5
  156. Intersect(k, l_4, 1) → R_1
  157. CircleSector(D, E_1, R_1) → h_5
  158. Dilate(D, If[4 < l < 5, 5 - l, 0], N_1) → D'_2
  159. Dilate(C, If[4 < l < 5, 5 - l, 0], N_1) → C'_5
  160. Vector(C, N_1) → w_4
  161. Vector(D, N_1) → j_4
  162. Translate(h_5, j_4) → p_5
  163. Vector(D, D'_2) → m_4
  164. Vector(C, C'_5) → n_4
  165. Translate(h_5, m_4) → r_5
  166. Polygon(D, C, N_1) → poly5, n_5, d_6, c_8
  167. Segment(D, C) → b_5
  168. Ray(C, E) → i_5
  169. Ray(C, A_1) → j_5
  170. Ray(C, D) → l_5
  171. Point(j_5) → T_1
  172. Point(l_5) → U_1
  173. Ray(A_1, T_1) → m_5
  174. Ray(D, U_1) → b_6
  175. Polygon(A_1, E, A, B, C, N_1, D) → poly6, a_8, e_6, a_9, b_7, c_9, n_6, d_7
  176. Intersect(d_5, l_4, 1) → S_1
  177. Intersect(d_5, i_4, 2) → V_1
  178. CircleSector(N_1, V_1, S_1) → f_6
  179. CircleSector(C, Z, Q_1) → r_1
  180. Vector(N_1, C) → u_5
  181. Translate(f_6, u_5) → g_6
  182. Dilate(N_1, If[5 < o < 6, 6 - o, 0], C) → A_2
  183. Vector(N_1, A_2) → v_5
  184. Translate(f_6, v_5) → h_6
  185. Vector(D, C) → w_5
  186. Translate(h_4, w_5) → k_6
  187. Segment(E, A) → i_6
  188. Segment(A, B) → j_6
  189. Segment(B, C) → l_6
  190. Segment(C, N_1) → m_6
  191. Segment(N_1, D) → p_6
  192. Segment(D, A_1) → q_6
  193. Segment(A_1, E) → r_6
  194. Midpoint(i_6) → B_2
  195. Midpoint(j_6) → C_2
  196. Midpoint(l_6) → D_2
  197. Midpoint(m_6) → E_2
  198. Midpoint(p_6) → F_2
  199. Midpoint(q_6) → G_2
  200. Midpoint(r_6) → I_2
  201. Rotate(d_1, If[0 < l ≤ 1, ((-l) * 180°), -180°], D_2) → t_1
  202. Rotate(C, If[0 < l ≤ 1, ((-l) * 180°), -180°], D_2) → C'_6
  203. Segment(D_2, C'_6) → k_2
  204. Rotate(A, If[0 < l ≤ 1, (l * 180°), 180°], C_2) → A'_3
  205. Segment(C_2, A'_3) → s_6
  206. Rotate(q, If[0 < l ≤ 1, (l * 180°), 180°], C_2) → q'
  207. Rotate(R, 180°, C_2) → R'
  208. Rotate(R, 180°, D_2) → R'_1
  209. Line(B, R'_1) → t_6
  210. Rotate(A, If[1 < l ≤ 2, ((-(l - 1)) * 180°), 180°], B_2) → A'_4
  211. Rotate(r, If[1 < l ≤ 2, ((-(l - 1)) * 180°), 180°], B_2) → r'_3
  212. Segment(B_2, A'_4) → q_2
  213. Ray(E, H_2) → e_7
  214. Rotate(e_1, If[2 < l ≤ 3, ((-(l - 2)) * 180°), 180°], I_2) → e_2
  215. Rotate(E, If[2 < l ≤ 3, ((-(l - 2)) * 180°), 180°], I_2) → E'_4
  216. Segment(I_2, E'_4) → f_7
  217. Rotate(g_3, If[3 < l ≤ 4, ((-(l - 3)) * 180°), 180°], G_2) → t_3
  218. Rotate(A_1, If[3 < l ≤ 4, ((-(l - 3)) * 180°), 180°], G_2) → J_2
  219. Segment(G_2, J_2) → g_7
  220. Rotate(h_5, If[4 < l ≤ 5, ((-(l - 4)) * 180°), 180°], F_2) → t_5
  221. Rotate(D, If[4 < l ≤ 5, ((-(l - 4)) * 180°), 180°], F_2) → D'_3
  222. Segment(F_2, D'_3) → h_7
  223. Rotate(f_5, If[4 < l ≤ 5, ((l - 4) * 180°), 180°], E_2) → s_5
  224. Rotate(C, If[4 < l ≤ 5, ((l - 4) * 180°), 180°], E_2) → C'_7
  225. Segment(E_2, C'_7) → i_7
  226. Rotate(W, 180°, F_2) → W'
  227. Line(N_1, W') → k_5

AI 绘图提示语参考

在平面内以三个以同一点为圆心、半径相同的圆来构建七边形的几何结构。先取基准圆心D，在以D为圆心的圆上确定多条射线的交点，配合以另一圆心C与点A、B等作辅助圆与相交，得到一组用于标定方向的交点与端点。再以若干圆周扇形标记关键角度，用不同的角度扇形围绕A、B、C与E来突出构造所需的分角与旋转关系。最后把这些关键端点连接成围成的多边形边界，并保持所有顶点落在相应圆上，同时可用平移把某个扇形位置映射到另一处以强调对称性。
以上提示语为根据原始绘图命令整理而来，仅供参考。