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变量部分视角下的几何相似性

变量部分视角下的几何相似性
几何画板及绘图内容加载中，请稍等……
2020-01-14 22:39
测试改名0多边形
所属专题 The variable-parts perspective across the curriculum
本范例通过变量部分视角展示了几何相似性。核心数学概念包括相似三角形和多边形的性质。通过使用GeoGebra命令如Intersect、Line、Circle等，可以动态地探索相似图形的变化规律。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, xAxis) → f
  3. Line(A, yAxis) → g
  4. Circle(A, a) → c
  5. Intersect(c, g, 2) → C
  6. Intersect(c, f, 2) → D
  7. Line(D, g) → h
  8. Line(C, f) → i
  9. Circle(D, a) → d
  10. Circle(C, a) → e
  11. Intersect(e, g, 2) → E
  12. Intersect(d, f, 2) → F
  13. Circle(F, a) → k
  14. Circle(E, a) → p
  15. Intersect(p, g, 2) → G
  16. Intersect(k, f, 2) → H
  17. Circle(H, a) → q
  18. Circle(G, a) → r
  19. Intersect(r, g, 2) → I
  20. Intersect(q, f, 2) → J
  21. Circle(J, a) → s
  22. Circle(I, a) → t
  23. Intersect(s, f, 2) → K
  24. Intersect(t, g, 2) → L
  25. Circle(K, a) → c_1
  26. Circle(L, a) → d_1
  27. Intersect(c_1, f, 2) → M
  28. Intersect(d_1, g, 2) → N
  29. Circle(M, a) → e_1
  30. Circle(N, a) → f_1
  31. Intersect(e_1, f, 2) → O
  32. Intersect(f_1, g, 2) → P
  33. Circle(O, a) → g_1
  34. Circle(P, a) → h_1
  35. Intersect(g_1, f, 2) → Q
  36. Intersect(h_1, g, 2) → R
  37. Circle(Q, a) → k_1
  38. Circle(R, a) → p_1
  39. Intersect(p_1, g, 2) → S
  40. Intersect(k_1, f, 2) → T
  41. Circle(T, a) → q_1
  42. Circle(S, a) → r_1
  43. Intersect(r_1, g, 2) → U
  44. Intersect(q_1, f, 2) → V
  45. Circle(V, a) → s_1
  46. Circle(U, a) → t_1
  47. Intersect(s_1, f, 2) → W
  48. Circle(W, a) → c_2
  49. Intersect(t_1, g, 2) → Z
  50. Circle(Z, a) → d_2
  51. Intersect(c_2, f, 2) → A_1
  52. Intersect(d_2, g, 2) → B_1
  53. Circle(A_1, a) → e_2
  54. Circle(B_1, a) → f_2
  55. Intersect(e_2, f, 2) → C_1
  56. Intersect(f_2, g, 2) → D_1
  57. Circle(C_1, a) → g_2
  58. Circle(D_1, a) → h_2
  59. Intersect(g_2, f, 2) → E_1
  60. Intersect(h_2, g, 2) → F_1
  61. Circle(E_1, a) → k_2
  62. Circle(F_1, a) → p_2
  63. Intersect(k_2, f, 2) → G_1
  64. Intersect(p_2, g, 2) → H_1
  65. Circle(G_1, a) → q_2
  66. Circle(H_1, a) → r_2
  67. Intersect(q_2, f, 2) → I_1
  68. Intersect(r_2, g, 2) → J_1
  69. Circle(I_1, a) → s_2
  70. Circle(J_1, a) → t_2
  71. Intersect(s_2, f, 2) → K_1
  72. Intersect(t_2, g, 2) → L_1
  73. Circle(K_1, a) → c_3
  74. Circle(L_1, a) → d_3
  75. Intersect(c_3, f, 2) → M_1
  76. Intersect(d_3, g, 2) → N_1
  77. Circle(M_1, a) → e_3
  78. Circle(N_1, a) → f_3
  79. Intersect(e_3, f, 2) → O_1
  80. Intersect(f_3, g, 2) → P_1
  81. Circle(O_1, a) → g_3
  82. Circle(P_1, a) → h_3
  83. Intersect(g_3, f, 2) → Q_1
  84. Intersect(h_3, g, 2) → R_1
  85. Circle(Q_1, a) → k_3
  86. Circle(R_1, a) → p_3
  87. Intersect(k_3, f, 2) → S_1
  88. Intersect(p_3, g, 2) → T_1
  89. Circle(S_1, a) → q_3
  90. Circle(T_1, a) → r_3
  91. Intersect(q_3, f, 2) → U_1
  92. Intersect(r_3, g, 2) → V_1
  93. Circle(U_1, a) → s_3
  94. Circle(V_1, a) → t_3
  95. Intersect(s_3, f, 2) → W_1
  96. Intersect(t_3, g, 2) → Z_1
  97. Circle(W_1, a) → c_4
  98. Circle(Z_1, a) → d_4
  99. Intersect(c_4, f, 2) → A_2
  100. Intersect(d_4, g, 2) → B_2
  101. Circle(A_2, a) → e_4
  102. Circle(B_2, a) → f_4
  103. Intersect(e_4, f, 2) → C_2
  104. Intersect(f_4, g, 2) → D_2
  105. OrthogonalLine(E, g) → j
  106. OrthogonalLine(G, g) → l
  107. OrthogonalLine(I, g) → m
  108. OrthogonalLine(L, g) → n
  109. OrthogonalLine(N, g) → b
  110. OrthogonalLine(P, g) → i_1
  111. OrthogonalLine(R, g) → j_1
  112. OrthogonalLine(S, g) → l_1
  113. OrthogonalLine(U, g) → m_1
  114. OrthogonalLine(Z, g) → n_1
  115. OrthogonalLine(B_1, g) → a_1
  116. OrthogonalLine(D_1, g) → b_1
  117. OrthogonalLine(F_1, g) → i_2
  118. OrthogonalLine(H_1, g) → j_2
  119. OrthogonalLine(J_1, g) → l_2
  120. OrthogonalLine(L_1, g) → m_2
  121. OrthogonalLine(N_1, g) → n_2
  122. OrthogonalLine(P_1, g) → a_2
  123. OrthogonalLine(R_1, g) → b_2
  124. OrthogonalLine(T_1, g) → i_3
  125. OrthogonalLine(V_1, g) → j_3
  126. OrthogonalLine(Z_1, g) → l_3
  127. OrthogonalLine(B_2, g) → m_3
  128. OrthogonalLine(D_2, g) → n_3
  129. OrthogonalLine(F, f) → a_3
  130. OrthogonalLine(H, f) → b_3
  131. OrthogonalLine(J, f) → g_4
  132. OrthogonalLine(K, f) → h_4
  133. OrthogonalLine(M, f) → i_4
  134. OrthogonalLine(O, f) → j_4
  135. OrthogonalLine(Q, f) → k_4
  136. OrthogonalLine(T, f) → l_4
  137. OrthogonalLine(V, f) → m_4
  138. OrthogonalLine(W, f) → n_4
  139. OrthogonalLine(A_1, f) → p_4
  140. OrthogonalLine(C_1, f) → q_4
  141. OrthogonalLine(E_1, f) → r_4
  142. OrthogonalLine(G_1, f) → s_4
  143. OrthogonalLine(I_1, f) → t_4
  144. OrthogonalLine(K_1, f) → a_4
  145. OrthogonalLine(M_1, f) → b_4
  146. OrthogonalLine(O_1, f) → f_5
  147. OrthogonalLine(Q_1, f) → g_5
  148. OrthogonalLine(S_1, f) → h_5
  149. OrthogonalLine(U_1, f) → i_5
  150. OrthogonalLine(W_1, f) → j_5
  151. OrthogonalLine(A_2, f) → k_5
  152. OrthogonalLine(C_2, f) → l_5
  153. Intersect(h, n_3) → E_2
  154. Intersect(n_3, a_3) → F_2
  155. Intersect(n_3, b_3) → G_2
  156. Intersect(n_3, g_4) → H_2
  157. Intersect(n_3, h_4) → I_2
  158. Intersect(n_3, i_4) → J_2
  159. Intersect(n_3, j_4) → K_2
  160. Intersect(n_3, k_4) → L_2
  161. Intersect(n_3, l_4) → M_2
  162. Intersect(n_3, m_4) → N_2
  163. Intersect(n_3, n_4) → O_2
  164. Intersect(n_3, p_4) → P_2
  165. Intersect(n_3, q_4) → Q_2
  166. Intersect(n_3, r_4) → R_2
  167. Intersect(n_3, s_4) → S_2
  168. Intersect(n_3, t_4) → T_2
  169. Intersect(n_3, a_4) → U_2
  170. Intersect(b_4, n_3) → V_2
  171. Intersect(n_3, f_5) → W_2
  172. Intersect(n_3, g_5) → Z_2
  173. Intersect(n_3, h_5) → A_3
  174. Intersect(n_3, i_5) → B_3
  175. Intersect(n_3, j_5) → C_3
  176. Intersect(n_3, k_5) → D_3
  177. Intersect(n_3, l_5) → E_3
  178. Intersect(m_3, l_5) → F_3
  179. Intersect(l_3, l_5) → G_3
  180. Intersect(j_3, l_5) → H_3
  181. Intersect(i_3, l_5) → I_3
  182. Intersect(b_2, l_5) → J_3
  183. Intersect(a_2, l_5) → K_3
  184. Intersect(n_2, l_5) → L_3
  185. Intersect(m_2, l_5) → M_3
  186. Intersect(l_2, l_5) → N_3
  187. Intersect(j_2, l_5) → O_3
  188. Intersect(i_2, l_5) → P_3
  189. Intersect(b_1, l_5) → Q_3
  190. Intersect(a_1, l_5) → R_3
  191. Intersect(n_1, l_5) → S_3
  192. Intersect(m_1, l_5) → T_3
  193. Intersect(l_1, l_5) → U_3
  194. Intersect(j_1, l_5) → V_3
  195. Intersect(i_1, l_5) → W_3
  196. Intersect(b, l_5) → Z_3
  197. Intersect(n, l_5) → A_4
  198. Intersect(m, l_5) → B_4
  199. Intersect(l, l_5) → C_4
  200. Intersect(j, l_5) → D_4
  201. Intersect(i, l_5) → E_4
  202. Segment(A, D_2) → m_5
  203. Segment(D, E_2) → n_5
  204. Segment(F, F_2) → p_5
  205. Segment(H, G_2) → q_5
  206. Segment(J, H_2) → r_5
  207. Segment(K, I_2) → s_5
  208. Segment(M, J_2) → t_5
  209. Segment(O, K_2) → a_5
  210. Segment(Q, L_2) → b_5
  211. Segment(T, M_2) → c_5
  212. Segment(V, N_2) → d_5
  213. Segment(W, O_2) → e_5
  214. Segment(A_1, P_2) → f_6
  215. Segment(C_1, Q_2) → g_6
  216. Segment(E_1, R_2) → h_6
  217. Segment(G_1, S_2) → i_6
  218. Segment(I_1, T_2) → j_6
  219. Segment(K_1, U_2) → k_6
  220. Segment(M_1, V_2) → l_6
  221. Segment(O_1, W_2) → m_6
  222. Segment(Q_1, Z_2) → n_6
  223. Segment(S_1, A_3) → p_6
  224. Segment(U_1, B_3) → q_6
  225. Segment(W_1, C_3) → r_6
  226. Segment(A_2, D_3) → s_6
  227. Segment(C_2, E_3) → t_6
  228. Segment(D_2, E_3) → a_6
  229. Segment(B_2, F_3) → b_6
  230. Segment(Z_1, G_3) → c_6
  231. Segment(V_1, H_3) → d_6
  232. Segment(T_1, I_3) → e_6
  233. Segment(R_1, J_3) → f_7
  234. Segment(P_1, K_3) → g_7
  235. Segment(N_1, L_3) → h_7
  236. Segment(L_1, M_3) → i_7
  237. Segment(J_1, N_3) → j_7
  238. Segment(H_1, O_3) → k_7
  239. Segment(F_1, P_3) → l_7
  240. Segment(D_1, Q_3) → m_7
  241. Segment(B_1, R_3) → n_7
  242. Segment(Z, S_3) → p_7
  243. Segment(U, T_3) → q_7
  244. Segment(S, U_3) → r_7
  245. Segment(R, V_3) → s_7
  246. Segment(P, W_3) → t_7
  247. Segment(N, Z_3) → a_7
  248. Segment(L, A_4) → b_7
  249. Segment(I, B_4) → c_7
  250. Segment(G, C_4) → d_7
  251. Segment(E, D_4) → e_7
  252. Segment(C, E_4) → f_8
  253. Segment(A, C_2) → g_8
  254. Intersect(r_5, d_7) → F_4
  255. Polygon(A, J, F_4) → t1, f_9, a_8, j_8

AI 绘图提示语参考

绘制一个以点A为中心的圆c，然后通过点C和D分别与y轴和x轴的交点绘制两条线h和i，接着以点D和C为圆心，半径为a分别绘制圆d和e，再通过点E和F与y轴和x轴的交点绘制两条线j和k，以此类推，最终形成一系列相似的三角形和圆，注意保持每个圆的半径相同。
以上提示语为根据原始绘图命令整理而来，仅供参考。