前n个自然数和的公式推导

前n个自然数和的公式推导
几何画板及绘图内容加载中,请稍等……
2014-03-27 04:28
①本范例演示如何通过动态图形推导前n个自然数和的公式;②涉及的核心数学概念包括数列求和、代数推导、几何直观;③作图要点——使用了Line(线)、Circle(圆)、Intersect(交点)、Polygon(多边形)、Segment(线段)、Vector(向量)、Translate(平移)、Point(点)、OrthogonalLine(垂线);④适合高中数学教学,用于理解数列求和公式的几何意义和代数推导过程。

GeoGebra 命令及参数

  1. Line(A, xAxis) → b
  2. Line(A, yAxis) → c
  3. Circle(A, a) → d
  4. Intersect(d, b, 2) → C
  5. Line(C, c) → e
  6. Intersect(d, c, 1) → D
  7. Line(D, b) → f
  8. Circle(C, A) → g
  9. Circle(D, A) → h
  10. Intersect(g, b, 2) → E
  11. Circle(E, C) → k
  12. Intersect(h, c, 2) → H
  13. Circle(H, D) → r
  14. Line(E, e) → i
  15. Line(H, f) → j
  16. Intersect(r, c, 2) → I
  17. Line(I, j) → l
  18. Intersect(k, b, 2) → G
  19. Circle(G, E) → p
  20. Intersect(p, b, 2) → J
  21. Circle(J, G) → q
  22. Intersect(q, b, 2) → K
  23. Circle(K, J) → s
  24. Intersect(s, b, 2) → L
  25. Circle(L, K) → t
  26. Intersect(t, b, 2) → M
  27. Circle(M, L) → c_1
  28. Intersect(c_1, b, 2) → N
  29. Circle(N, M) → d_1
  30. Intersect(d_1, b, 2) → O
  31. Circle(O, N) → e_1
  32. Intersect(e_1, b, 2) → P
  33. Circle(P, O) → f_1
  34. Circle(I, H) → g_1
  35. Intersect(g_1, c, 2) → Q
  36. Circle(Q, I) → h_1
  37. Intersect(h_1, c, 2) → R
  38. Circle(R, Q) → k_1
  39. Intersect(k_1, c, 2) → S
  40. Circle(S, R) → p_1
  41. Intersect(p_1, c, 2) → T
  42. Circle(T, S) → q_1
  43. Intersect(q_1, c, 2) → U
  44. Circle(U, T) → r_1
  45. Line(Q, f) → m
  46. Line(R, l) → n
  47. Line(S, m) → a_1
  48. Line(T, n) → b_1
  49. Line(U, a_1) → i_1
  50. Line(G, i) → j_1
  51. Line(J, i) → l_1
  52. Line(K, j_1) → m_1
  53. Line(L, m_1) → n_1
  54. Line(M, n_1) → s_1
  55. Line(N, s_1) → t_1
  56. Line(O, t_1) → a_2
  57. Line(P, a_2) → b_2
  58. Circle(P, O) → c_2
  59. Intersect(c_2, b, 2) → B
  60. Circle(B, P) → d_2
  61. Intersect(d_2, b, 2) → F
  62. Circle(F, B) → e_2
  63. Intersect(e_2, b, 2) → V
  64. Circle(V, F) → f_2
  65. Intersect(f_2, b, 2) → W
  66. Circle(W, V) → g_2
  67. Intersect(g_2, b, 2) → Z
  68. Circle(Z, W) → h_2
  69. Circle(U, T) → c_3
  70. Intersect(c_3, c, 2) → G_1
  71. Circle(G_1, U) → d_3
  72. Intersect(d_3, c, 2) → H_1
  73. Circle(H_1, G_1) → e_3
  74. Intersect(e_3, c, 2) → I_1
  75. Circle(I_1, H_1) → f_3
  76. Intersect(f_3, c, 2) → J_1
  77. Circle(J_1, I_1) → g_3
  78. Intersect(g_3, c, 2) → K_1
  79. Circle(K_1, J_1) → h_3
  80. Intersect(h_3, c, 2) → L_1
  81. Circle(L_1, K_1) → k_3
  82. Intersect(k_3, c, 2) → M_1
  83. Line(G_1, i_1) → i_2
  84. Line(H_1, i_2) → j_2
  85. Line(I_1, j_2) → l_2
  86. Line(J_1, l_2) → m_2
  87. Line(K_1, m_2) → n_2
  88. Line(L_1, n_2) → a_3
  89. Line(M_1, a_3) → b_3
  90. Line(B, b_2) → i_3
  91. Line(F, i_3) → j_3
  92. Line(V, j_3) → l_3
  93. Line(W, j_3) → m_3
  94. Line(Z, l_3) → n_3
  95. Intersect(e, f) → O_1
  96. Polygon(A, D, O_1, C) → mnohoúhelník1, a_5, d_4, o_1, c_4
  97. Intersect(f, i) → P_1
  98. Intersect(f, j_1) → Q_1
  99. Polygon(E, P_1, Q_1, G) → mnohoúhelník2, e_4, p_4, q_4, g_4
  100. Intersect(j, j_1) → R_1
  101. Intersect(i, j) → S_1
  102. Polygon(P_1, Q_1, R_1, S_1) → mnohoúhelník3, p_5, q_5, r_4, s_4
  103. Intersect(f, m_1) → T_1
  104. Intersect(f, l_1) → U_1
  105. Polygon(J, K, T_1, U_1) → mnohoúhelník4, j_4, k_4, t_4, u_1
  106. Intersect(j, l_1) → V_1
  107. Intersect(j, m_1) → W_1
  108. Polygon(U_1, V_1, W_1, T_1) → mnohoúhelník5, u_2, v_1, w_1, t_5
  109. Intersect(l, m_1) → Z_1
  110. Intersect(l, l_1) → A_2
  111. Polygon(V_1, W_1, Z_1, A_2) → mnohoúhelník6, v_2, w_2, z_1, a_6
  112. Intersect(f, s_1) → B_2
  113. Intersect(f, n_1) → C_2
  114. Polygon(L, M, B_2, C_2) → mnohoúhelník7, l_4, m_4, b_5, c_5
  115. Intersect(j, s_1) → D_2
  116. Intersect(j, n_1) → E_2
  117. Polygon(C_2, B_2, D_2, E_2) → mnohoúhelník8, c_6, b_6, d_5, e_5
  118. Intersect(l, s_1) → F_2
  119. Intersect(l, n_1) → G_2
  120. Polygon(E_2, D_2, F_2, G_2) → mnohoúhelník9, e_6, d_6, f_4, g_5
  121. Intersect(m, n_1) → H_2
  122. Intersect(m, s_1) → I_2
  123. Polygon(F_2, G_2, H_2, I_2) → mnohoúhelník10, f_5, g_6, h_4, i_4
  124. Intersect(f, a_2) → J_2
  125. Intersect(f, t_1) → K_2
  126. Polygon(N, O, J_2, K_2) → mnohoúhelník11, n_4, o, j_5, k_5
  127. Intersect(j, a_2) → L_2
  128. Intersect(j, t_1) → M_2
  129. Polygon(K_2, J_2, L_2, M_2) → mnohoúhelník12, k_6, j_6, l_5, m_5
  130. Intersect(l, a_2) → N_2
  131. Intersect(l, t_1) → O_2
  132. Polygon(M_2, L_2, N_2, O_2) → mnohoúhelník13, m_6, l_6, n_5, o_2
  133. Intersect(m, a_2) → P_2
  134. Intersect(m, t_1) → Q_2
  135. Polygon(O_2, N_2, P_2, Q_2) → mnohoúhelník14, o_3, n_6, p_6, q_6
  136. Intersect(n, a_2) → R_2
  137. Intersect(n, t_1) → S_2
  138. Polygon(Q_2, P_2, R_2, S_2) → mnohoúhelník15, q_7, p_7, r_5, s_5
  139. Intersect(f, i_3) → T_2
  140. Intersect(f, b_2) → U_2
  141. Polygon(P, B, T_2, U_2) → mnohoúhelník16, p_8, b_7, t_6, u_3
  142. Intersect(j, i_3) → V_2
  143. Intersect(j, b_2) → W_2
  144. Polygon(U_2, T_2, V_2, W_2) → mnohoúhelník17, u_4, t_7, v_3, w_3
  145. Intersect(l, i_3) → Z_2
  146. Intersect(l, b_2) → A_3
  147. Polygon(W_2, V_2, Z_2, A_3) → mnohoúhelník18, w_4, v_4, z_2, a_7
  148. Intersect(m, i_3) → B_3
  149. Intersect(m, b_2) → C_3
  150. Polygon(A_3, Z_2, B_3, C_3) → mnohoúhelník19, a_8, z_3, b_8, c_7
  151. Intersect(n, i_3) → D_3
  152. Intersect(n, b_2) → E_3
  153. Polygon(C_3, B_3, D_3, E_3) → mnohoúhelník20, c_8, b_9, d_7, e_7
  154. Intersect(a_1, i_3) → F_3
  155. Intersect(a_1, b_2) → G_3
  156. Polygon(E_3, D_3, F_3, G_3) → mnohoúhelník21, e_8, d_8, f_6, g_7
  157. Intersect(f, l_3) → H_3
  158. Intersect(f, j_3) → I_3
  159. Polygon(F, V, H_3, I_3) → mnohoúhelník22, f_7, v, h_5, i_5
  160. Intersect(j, l_3) → J_3
  161. Intersect(j, j_3) → K_3
  162. Polygon(I_3, H_3, J_3, K_3) → mnohoúhelník23, i_6, h_6, j_7, k_7
  163. Intersect(l, l_3) → L_3
  164. Intersect(l, j_3) → M_3
  165. Polygon(K_3, J_3, L_3, M_3) → mnohoúhelník24, k_8, j_8, l_7, m_7
  166. Intersect(m, l_3) → N_3
  167. Intersect(m, j_3) → O_3
  168. Polygon(M_3, L_3, N_3, O_3) → mnohoúhelník25, m_8, l_8, n_7, o_4
  169. Intersect(n, l_3) → P_3
  170. Intersect(n, j_3) → Q_3
  171. Polygon(O_3, N_3, P_3, Q_3) → mnohoúhelník26, o_5, n_8, p_9, q_8
  172. Intersect(a_1, l_3) → R_3
  173. Intersect(a_1, j_3) → S_3
  174. Polygon(Q_3, P_3, R_3, S_3) → mnohoúhelník27, q_9, p_{10}, r_6, s_6
  175. Intersect(b_1, l_3) → T_3
  176. Intersect(b_1, j_3) → U_3
  177. Polygon(S_3, R_3, T_3, U_3) → mnohoúhelník28, s_7, r_7, t_8, u_5
  178. Circle(M_1, L_1) → h_7
  179. Intersect(h_7, c, 2) → V_3
  180. Circle(V_3, M_1) → f_8
  181. Line(V_3, b_3) → i_7
  182. Intersect(f_8, c, 2) → W_3
  183. Line(W_3, i_7) → g_8
  184. Intersect(f, n_3) → Z_3
  185. Intersect(f, m_3) → A_4
  186. Polygon(W, Z, Z_3, A_4) → mnohoúhelník29, w_{13}, z, z_4, a_9
  187. Intersect(j, n_3) → B_4
  188. Intersect(j, m_3) → C_4
  189. Polygon(A_4, Z_3, B_4, C_4) → mnohoúhelník30, a_{10}, z_5, b_{10}, c_9
  190. Intersect(l, n_3) → D_4
  191. Intersect(l, m_3) → E_4
  192. Polygon(C_4, B_4, D_4, E_4) → mnohoúhelník31, c_{10}, b_{11}, d_9, e_9
  193. Intersect(m, n_3) → F_4
  194. Intersect(m, m_3) → G_4
  195. Polygon(E_4, D_4, F_4, G_4) → mnohoúhelník32, e_{10}, d_{10}, f_9, g_9
  196. Intersect(n, n_3) → H_4
  197. Intersect(n, m_3) → I_4
  198. Polygon(G_4, F_4, H_4, I_4) → mnohoúhelník33, g_{10}, f_{10}, h_8, i_8
  199. Intersect(a_1, n_3) → J_4
  200. Intersect(a_1, m_3) → K_4
  201. Polygon(I_4, H_4, J_4, K_4) → mnohoúhelník34, i_9, h_9, j_9, k_9
  202. Intersect(b_1, n_3) → L_4
  203. Intersect(b_1, m_3) → M_4
  204. Polygon(K_4, J_4, L_4, M_4) → mnohoúhelník35, k_{10}, j_{10}, l_9, m_9
  205. Intersect(i_1, n_3) → N_4
  206. Intersect(i_1, m_3) → O_4
  207. Polygon(M_4, L_4, N_4, O_4) → mnohoúhelník36, m_{10}, l_{10}, n_9, o_6
  208. Intersect(e, g_8) → P_4
  209. Intersect(e, i_7) → Q_4
  210. Polygon(W_3, P_4, Q_4, V_3) → mnohoúhelník37, w_5, p_{11}, q_{10}, v_5
  211. Intersect(i, g_8) → R_4
  212. Intersect(j_1, g_8) → S_4
  213. Intersect(j_1, i_7) → T_4
  214. Intersect(i, i_7) → U_4
  215. Polygon(R_4, S_4, T_4, U_4) → mnohoúhelník38, r_8, s_8, t_9, u_6
  216. Intersect(j_1, b_3) → V_4
  217. Intersect(i, b_3) → W_4
  218. Polygon(U_4, T_4, V_4, W_4) → mnohoúhelník39, u_7, t_{10}, v_6, w_6
  219. Intersect(l_1, g_8) → Z_4
  220. Intersect(m_1, g_8) → A_5
  221. Intersect(m_1, i_7) → B_5
  222. Intersect(l_1, i_7) → C_5
  223. Polygon(Z_4, A_5, B_5, C_5) → mnohoúhelník40, z_6, a_{11}, b_{12}, c_{11}
  224. Intersect(m_1, b_3) → D_5
  225. Intersect(l_1, b_3) → E_5
  226. Polygon(C_5, B_5, D_5, E_5) → mnohoúhelník41, c_{12}, b_{13}, d_{11}, e_{11}
  227. Intersect(m_1, a_3) → F_5
  228. Intersect(l_1, a_3) → G_5
  229. Polygon(E_5, D_5, F_5, G_5) → mnohoúhelník42, e_{12}, d_{12}, f_{11}, g_{11}
  230. Intersect(m_1, n_2) → H_5
  231. Intersect(l_1, n_2) → I_5
  232. Intersect(n_1, g_8) → J_5
  233. Intersect(s_1, g_8) → K_5
  234. Intersect(s_1, i_7) → L_5
  235. Intersect(n_1, i_7) → M_5
  236. Polygon(J_5, K_5, L_5, M_5) → mnohoúhelník43, j_{11}, k_{11}, l_{11}, m_{11}
  237. Intersect(s_1, b_3) → N_5
  238. Intersect(n_1, b_3) → O_5
  239. Polygon(M_5, L_5, N_5, O_5) → mnohoúhelník44, m_{12}, l_{12}, n_{10}, o_7
  240. Intersect(s_1, a_3) → P_5
  241. Intersect(n_1, a_3) → Q_5
  242. Polygon(O_5, N_5, P_5, Q_5) → mnohoúhelník45, o_8, n_{11}, p_{12}, q_{11}
  243. Intersect(s_1, n_2) → R_5
  244. Intersect(n_1, n_2) → S_5
  245. Polygon(Q_5, P_5, R_5, S_5) → mnohoúhelník46, q_{12}, p_{13}, r_9, s_9
  246. Intersect(t_1, g_8) → T_5
  247. Intersect(a_2, g_8) → U_5
  248. Intersect(a_2, i_7) → V_5
  249. Intersect(t_1, i_7) → W_5
  250. Polygon(T_5, U_5, V_5, W_5) → mnohoúhelník47, t_{11}, u_8, v_7, w_7
  251. Intersect(a_2, b_3) → Z_5
  252. Intersect(t_1, b_3) → A_6
  253. Polygon(W_5, V_5, Z_5, A_6) → mnohoúhelník48, w_8, v_8, z_7, a_{12}
  254. Intersect(a_2, a_3) → B_6
  255. Intersect(t_1, a_3) → C_6
  256. Polygon(A_6, Z_5, B_6, C_6) → mnohoúhelník49, a_{13}, z_8, b_{14}, c_{13}
  257. Intersect(a_2, n_2) → D_6
  258. Intersect(t_1, n_2) → E_6
  259. Polygon(C_6, B_6, D_6, E_6) → mnohoúhelník50, c_{14}, b_{15}, d_{13}, e_{13}
  260. Intersect(e, b_3) → H_6
  261. Polygon(V_3, Q_4, H_6, M_1) → mnohoúhelník52, v_9, q_{13}, h_{10}, m_{13}
  262. Intersect(e, a_3) → I_6
  263. Polygon(M_1, H_6, I_6, L_1) → mnohoúhelník53, m_{14}, h_{11}, i_{10}, l_{13}
  264. Intersect(e, n_2) → J_6
  265. Polygon(L_1, I_6, J_6, K_1) → mnohoúhelník54, l_{14}, i_{11}, j_{12}, k_{12}
  266. Intersect(e, m_2) → K_6
  267. Polygon(K_1, J_6, K_6, J_1) → mnohoúhelník55, k_{13}, j_{13}, k_{14}, j_{14}
  268. Intersect(e, l_2) → L_6
  269. Polygon(J_1, K_6, L_6, I_1) → mnohoúhelník56, j_{15}, k_{15}, l_{15}, i_{12}
  270. Intersect(e, j_2) → M_6
  271. Polygon(I_1, L_6, M_6, H_1) → mnohoúhelník57, i_{13}, l_{16}, m_{15}, h_{12}
  272. Intersect(e, i_2) → N_6
  273. Polygon(H_1, M_6, N_6, G_1) → mnohoúhelník58, h_{13}, m_{16}, n_{12}, g_{13}
  274. Intersect(j_1, a_3) → O_6
  275. Intersect(i, a_3) → P_6
  276. Polygon(W_4, V_4, O_6, P_6) → mnohoúhelník59, w_9, v_{10}, o_9, p_{14}
  277. Intersect(j_1, n_2) → Q_6
  278. Intersect(i, n_2) → R_6
  279. Polygon(P_6, O_6, Q_6, R_6) → mnohoúhelník60, p_{15}, o_{10}, q_{14}, r_{10}
  280. Intersect(j_1, m_2) → S_6
  281. Intersect(i, m_2) → T_6
  282. Polygon(R_6, Q_6, S_6, T_6) → mnohoúhelník61, r_{11}, q_{15}, s_{10}, t_{12}
  283. Intersect(j_1, l_2) → U_6
  284. Intersect(i, l_2) → V_6
  285. Polygon(T_6, S_6, U_6, V_6) → mnohoúhelník62, t_{13}, s_{11}, u_9, v_{11}
  286. Intersect(j_1, j_2) → W_6
  287. Intersect(i, j_2) → Z_6
  288. Polygon(V_6, U_6, W_6, Z_6) → mnohoúhelník63, v_{12}, u_{10}, w_{10}, z_9
  289. Intersect(m_1, n_2) → A_7
  290. Intersect(l_1, n_2) → B_7
  291. Polygon(G_5, F_5, A_7, B_7) → mnohoúhelník64, g_{14}, f_{13}, a_{14}, b_{16}
  292. Intersect(m_1, m_2) → C_7
  293. Intersect(l_1, m_2) → D_7
  294. Polygon(B_7, A_7, C_7, D_7) → mnohoúhelník65, b_{17}, a_{15}, c_{15}, d_{15}
  295. Intersect(m_1, l_2) → E_7
  296. Intersect(l_1, l_2) → F_7
  297. Polygon(D_7, C_7, E_7, F_7) → mnohoúhelník66, d_{16}, c_{16}, e_{15}, f_{14}
  298. Intersect(s_1, m_2) → G_7
  299. Intersect(n_1, m_2) → H_7
  300. Polygon(S_5, R_5, G_7, H_7) → mnohoúhelník67, s_{12}, r_{12}, g_{15}, h_{14}
  301. Intersect(b_2, g_8) → F_6
  302. Intersect(i_3, g_8) → G_6
  303. Intersect(i_3, i_7) → I_7
  304. Intersect(b_2, i_7) → J_7
  305. Polygon(F_6, G_6, I_7, J_7) → mnohoúhelník51, f_{12}, g_{12}, i_{14}, j_{16}
  306. Intersect(b_3, i_3) → K_7
  307. Intersect(b_2, b_3) → L_7
  308. Polygon(J_7, I_7, K_7, L_7) → mnohoúhelník68, j_{17}, i_{15}, k_{16}, l_{17}
  309. Intersect(a_3, i_3) → M_7
  310. Intersect(b_2, a_3) → N_7
  311. Polygon(L_7, K_7, M_7, N_7) → mnohoúhelník69, l_{18}, k_{17}, m_{17}, n_{13}
  312. Intersect(j_3, g_8) → O_7
  313. Intersect(l_3, g_8) → P_7
  314. Intersect(l_3, i_7) → Q_7
  315. Intersect(j_3, i_7) → R_7
  316. Polygon(O_7, P_7, Q_7, R_7) → mnohoúhelník70, o_{11}, p_{16}, q_{16}, r_{13}
  317. Intersect(b_3, l_3) → S_7
  318. Intersect(b_3, j_3) → T_7
  319. Polygon(R_7, Q_7, S_7, T_7) → mnohoúhelník71, r_{14}, q_{17}, s_{13}, t_{14}
  320. Intersect(m_3, g_8) → U_7
  321. Intersect(n_3, g_8) → V_7
  322. Intersect(n_3, i_7) → W_7
  323. Intersect(m_3, i_7) → Z_7
  324. Polygon(U_7, V_7, W_7, Z_7) → mnohoúhelník72, u_{11}, v_{13}, w_{11}, z_{10}
  325. Circle(A, 0.4) → d_{14}
  326. Circle(Z, 0.4) → k_2
  327. Circle(W_3, 0.4) → p_2
  328. Circle(V_7, 0.4) → q_2
  329. Intersect(d_{14}, b, 1) → A_1
  330. Intersect(d_{14}, c, 2) → B_1
  331. Intersect(k_2, n_3, 2) → C_1
  332. Intersect(k_2, b, 2) → D_1
  333. Intersect(p_2, c, 1) → E_1
  334. Line(A_1, e) → r_2
  335. Line(E_1, m_2) → s_2
  336. Line(D_1, n_3) → t_2
  337. Line(B_1, b) → p_3
  338. Intersect(r_2, p_3) → F_1
  339. Intersect(t_2, p_3) → N_1
  340. Segment(F_1, N_1) → q_3
  341. Intersect(r_2, s_2) → A_8
  342. Segment(F_1, A_8) → r_3
  343. Intersect(s_2, t_2) → B_8
  344. Segment(A_8, B_8) → s_3
  345. Segment(B_8, N_1) → t_3
  346. Intersect(e, p_3) → C_8
  347. Intersect(i, p_3) → D_8
  348. Intersect(j_1, p_3) → E_8
  349. Intersect(l_1, p_3) → F_8
  350. Intersect(m_1, p_3) → G_8
  351. Intersect(n_1, p_3) → H_8
  352. Intersect(s_1, p_3) → I_8
  353. Intersect(t_1, p_3) → J_8
  354. Intersect(a_2, p_3) → K_8
  355. Intersect(b_2, p_3) → L_8
  356. Intersect(i_3, p_3) → M_8
  357. Intersect(j_3, p_3) → N_8
  358. Intersect(l_3, p_3) → O_8
  359. Intersect(m_3, p_3) → P_8
  360. Intersect(f, r_2) → Q_8
  361. Intersect(j, r_2) → R_8
  362. Intersect(l, r_2) → S_8
  363. Intersect(m, r_2) → T_8
  364. Intersect(n, r_2) → U_8
  365. Intersect(a_1, r_2) → V_8
  366. Intersect(b_1, r_2) → W_8
  367. Intersect(i_1, r_2) → Z_8
  368. Intersect(i_2, r_2) → A_9
  369. Intersect(j_2, r_2) → B_9
  370. Intersect(l_2, r_2) → C_9
  371. Intersect(m_2, r_2) → D_9
  372. Intersect(n_2, r_2) → E_9
  373. Intersect(a_3, r_2) → F_9
  374. Intersect(b_3, r_2) → G_9
  375. Intersect(i_7, r_2) → H_9
  376. Intersect(g_8, r_2) → I_9
  377. Intersect(e, s_2) → J_9
  378. Intersect(i, s_2) → K_9
  379. Intersect(j_1, s_2) → L_9
  380. Intersect(l_1, s_2) → M_9
  381. Intersect(m_1, s_2) → N_9
  382. Intersect(n_1, s_2) → O_9
  383. Intersect(s_1, s_2) → P_9
  384. Intersect(t_1, s_2) → Q_9
  385. Intersect(a_2, s_2) → R_9
  386. Intersect(b_2, s_2) → S_9
  387. Intersect(i_3, s_2) → T_9
  388. Intersect(j_3, s_2) → U_9
  389. Intersect(l_3, s_2) → V_9
  390. Intersect(m_3, s_2) → W_9
  391. Intersect(n_3, s_2) → Z_9
  392. Intersect(g_8, t_2) → A_{10}
  393. Intersect(i_7, t_2) → B_{10}
  394. Intersect(b_3, t_2) → C_{10}
  395. Intersect(a_3, t_2) → D_{10}
  396. Intersect(n_2, t_2) → E_{10}
  397. Intersect(m_2, t_2) → F_{10}
  398. Intersect(l_2, t_2) → G_{10}
  399. Intersect(j_2, t_2) → H_{10}
  400. Intersect(i_2, t_2) → I_{10}
  401. Intersect(i_1, t_2) → J_{10}
  402. Intersect(b_1, t_2) → K_{10}
  403. Intersect(a_1, t_2) → L_{10}
  404. Intersect(n, t_2) → M_{10}
  405. Intersect(m, t_2) → N_{10}
  406. Intersect(l, t_2) → O_{10}
  407. Intersect(j, t_2) → P_{10}
  408. Intersect(f, t_2) → Q_{10}
  409. Vector(G_1, D) → u
  410. Translate(H_1, u_x) → R_{10}
  411. Translate(M_6, u_x) → S_{10}
  412. Translate(N_6, u_x) → T_{10}
  413. Translate(G_1, u_x) → U_{10}
  414. Polygon(R_{10}, S_{10}, T_{10}, U_{10}) → mnohoúhelník58', r_{15}, s_{14}, t_{15}, u_{14}
  415. Translate(I_1, u_x) → V_{10}
  416. Translate(L_6, u_x) → W_{10}
  417. Translate(M_6, u_x) → Z_{10}
  418. Translate(H_1, u_x) → A_{11}
  419. Polygon(V_{10}, W_{10}, Z_{10}, A_{11}) → mnohoúhelník57', v_{14}, w_{14}, z_{13}, a_{16}
  420. Translate(J_1, u_x) → B_{11}
  421. Translate(K_6, u_x) → C_{11}
  422. Translate(L_6, u_x) → D_{11}
  423. Translate(I_1, u_x) → E_{11}
  424. Intersect(g_{13}, n_{12}) → F_{11}
  425. Intersect(n_{12}, m_{16}) → G_{11}
  426. Segment(F_{11}, G_{11}) → e_{14}
  427. Intersect(p_{11}, w_5) → H_{11}
  428. Segment(G_{11}, H_{11}) → n_{14}
  429. Intersect(v_5, w_5) → I_{11}
  430. Segment(H_{11}, I_{11}) → f_{15}
  431. Segment(I_{11}, F_{11}) → h_{15}
  432. Translate(J_1, u_x) → J_{11}
  433. Translate(K_6, u_x) → K_{11}
  434. Translate(L_6, u_x) → L_{11}
  435. Translate(I_1, u_x) → M_{11}
  436. Polygon(J_{11}, K_{11}, L_{11}, M_{11}) → mnohoúhelník56', j_{18}, k_{18}, l_{19}, m_{18}
  437. Translate(K_1, u_x) → N_{11}
  438. Translate(J_6, u_x) → O_{11}
  439. Translate(K_6, u_x) → P_{11}
  440. Translate(J_1, u_x) → Q_{11}
  441. Polygon(N_{11}, O_{11}, P_{11}, Q_{11}) → mnohoúhelník55', n_{15}, o_{12}, p_{17}, q_{18}
  442. Translate(L_1, u_x) → R_{11}
  443. Translate(I_6, u_x) → S_{11}
  444. Translate(J_6, u_x) → T_{11}
  445. Translate(K_1, u_x) → U_{11}
  446. Polygon(R_{11}, S_{11}, T_{11}, U_{11}) → mnohoúhelník54', r_{16}, s_{15}, t_{16}, u_{15}
  447. Translate(M_1, u_x) → V_{11}
  448. Translate(H_6, u_x) → W_{11}
  449. Translate(I_6, u_x) → Z_{11}
  450. Translate(L_1, u_x) → A_{12}
  451. Polygon(V_{11}, W_{11}, Z_{11}, A_{12}) → mnohoúhelník53', v_{15}, w_{15}, z_{14}, a_{17}
  452. Translate(V_3, u_x) → B_{12}
  453. Translate(Q_4, u_x) → C_{12}
  454. Translate(H_6, u_x) → D_{12}
  455. Translate(M_1, u_x) → E_{12}
  456. Polygon(B_{12}, C_{12}, D_{12}, E_{12}) → mnohoúhelník52', b_{18}, c_{17}, d_{17}, e_{16}
  457. Translate(W_3, u_x) → F_{12}
  458. Translate(P_4, u_x) → G_{12}
  459. Translate(Q_4, u_x) → H_{12}
  460. Translate(V_3, u_x) → I_{12}
  461. Polygon(F_{12}, G_{12}, H_{12}, I_{12}) → mnohoúhelník37', f_{16}, g_{16}, h_{16}, i_{16}
  462. Translate(R_{10}, u_x) → J_{12}
  463. Translate(S_{10}, u_x) → K_{12}
  464. Translate(T_{10}, u_x) → L_{12}
  465. Translate(U_{10}, u_x) → M_{12}
  466. Polygon(J_{12}, K_{12}, L_{12}, M_{12}) → mnohoúhelník58'', j_{19}, k_{19}, l_{20}, m_{19}
  467. Translate(V_{10}, u_x) → N_{12}
  468. Translate(W_{10}, u_x) → O_{12}
  469. Translate(Z_{10}, u_x) → P_{12}
  470. Translate(A_{11}, u_x) → Q_{12}
  471. Polygon(N_{12}, O_{12}, P_{12}, Q_{12}) → mnohoúhelník57'', n_{16}, o_{13}, p_{18}, q_{19}
  472. Translate(J_{11}, u_x) → R_{12}
  473. Translate(K_{11}, u_x) → S_{12}
  474. Translate(L_{11}, u_x) → T_{12}
  475. Translate(M_{11}, u_x) → U_{12}
  476. Polygon(R_{12}, S_{12}, T_{12}, U_{12}) → mnohoúhelník56'', r_{17}, s_{16}, t_{17}, u_{16}
  477. Translate(N_{11}, u_x) → V_{12}
  478. Translate(O_{11}, u_x) → W_{12}
  479. Translate(P_{11}, u_x) → Z_{12}
  480. Translate(Q_{11}, u_x) → A_{13}
  481. Polygon(V_{12}, W_{12}, Z_{12}, A_{13}) → mnohoúhelník55'', v_{16}, w_{16}, z_{15}, a_{18}
  482. Translate(R_{11}, u_x) → B_{13}
  483. Translate(S_{11}, u_x) → C_{13}
  484. Translate(T_{11}, u_x) → D_{13}
  485. Translate(U_{11}, u_x) → E_{13}
  486. Polygon(B_{13}, C_{13}, D_{13}, E_{13}) → mnohoúhelník54'', b_{19}, c_{18}, d_{18}, e_{17}
  487. Translate(V_{11}, u_x) → F_{13}
  488. Translate(W_{11}, u_x) → G_{13}
  489. Translate(Z_{11}, u_x) → H_{13}
  490. Translate(A_{12}, u_x) → I_{13}
  491. Polygon(F_{13}, G_{13}, H_{13}, I_{13}) → mnohoúhelník53'', f_{17}, g_{17}, h_{17}, i_{17}
  492. Translate(B_{12}, u_x) → J_{13}
  493. Translate(C_{12}, u_x) → K_{13}
  494. Translate(D_{12}, u_x) → L_{13}
  495. Translate(E_{12}, u_x) → M_{13}
  496. Polygon(J_{13}, K_{13}, L_{13}, M_{13}) → mnohoúhelník52'', j_{20}, k_{20}, l_{21}, m_{20}
  497. Translate(F_{12}, u_x) → N_{13}
  498. Translate(G_{12}, u_x) → O_{13}
  499. Translate(H_{12}, u_x) → P_{13}
  500. Translate(I_{12}, u_x) → Q_{13}
  501. Polygon(N_{13}, O_{13}, P_{13}, Q_{13}) → mnohoúhelník37'', n_{17}, o_{14}, p_{19}, q_{20}
  502. Translate(F_{11}, u_x) → R_{13}
  503. Translate(G_{11}, u_x) → S_{13}
  504. Segment(R_{13}, S_{13}) → s_{17}
  505. Translate(J_{12}, u_x) → T_{13}
  506. Translate(K_{12}, u_x) → U_{13}
  507. Translate(L_{12}, u_x) → V_{13}
  508. Translate(M_{12}, u_x) → W_{13}
  509. Polygon(T_{13}, U_{13}, V_{13}, W_{13}) → mnohoúhelník58''', t_{18}, u_{17}, v_{17}, w_{17}
  510. Translate(N_{12}, u_x) → Z_{13}
  511. Translate(O_{12}, u_x) → A_{14}
  512. Translate(P_{12}, u_x) → B_{14}
  513. Translate(Q_{12}, u_x) → C_{14}
  514. Polygon(Z_{13}, A_{14}, B_{14}, C_{14}) → mnohoúhelník57''', z_{16}, a_{19}, b_{20}, c_{19}
  515. Translate(R_{12}, u_x) → D_{14}
  516. Translate(S_{12}, u_x) → E_{14}
  517. Translate(T_{12}, u_x) → F_{14}
  518. Translate(U_{12}, u_x) → G_{14}
  519. Polygon(D_{14}, E_{14}, F_{14}, G_{14}) → mnohoúhelník56''', d_{19}, e_{18}, f_{18}, g_{18}
  520. Translate(V_{12}, u_x) → H_{14}
  521. Translate(W_{12}, u_x) → I_{14}
  522. Translate(Z_{12}, u_x) → J_{14}
  523. Translate(A_{13}, u_x) → K_{14}
  524. Polygon(H_{14}, I_{14}, J_{14}, K_{14}) → mnohoúhelník55''', h_{18}, i_{18}, j_{21}, k_{21}
  525. Translate(B_{13}, u_x) → L_{14}
  526. Translate(C_{13}, u_x) → M_{14}
  527. Translate(D_{13}, u_x) → N_{14}
  528. Translate(E_{13}, u_x) → O_{14}
  529. Polygon(L_{14}, M_{14}, N_{14}, O_{14}) → mnohoúhelník54''', l_{22}, m_{21}, n_{18}, o_{15}
  530. Translate(F_{13}, u_x) → P_{14}
  531. Translate(G_{13}, u_x) → Q_{14}
  532. Translate(H_{13}, u_x) → R_{14}
  533. Translate(I_{13}, u_x) → S_{14}
  534. Polygon(P_{14}, Q_{14}, R_{14}, S_{14}) → mnohoúhelník53''', p_{20}, q_{21}, r_{18}, s_{18}
  535. Translate(J_{13}, u_x) → T_{14}
  536. Translate(K_{13}, u_x) → U_{14}
  537. Translate(L_{13}, u_x) → V_{14}
  538. Translate(M_{13}, u_x) → W_{14}
  539. Polygon(T_{14}, U_{14}, V_{14}, W_{14}) → mnohoúhelník52''', t_{19}, u_{18}, v_{18}, w_{18}
  540. Translate(N_{13}, u_x) → Z_{14}
  541. Translate(O_{13}, u_x) → A_{15}
  542. Translate(P_{13}, u_x) → B_{15}
  543. Translate(Q_{13}, u_x) → C_{15}
  544. Polygon(Z_{14}, A_{15}, B_{15}, C_{15}) → mnohoúhelník37''', z_{17}, a_{20}, b_{21}, c_{20}
  545. Translate(F_{11}, u_x) → D_{15}
  546. Translate(G_{11}, u_x) → E_{15}
  547. Segment(D_{15}, E_{15}) → e_{19}
  548. Point(a_1) → F_{15}
  549. OrthogonalLine(F_{15}, a_1) → f_{19}
  550. Circle(F_{15}, a) → g_{19}
  551. Intersect(g_{19}, a_1, 2) → G_{15}
  552. OrthogonalLine(G_{15}, a_1) → h_{19}
  553. Intersect(b_1, f_{19}) → H_{15}
  554. Intersect(b_1, h_{19}) → I_{15}
  555. Translate(R_4, u_x) → J_{15}
  556. Translate(S_4, u_x) → K_{15}
  557. Translate(T_4, u_x) → L_{15}
  558. Translate(U_4, u_x) → M_{15}
  559. Polygon(J_{15}, K_{15}, L_{15}, M_{15}) → mnohoúhelník38', j_{22}, k_{22}, l_{23}, m_{22}
  560. Translate(U_4, u_x) → N_{15}
  561. Translate(T_4, u_x) → O_{15}
  562. Translate(V_4, u_x) → P_{15}
  563. Translate(W_4, u_x) → Q_{15}
  564. Polygon(N_{15}, O_{15}, P_{15}, Q_{15}) → mnohoúhelník39', n_{19}, o_{16}, p_{21}, q_{22}
  565. Translate(Z_4, u_x) → R_{15}
  566. Translate(A_5, u_x) → S_{15}
  567. Translate(B_5, u_x) → T_{15}
  568. Translate(C_5, u_x) → U_{15}
  569. Polygon(R_{15}, S_{15}, T_{15}, U_{15}) → mnohoúhelník40', r_{19}, s_{19}, t_{20}, u_{19}
  570. Translate(C_5, u_x) → V_{15}
  571. Translate(B_5, u_x) → W_{15}
  572. Translate(D_5, u_x) → Z_{15}
  573. Translate(E_5, u_x) → A_{16}
  574. Polygon(V_{15}, W_{15}, Z_{15}, A_{16}) → mnohoúhelník41', v_{19}, w_{19}, z_{18}, a_{21}
  575. Translate(E_5, u_x) → B_{16}
  576. Translate(D_5, u_x) → C_{16}
  577. Translate(F_5, u_x) → D_{16}
  578. Translate(G_5, u_x) → E_{16}
  579. Polygon(B_{16}, C_{16}, D_{16}, E_{16}) → mnohoúhelník42', b_{22}, c_{21}, d_{20}, e_{20}
  580. Translate(J_5, u_x) → F_{16}
  581. Translate(K_5, u_x) → G_{16}
  582. Translate(L_5, u_x) → H_{16}
  583. Translate(M_5, u_x) → I_{16}
  584. Polygon(F_{16}, G_{16}, H_{16}, I_{16}) → mnohoúhelník43', f_{21}, g_{21}, h_{21}, i_{20}
  585. Translate(M_5, u_x) → J_{16}
  586. Translate(L_5, u_x) → K_{16}
  587. Translate(N_5, u_x) → L_{16}
  588. Translate(O_5, u_x) → M_{16}
  589. Polygon(J_{16}, K_{16}, L_{16}, M_{16}) → mnohoúhelník44', j_{23}, k_{23}, l_{24}, m_{23}
  590. Translate(O_5, u_x) → N_{16}
  591. Translate(N_5, u_x) → O_{16}
  592. Translate(P_5, u_x) → P_{16}
  593. Translate(Q_5, u_x) → Q_{16}
  594. Polygon(N_{16}, O_{16}, P_{16}, Q_{16}) → mnohoúhelník45', n_{20}, o_{17}, p_{22}, q_{23}
  595. Translate(Q_5, u_x) → R_{16}
  596. Translate(P_5, u_x) → S_{16}
  597. Translate(R_5, u_x) → T_{16}
  598. Translate(S_5, u_x) → U_{16}
  599. Polygon(R_{16}, S_{16}, T_{16}, U_{16}) → mnohoúhelník46', r_{20}, s_{20}, t_{21}, u_{20}
  600. Translate(T_5, u_x) → V_{16}
  601. Translate(U_5, u_x) → W_{16}
  602. Translate(V_5, u_x) → Z_{16}
  603. Translate(W_5, u_x) → A_{17}
  604. Polygon(V_{16}, W_{16}, Z_{16}, A_{17}) → mnohoúhelník47', v_{20}, w_{20}, z_{19}, a_{22}
  605. Translate(W_5, u_x) → B_{17}
  606. Translate(V_5, u_x) → C_{17}
  607. Translate(Z_5, u_x) → D_{17}
  608. Translate(A_6, u_x) → E_{17}
  609. Polygon(B_{17}, C_{17}, D_{17}, E_{17}) → mnohoúhelník48', b_{23}, c_{22}, d_{21}, e_{21}
  610. Translate(A_6, u_x) → F_{17}
  611. Translate(Z_5, u_x) → G_{17}
  612. Translate(B_6, u_x) → H_{17}
  613. Translate(C_6, u_x) → I_{17}
  614. Polygon(F_{17}, G_{17}, H_{17}, I_{17}) → mnohoúhelník49', f_{22}, g_{22}, h_{22}, i_{21}
  615. Translate(C_6, u_x) → J_{17}
  616. Translate(B_6, u_x) → K_{17}
  617. Translate(D_6, u_x) → L_{17}
  618. Translate(E_6, u_x) → M_{17}
  619. Polygon(J_{17}, K_{17}, L_{17}, M_{17}) → mnohoúhelník50', j_{24}, k_{24}, l_{25}, m_{24}
  620. Translate(W_4, u_x) → N_{17}
  621. Translate(V_4, u_x) → O_{17}
  622. Translate(O_6, u_x) → P_{17}
  623. Translate(P_6, u_x) → Q_{17}
  624. Polygon(N_{17}, O_{17}, P_{17}, Q_{17}) → mnohoúhelník59', n_{21}, o_{18}, p_{23}, q_{24}
  625. Translate(P_6, u_x) → R_{17}
  626. Translate(O_6, u_x) → S_{17}
  627. Translate(Q_6, u_x) → T_{17}
  628. Translate(R_6, u_x) → U_{17}
  629. Polygon(R_{17}, S_{17}, T_{17}, U_{17}) → mnohoúhelník60', r_{21}, s_{21}, t_{22}, u_{21}
  630. Translate(R_6, u_x) → V_{17}
  631. Translate(Q_6, u_x) → W_{17}
  632. Translate(S_6, u_x) → Z_{17}
  633. Translate(T_6, u_x) → A_{18}
  634. Polygon(V_{17}, W_{17}, Z_{17}, A_{18}) → mnohoúhelník61', v_{21}, w_{21}, z_{20}, a_{23}
  635. Translate(T_6, u_x) → B_{18}
  636. Translate(S_6, u_x) → C_{18}
  637. Translate(U_6, u_x) → D_{18}
  638. Translate(V_6, u_x) → E_{18}
  639. Polygon(B_{18}, C_{18}, D_{18}, E_{18}) → mnohoúhelník62', b_{24}, c_{23}, d_{22}, e_{22}
  640. Translate(V_6, u_x) → F_{18}
  641. Translate(U_6, u_x) → G_{18}
  642. Translate(W_6, u_x) → H_{18}
  643. Translate(Z_6, u_x) → I_{18}
  644. Polygon(F_{18}, G_{18}, H_{18}, I_{18}) → mnohoúhelník63', f_{23}, g_{23}, h_{23}, i_{22}
  645. Translate(G_5, u_x) → J_{18}
  646. Translate(F_5, u_x) → K_{18}
  647. Translate(A_7, u_x) → L_{18}
  648. Translate(B_7, u_x) → M_{18}
  649. Polygon(J_{18}, K_{18}, L_{18}, M_{18}) → mnohoúhelník64', j_{25}, k_{25}, l_{26}, m_{25}
  650. Translate(B_7, u_x) → N_{18}
  651. Translate(A_7, u_x) → O_{18}
  652. Translate(C_7, u_x) → P_{18}
  653. Translate(D_7, u_x) → Q_{18}
  654. Polygon(N_{18}, O_{18}, P_{18}, Q_{18}) → mnohoúhelník65', n_{22}, o_{19}, p_{24}, q_{25}
  655. Translate(D_7, u_x) → R_{18}
  656. Translate(C_7, u_x) → S_{18}
  657. Translate(E_7, u_x) → T_{18}
  658. Translate(F_7, u_x) → U_{18}
  659. Polygon(R_{18}, S_{18}, T_{18}, U_{18}) → mnohoúhelník66', r_{22}, s_{22}, t_{23}, u_{22}
  660. Translate(S_5, u_x) → V_{18}
  661. Translate(R_5, u_x) → W_{18}
  662. Translate(G_7, u_x) → Z_{18}
  663. Translate(H_7, u_x) → A_{19}
  664. Polygon(V_{18}, W_{18}, Z_{18}, A_{19}) → mnohoúhelník67', v_{22}, w_{22}, z_{21}, a_{24}
  665. Translate(F_6, u_x) → B_{19}
  666. Translate(G_6, u_x) → C_{19}
  667. Translate(I_7, u_x) → D_{19}
  668. Translate(J_7, u_x) → E_{19}
  669. Polygon(B_{19}, C_{19}, D_{19}, E_{19}) → mnohoúhelník51', b_{25}, c_{24}, d_{23}, e_{23}
  670. Translate(J_7, u_x) → F_{19}
  671. Translate(I_7, u_x) → G_{19}
  672. Translate(K_7, u_x) → H_{19}
  673. Translate(L_7, u_x) → I_{19}
  674. Polygon(F_{19}, G_{19}, H_{19}, I_{19}) → mnohoúhelník68', f_{24}, g_{24}, h_{24}, i_{23}
  675. Translate(L_7, u_x) → J_{19}
  676. Translate(K_7, u_x) → K_{19}
  677. Translate(M_7, u_x) → L_{19}
  678. Translate(N_7, u_x) → M_{19}
  679. Polygon(J_{19}, K_{19}, L_{19}, M_{19}) → mnohoúhelník69', j_{26}, k_{26}, l_{27}, m_{26}
  680. Translate(O_7, u_x) → N_{19}
  681. Translate(P_7, u_x) → O_{19}
  682. Translate(Q_7, u_x) → P_{19}
  683. Translate(R_7, u_x) → Q_{19}
  684. Polygon(N_{19}, O_{19}, P_{19}, Q_{19}) → mnohoúhelník70', n_{23}, o_{20}, p_{25}, q_{26}
  685. Translate(R_7, u_x) → R_{19}
  686. Translate(Q_7, u_x) → S_{19}
  687. Translate(S_7, u_x) → T_{19}
  688. Translate(T_7, u_x) → U_{19}
  689. Polygon(R_{19}, S_{19}, T_{19}, U_{19}) → mnohoúhelník71', r_{23}, s_{23}, t_{24}, u_{23}
  690. Translate(U_7, u_x) → V_{19}
  691. Translate(V_7, u_x) → W_{19}
  692. Translate(W_7, u_x) → Z_{19}
  693. Translate(Z_7, u_x) → A_{20}
  694. Polygon(V_{19}, W_{19}, Z_{19}, A_{20}) → mnohoúhelník72', v_{23}, w_{23}, z_{22}, a_{25}
  695. Translate(F_{16}, u_x) → B_{20}
  696. Translate(G_{16}, u_x) → C_{20}
  697. Translate(H_{16}, u_x) → D_{20}
  698. Translate(I_{16}, u_x) → E_{20}
  699. Polygon(B_{20}, C_{20}, D_{20}, E_{20}) → mnohoúhelník43'', b_4, c_{25}, d_{24}, e_{24}
  700. Translate(J_{16}, u_x) → F_{20}
  701. Translate(K_{16}, u_x) → G_{20}
  702. Translate(L_{16}, u_x) → H_{20}
  703. Translate(M_{16}, u_x) → I_{20}
  704. Polygon(F_{20}, G_{20}, H_{20}, I_{20}) → mnohoúhelník44'', f_{25}, g_{25}, h_{25}, i_{24}
  705. Translate(N_{16}, u_x) → J_{20}
  706. Translate(O_{16}, u_x) → K_{20}
  707. Translate(P_{16}, u_x) → L_{20}
  708. Translate(Q_{16}, u_x) → M_{20}
  709. Polygon(J_{20}, K_{20}, L_{20}, M_{20}) → mnohoúhelník45'', j_{27}, k_{27}, l_{28}, m_{27}
  710. Translate(R_{16}, u_x) → N_{20}
  711. Translate(S_{16}, u_x) → O_{20}
  712. Translate(T_{16}, u_x) → P_{20}
  713. Translate(U_{16}, u_x) → Q_{20}
  714. Polygon(N_{20}, O_{20}, P_{20}, Q_{20}) → mnohoúhelník46'', n_{24}, o_{21}, p_{26}, q_{27}
  715. Translate(V_{16}, u_x) → R_{20}
  716. Translate(W_{16}, u_x) → S_{20}
  717. Translate(Z_{16}, u_x) → T_{20}
  718. Translate(A_{17}, u_x) → U_{20}
  719. Polygon(R_{20}, S_{20}, T_{20}, U_{20}) → mnohoúhelník47'', r_{24}, s_{24}, t_{25}, u_{12}
  720. Translate(B_{17}, u_x) → V_{20}
  721. Translate(C_{17}, u_x) → W_{20}
  722. Translate(D_{17}, u_x) → Z_{20}
  723. Translate(E_{17}, u_x) → A_{21}
  724. Polygon(V_{20}, W_{20}, Z_{20}, A_{21}) → mnohoúhelník48'', v_{24}, w_{12}, z_{11}, a_4
  725. Translate(F_{17}, u_x) → B_{21}
  726. Translate(G_{17}, u_x) → C_{21}
  727. Translate(H_{17}, u_x) → D_{21}
  728. Translate(I_{17}, u_x) → E_{21}
  729. Polygon(B_{21}, C_{21}, D_{21}, E_{21}) → mnohoúhelník49'', b_{26}, c_{26}, d_{25}, e_{25}
  730. Translate(J_{17}, u_x) → F_{21}
  731. Translate(K_{17}, u_x) → G_{21}
  732. Translate(L_{17}, u_x) → H_{21}
  733. Translate(M_{17}, u_x) → I_{21}
  734. Polygon(F_{21}, G_{21}, H_{21}, I_{21}) → mnohoúhelník50'', f_{26}, g_{26}, h_{26}, i_{25}
  735. Translate(V_{18}, u_x) → J_{21}
  736. Translate(W_{18}, u_x) → K_{21}
  737. Translate(Z_{18}, u_x) → L_{21}
  738. Translate(A_{19}, u_x) → M_{21}
  739. Polygon(J_{21}, K_{21}, L_{21}, M_{21}) → mnohoúhelník67'', j_{28}, k_{28}, l_{29}, m_{28}
  740. Translate(B_{19}, u_x) → N_{21}
  741. Translate(C_{19}, u_x) → O_{21}
  742. Translate(D_{19}, u_x) → P_{21}
  743. Translate(E_{19}, u_x) → Q_{21}
  744. Polygon(N_{21}, O_{21}, P_{21}, Q_{21}) → mnohoúhelník51'', n_{25}, o_{22}, p_{27}, q_{28}
  745. Translate(F_{19}, u_x) → R_{21}
  746. Translate(G_{19}, u_x) → S_{21}
  747. Translate(H_{19}, u_x) → T_{21}
  748. Translate(I_{19}, u_x) → U_{21}
  749. Polygon(R_{21}, S_{21}, T_{21}, U_{21}) → mnohoúhelník68'', r_{25}, s_{25}, t_{26}, u_{13}
  750. Translate(J_{19}, u_x) → V_{21}
  751. Translate(K_{19}, u_x) → W_{21}
  752. Translate(L_{19}, u_x) → Z_{21}
  753. Translate(M_{19}, u_x) → A_{22}
  754. Polygon(V_{21}, W_{21}, Z_{21}, A_{22}) → mnohoúhelník69'', v_{25}, w_{24}, z_{12}, a_{26}
  755. Translate(N_{19}, u_x) → B_{22}
  756. Translate(O_{19}, u_x) → C_{22}
  757. Translate(P_{19}, u_x) → D_{22}
  758. Translate(Q_{19}, u_x) → E_{22}
  759. Polygon(B_{22}, C_{22}, D_{22}, E_{22}) → mnohoúhelník70'', b_{27}, c_{27}, d_{26}, e_{26}
  760. Translate(R_{19}, u_x) → F_{22}
  761. Translate(S_{19}, u_x) → G_{22}
  762. Translate(T_{19}, u_x) → H_{22}
  763. Translate(U_{19}, u_x) → I_{22}
  764. Polygon(F_{22}, G_{22}, H_{22}, I_{22}) → mnohoúhelník71'', f_{27}, g_{27}, h_{27}, i_{26}
  765. Translate(V_{19}, u_x) → J_{22}
  766. Translate(W_{19}, u_x) → K_{22}
  767. Translate(Z_{19}, u_x) → L_{22}
  768. Translate(A_{20}, u_x) → M_{22}
  769. Polygon(J_{22}, K_{22}, L_{22}, M_{22}) → mnohoúhelník72'', j_{29}, k_{29}, l_{30}, m_{29}
  770. Translate(J_{15}, u_x) → N_{22}
  771. Translate(K_{15}, u_x) → O_{22}
  772. Translate(L_{15}, u_x) → P_{22}
  773. Translate(M_{15}, u_x) → Q_{22}
  774. Polygon(N_{22}, O_{22}, P_{22}, Q_{22}) → mnohoúhelník38'', n_{26}, o_{23}, p_{28}, q_{29}
  775. Translate(N_{15}, u_x) → R_{22}
  776. Translate(O_{15}, u_x) → S_{22}
  777. Translate(P_{15}, u_x) → T_{22}
  778. Translate(Q_{15}, u_x) → U_{22}
  779. Polygon(R_{22}, S_{22}, T_{22}, U_{22}) → mnohoúhelník39'', r_{26}, s_{26}, t_{27}, u_{24}
  780. Translate(R_{15}, u_x) → V_{22}
  781. Translate(S_{15}, u_x) → W_{22}
  782. Translate(T_{15}, u_x) → Z_{22}
  783. Translate(U_{15}, u_x) → A_{23}
  784. Polygon(V_{22}, W_{22}, Z_{22}, A_{23}) → mnohoúhelník40'', v_{26}, w_{25}, z_{23}, a_{27}
  785. Translate(V_{15}, u_x) → B_{23}
  786. Translate(W_{15}, u_x) → C_{23}
  787. Translate(Z_{15}, u_x) → D_{23}
  788. Translate(A_{16}, u_x) → E_{23}
  789. Polygon(B_{23}, C_{23}, D_{23}, E_{23}) → mnohoúhelník41'', b_{28}, c_{28}, d_{27}, e_{27}
  790. Translate(B_{16}, u_x) → F_{23}
  791. Translate(C_{16}, u_x) → G_{23}
  792. Translate(D_{16}, u_x) → H_{23}
  793. Translate(E_{16}, u_x) → I_{23}
  794. Polygon(F_{23}, G_{23}, H_{23}, I_{23}) → mnohoúhelník42'', f_{28}, g_{28}, h_{28}, i_{27}
  795. Translate(N_{17}, u_x) → J_{23}
  796. Translate(O_{17}, u_x) → K_{23}
  797. Translate(P_{17}, u_x) → L_{23}
  798. Translate(Q_{17}, u_x) → M_{23}
  799. Polygon(J_{23}, K_{23}, L_{23}, M_{23}) → mnohoúhelník59'', j_{30}, k_{30}, l_{31}, m_{30}
  800. Translate(R_{17}, u_x) → N_{23}
  801. Translate(S_{17}, u_x) → O_{23}
  802. Translate(T_{17}, u_x) → P_{23}
  803. Translate(U_{17}, u_x) → Q_{23}
  804. Polygon(N_{23}, O_{23}, P_{23}, Q_{23}) → mnohoúhelník60'', n_{27}, o_{24}, p_{29}, q_{30}
  805. Translate(V_{17}, u_x) → R_{23}
  806. Translate(W_{17}, u_x) → S_{23}
  807. Translate(Z_{17}, u_x) → T_{23}
  808. Translate(A_{18}, u_x) → U_{23}
  809. Polygon(R_{23}, S_{23}, T_{23}, U_{23}) → mnohoúhelník61'', r_{27}, s_{27}, t_{28}, u_{25}
  810. Translate(B_{18}, u_x) → V_{23}
  811. Translate(C_{18}, u_x) → W_{23}
  812. Translate(D_{18}, u_x) → Z_{23}
  813. Translate(E_{18}, u_x) → A_{24}
  814. Polygon(V_{23}, W_{23}, Z_{23}, A_{24}) → mnohoúhelník62'', v_{27}, w_{26}, z_{24}, a_{28}
  815. Translate(F_{18}, u_x) → B_{24}
  816. Translate(G_{18}, u_x) → C_{24}
  817. Translate(H_{18}, u_x) → D_{24}
  818. Translate(I_{18}, u_x) → E_{24}
  819. Polygon(B_{24}, C_{24}, D_{24}, E_{24}) → mnohoúhelník63'', b_{29}, c_{29}, d_{28}, e_{28}
  820. Translate(J_{18}, u_x) → F_{24}
  821. Translate(K_{18}, u_x) → G_{24}
  822. Translate(L_{18}, u_x) → H_{24}
  823. Translate(M_{18}, u_x) → I_{24}
  824. Polygon(F_{24}, G_{24}, H_{24}, I_{24}) → mnohoúhelník64'', f_{29}, g_{29}, h_{29}, i_{28}
  825. Translate(N_{18}, u_x) → J_{24}
  826. Translate(O_{18}, u_x) → K_{24}
  827. Translate(P_{18}, u_x) → L_{24}
  828. Translate(Q_{18}, u_x) → M_{24}
  829. Polygon(J_{24}, K_{24}, L_{24}, M_{24}) → mnohoúhelník65'', j_{31}, k_{31}, l_{32}, m_{31}
  830. Translate(R_{18}, u_x) → N_{24}
  831. Translate(S_{18}, u_x) → O_{24}
  832. Translate(T_{18}, u_x) → P_{24}
  833. Translate(U_{18}, u_x) → Q_{24}
  834. Polygon(N_{24}, O_{24}, P_{24}, Q_{24}) → mnohoúhelník66'', n_{28}, o_{25}, p_{30}, q_{31}
  835. Translate(N_{21}, u_x) → R_{24}
  836. Translate(O_{21}, u_x) → S_{24}
  837. Translate(P_{21}, u_x) → T_{24}
  838. Translate(Q_{21}, u_x) → U_{24}
  839. Polygon(R_{24}, S_{24}, T_{24}, U_{24}) → mnohoúhelník51''', r_{28}, s_{28}, t_{29}, u_{26}
  840. Translate(R_{21}, u_x) → V_{24}
  841. Translate(S_{21}, u_x) → W_{24}
  842. Translate(T_{21}, u_x) → Z_{24}
  843. Translate(U_{21}, u_x) → A_{25}
  844. Polygon(V_{24}, W_{24}, Z_{24}, A_{25}) → mnohoúhelník68''', v_{28}, w_{27}, z_{25}, a_{29}
  845. Translate(V_{21}, u_x) → B_{25}
  846. Translate(W_{21}, u_x) → C_{25}
  847. Translate(Z_{21}, u_x) → D_{25}
  848. Translate(A_{22}, u_x) → E_{25}
  849. Polygon(B_{25}, C_{25}, D_{25}, E_{25}) → mnohoúhelník69''', b_{30}, c_{30}, d_{29}, e_{29}
  850. Translate(B_{22}, u_x) → F_{25}
  851. Translate(C_{22}, u_x) → G_{25}
  852. Translate(D_{22}, u_x) → H_{25}
  853. Translate(E_{22}, u_x) → I_{25}
  854. Polygon(F_{25}, G_{25}, H_{25}, I_{25}) → mnohoúhelník70''', f_{30}, g_{30}, h_{30}, i_{29}
  855. Translate(F_{22}, u_x) → J_{25}
  856. Translate(G_{22}, u_x) → K_{25}
  857. Translate(H_{22}, u_x) → L_{25}
  858. Translate(I_{22}, u_x) → M_{25}
  859. Polygon(J_{25}, K_{25}, L_{25}, M_{25}) → mnohoúhelník71''', j_{32}, k_{32}, l_{33}, m_{32}
  860. Translate(J_{22}, u_x) → N_{25}
  861. Translate(K_{22}, u_x) → O_{25}
  862. Translate(L_{22}, u_x) → P_{25}
  863. Translate(M_{22}, u_x) → Q_{25}
  864. Polygon(N_{25}, O_{25}, P_{25}, Q_{25}) → mnohoúhelník72''', n_{29}, o_{26}, p_{31}, q_{32}
  865. Translate(B_{20}, u_x) → R_{25}
  866. Translate(C_{20}, u_x) → S_{25}
  867. Translate(D_{20}, u_x) → T_{25}
  868. Translate(E_{20}, u_x) → U_{25}
  869. Polygon(R_{25}, S_{25}, T_{25}, U_{25}) → mnohoúhelník43''', r_{29}, s_{29}, t_{30}, u_{27}
  870. Translate(F_{20}, u_x) → V_{25}
  871. Translate(G_{20}, u_x) → W_{25}
  872. Translate(H_{20}, u_x) → Z_{25}
  873. Translate(I_{20}, u_x) → A_{26}
  874. Polygon(V_{25}, W_{25}, Z_{25}, A_{26}) → mnohoúhelník44''', v_{29}, w_{28}, z_{26}, a_{30}
  875. Translate(J_{20}, u_x) → B_{26}
  876. Translate(K_{20}, u_x) → C_{26}
  877. Translate(L_{20}, u_x) → D_{26}
  878. Translate(M_{20}, u_x) → E_{26}
  879. Polygon(B_{26}, C_{26}, D_{26}, E_{26}) → mnohoúhelník45''', b_{31}, c_{31}, d_{30}, e_{30}
  880. Translate(N_{20}, u_x) → F_{26}
  881. Translate(O_{20}, u_x) → G_{26}
  882. Translate(P_{20}, u_x) → H_{26}
  883. Translate(Q_{20}, u_x) → I_{26}
  884. Polygon(F_{26}, G_{26}, H_{26}, I_{26}) → mnohoúhelník46''', f_{31}, g_{31}, h_{31}, i_{30}
  885. Translate(R_{20}, u_x) → J_{26}
  886. Translate(S_{20}, u_x) → K_{26}
  887. Translate(T_{20}, u_x) → L_{26}
  888. Translate(U_{20}, u_x) → M_{26}
  889. Polygon(J_{26}, K_{26}, L_{26}, M_{26}) → mnohoúhelník47''', j_{33}, k_{33}, l_{34}, m_{33}
  890. Translate(V_{20}, u_x) → N_{26}
  891. Translate(W_{20}, u_x) → O_{26}
  892. Translate(Z_{20}, u_x) → P_{26}
  893. Translate(A_{21}, u_x) → Q_{26}
  894. Polygon(N_{26}, O_{26}, P_{26}, Q_{26}) → mnohoúhelník48''', n_{30}, o_{27}, p_{32}, q_{33}
  895. Translate(B_{21}, u_x) → R_{26}
  896. Translate(C_{21}, u_x) → S_{26}
  897. Translate(D_{21}, u_x) → T_{26}
  898. Translate(E_{21}, u_x) → U_{26}
  899. Polygon(R_{26}, S_{26}, T_{26}, U_{26}) → mnohoúhelník49''', r_{30}, s_{30}, t_{31}, u_{28}
  900. Translate(F_{21}, u_x) → V_{26}
  901. Translate(G_{21}, u_x) → W_{26}
  902. Translate(H_{21}, u_x) → Z_{26}
  903. Translate(I_{21}, u_x) → A_{27}
  904. Polygon(V_{26}, W_{26}, Z_{26}, A_{27}) → mnohoúhelník50''', v_{30}, w_{29}, z_{27}, a_{31}
  905. Translate(J_{21}, u_x) → B_{27}
  906. Translate(K_{21}, u_x) → C_{27}
  907. Translate(L_{21}, u_x) → D_{27}
  908. Translate(M_{21}, u_x) → E_{27}
  909. Polygon(B_{27}, C_{27}, D_{27}, E_{27}) → mnohoúhelník67''', b_{32}, c_{32}, d_{31}, e_{31}
  910. Translate(V_{22}, u_x) → F_{27}
  911. Translate(W_{22}, u_x) → G_{27}
  912. Translate(Z_{22}, u_x) → H_{27}
  913. Translate(A_{23}, u_x) → I_{27}
  914. Polygon(F_{27}, G_{27}, H_{27}, I_{27}) → mnohoúhelník40''', f_{32}, g_{32}, h_{32}, i_{31}
  915. Translate(B_{23}, u_x) → J_{27}
  916. Translate(C_{23}, u_x) → K_{27}
  917. Translate(D_{23}, u_x) → L_{27}
  918. Translate(E_{23}, u_x) → M_{27}
  919. Polygon(J_{27}, K_{27}, L_{27}, M_{27}) → mnohoúhelník41''', j_{34}, k_{34}, l_{35}, m_{34}
  920. Translate(F_{23}, u_x) → N_{27}
  921. Translate(G_{23}, u_x) → O_{27}
  922. Translate(H_{23}, u_x) → P_{27}
  923. Translate(I_{23}, u_x) → Q_{27}
  924. Polygon(N_{27}, O_{27}, P_{27}, Q_{27}) → mnohoúhelník42''', n_{31}, o_{28}, p_{33}, q_{34}
  925. Translate(F_{24}, u_x) → R_{27}
  926. Translate(G_{24}, u_x) → S_{27}
  927. Translate(H_{24}, u_x) → T_{27}
  928. Translate(I_{24}, u_x) → U_{27}
  929. Polygon(R_{27}, S_{27}, T_{27}, U_{27}) → mnohoúhelník64''', r_{31}, s_{31}, t_{32}, u_{29}
  930. Translate(J_{24}, u_x) → V_{27}
  931. Translate(K_{24}, u_x) → W_{27}
  932. Translate(L_{24}, u_x) → Z_{27}
  933. Translate(M_{24}, u_x) → A_{28}
  934. Polygon(V_{27}, W_{27}, Z_{27}, A_{28}) → mnohoúhelník65''', v_{31}, w_{30}, z_{28}, a_{32}
  935. Translate(N_{24}, u_x) → B_{28}
  936. Translate(O_{24}, u_x) → C_{28}
  937. Translate(P_{24}, u_x) → D_{28}
  938. Translate(Q_{24}, u_x) → E_{28}
  939. Polygon(B_{28}, C_{28}, D_{28}, E_{28}) → mnohoúhelník66''', b_{33}, c_{33}, d_{32}, e_{32}
  940. Translate(N_{22}, u_x) → F_{28}
  941. Translate(O_{22}, u_x) → G_{28}
  942. Translate(P_{22}, u_x) → H_{28}
  943. Translate(Q_{22}, u_x) → I_{28}
  944. Polygon(F_{28}, G_{28}, H_{28}, I_{28}) → mnohoúhelník38''', f_{33}, g_{33}, h_{33}, i_{32}
  945. Translate(R_{22}, u_x) → J_{28}
  946. Translate(S_{22}, u_x) → K_{28}
  947. Translate(T_{22}, u_x) → L_{28}
  948. Translate(U_{22}, u_x) → M_{28}
  949. Polygon(J_{28}, K_{28}, L_{28}, M_{28}) → mnohoúhelník39''', j_{35}, k_{35}, l_{36}, m_{35}
  950. Translate(J_{23}, u_x) → N_{28}
  951. Translate(K_{23}, u_x) → O_{28}
  952. Translate(L_{23}, u_x) → P_{28}
  953. Translate(M_{23}, u_x) → Q_{28}
  954. Polygon(N_{28}, O_{28}, P_{28}, Q_{28}) → mnohoúhelník59''', n_{32}, o_{29}, p_{34}, q_{35}
  955. Translate(N_{23}, u_x) → R_{28}
  956. Translate(O_{23}, u_x) → S_{28}
  957. Translate(P_{23}, u_x) → T_{28}
  958. Translate(Q_{23}, u_x) → U_{28}
  959. Polygon(R_{28}, S_{28}, T_{28}, U_{28}) → mnohoúhelník60''', r_{32}, s_{32}, t_{33}, u_{30}
  960. Translate(R_{23}, u_x) → V_{28}
  961. Translate(S_{23}, u_x) → W_{28}
  962. Translate(T_{23}, u_x) → Z_{28}
  963. Translate(U_{23}, u_x) → A_{29}
  964. Polygon(V_{28}, W_{28}, Z_{28}, A_{29}) → mnohoúhelník61''', v_{32}, w_{31}, z_{29}, a_{33}
  965. Translate(V_{23}, u_x) → B_{29}
  966. Translate(W_{23}, u_x) → C_{29}
  967. Translate(Z_{23}, u_x) → D_{29}
  968. Translate(A_{24}, u_x) → E_{29}
  969. Polygon(B_{29}, C_{29}, D_{29}, E_{29}) → mnohoúhelník62''', b_{34}, c_{34}, d_{33}, e_{33}
  970. Translate(B_{24}, u_x) → F_{29}
  971. Translate(C_{24}, u_x) → G_{29}
  972. Translate(D_{24}, u_x) → H_{29}
  973. Translate(E_{24}, u_x) → I_{29}
  974. Polygon(F_{29}, G_{29}, H_{29}, I_{29}) → mnohoúhelník63''', f_{34}, g_{34}, h_{34}, i_{33}

AI 绘图提示语参考

从坐标原点出发,沿水平轴和垂直轴各画一条直线作为参考轴。以原点为圆心画一个圆,与水平轴交于一点,过该点作垂直轴的平行线;再与垂直轴交于另一点,过该点作水平轴的平行线。以这两个交点为圆心分别画圆,逐步在两条轴上生成一系列等距的点。连接这些点形成一组平行线,构成网格状结构,展示前n个自然数求和的几何推导过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。