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Square and Integer Points

Square and Integer Points
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2023-03-22 22:39
PolygonCoordinate GeometryIntegral
In collections geometriadinamica.es
This example demonstrates the relationship between squares and integer points. Key mathematical concepts include the properties of squares, the definition of integer points, and the application of linear equations. Using GeoGebra commands such as Line, Vector, and Translate, one can construct squares and explore their relationship with integer points. Suitable for students at the junior high school level and above to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Line(A, C) → c
  3. Vector(A, B) → u
  4. Vector(A, C) → w
  5. Translate(E, u) → E'
  6. Translate(G_1, u) → H_1
  7. Translate(F, u) → F'
  8. Translate(D_1, w) → U_1
  9. Translate(E_1, w) → V_1
  10. Translate(F_1, w) → W_1
  11. Translate(B, w) → B'
  12. Polygon(C, G_1, E', H_1, B', W_1, V_1, U_1, E, F, A, D_1, E_1, F_1, B, F') → poly1, c_1, f', e', h_1, b', w_1, v_1, u_1, g_1, e, f, a_1, d_1, e_1, f_1, b_1
  13. Translate(C, w) → C'
  14. Translate(G_1, w) → Z_1
  15. Translate(E, w) → E'_1
  16. Translate(F, w) → F'_1
  17. Translate(A, w) → A'
  18. Translate(D_1, w) → A_2
  19. Translate(E_1, w) → B_2
  20. Translate(F_1, w) → C_2
  21. Translate(B, w) → B'_1
  22. Translate(F', w) → F''
  23. Translate(E', w) → E''
  24. Translate(H_1, w) → D_2
  25. Translate(B', w) → B''
  26. Translate(W_1, w) → E_2
  27. Translate(V_1, w) → F_2
  28. Translate(U_1, w) → G_2
  29. Translate(C', w) → C''
  30. Translate(Z_1, w) → H_2
  31. Translate(E'_1, w) → I_2
  32. Translate(F'_1, w) → J_2
  33. Translate(A', w) → A''
  34. Translate(A_2, w) → K_2
  35. Translate(B_2, w) → L_2
  36. Translate(C_2, w) → M_2
  37. Translate(B'_1, w) → N_2
  38. Translate(F'', w) → F'''
  39. Translate(E'', w) → E'''
  40. Translate(D_2, w) → O_2
  41. Translate(B'', w) → B'''
  42. Translate(E_2, w) → P_2
  43. Translate(F_2, w) → Q_2
  44. Translate(G_2, w) → R_2
  45. Translate(C, u) → C'_1
  46. Translate(G_1, u) → S_2
  47. Translate(E, u) → E'_2
  48. Translate(F, u) → F'_2
  49. Translate(A, u) → A'_1
  50. Translate(D_1, u) → T_2
  51. Translate(E_1, u) → U_2
  52. Translate(F_1, u) → V_2
  53. Translate(B, u) → B'_2
  54. Translate(F', u) → F''_1
  55. Translate(E', u) → E''_1
  56. Translate(H_1, u) → W_2
  57. Translate(B', u) → B''_1
  58. Translate(W_1, u) → Z_2
  59. Translate(V_1, u) → A_3
  60. Translate(U_1, u) → B_3
  61. Translate(C', u) → C''_1
  62. Translate(Z_1, u) → C_3
  63. Translate(E'_1, u) → D_3
  64. Translate(F'_1, u) → E_3
  65. Translate(A', u) → A''_1
  66. Translate(A_2, u) → F_3
  67. Translate(B_2, u) → G_3
  68. Translate(C_2, u) → H_3
  69. Translate(B'_1, u) → I_3
  70. Translate(F'', u) → F'''_1
  71. Translate(E'', u) → E'''_1
  72. Translate(D_2, u) → J_3
  73. Translate(B'', u) → B'''_1
  74. Translate(E_2, u) → K_3
  75. Translate(F_2, u) → L_3
  76. Translate(G_2, u) → M_3
  77. Translate(C'', u) → C'''
  78. Translate(H_2, u) → N_3
  79. Translate(I_2, u) → O_3
  80. Translate(J_2, u) → P_3
  81. Translate(A'', u) → A'''
  82. Translate(K_2, u) → Q_3
  83. Translate(L_2, u) → R_3
  84. Translate(M_2, u) → S_3
  85. Translate(N_2, u) → T_3
  86. Translate(F''', u) → U_3
  87. Translate(E''', u) → V_3
  88. Translate(O_2, u) → W_3
  89. Translate(B''', u) → Z_3
  90. Translate(P_2, u) → A_4
  91. Translate(Q_2, u) → B_4
  92. Translate(R_2, u) → C_4
  93. Translate(C'_1, u) → D_4
  94. Translate(S_2, u) → E_4
  95. Translate(E'_2, u) → F_4
  96. Translate(F'_2, u) → G_4
  97. Translate(A'_1, u) → H_4
  98. Translate(T_2, u) → I_4
  99. Translate(U_2, u) → J_4
  100. Translate(V_2, u) → K_4
  101. Translate(B'_2, u) → L_4
  102. Translate(F''_1, u) → M_4
  103. Translate(E''_1, u) → N_4
  104. Translate(W_2, u) → O_4
  105. Translate(B''_1, u) → P_4
  106. Translate(Z_2, u) → Q_4
  107. Translate(A_3, u) → R_4
  108. Translate(B_3, u) → S_4
  109. Translate(C''_1, u) → T_4
  110. Translate(C_3, u) → U_4
  111. Translate(D_3, u) → V_4
  112. Translate(E_3, u) → W_4
  113. Translate(A''_1, u) → Z_4
  114. Translate(F_3, u) → A_5
  115. Translate(G_3, u) → B_5
  116. Translate(H_3, u) → C_5
  117. Translate(I_3, u) → D_5
  118. Translate(F'''_1, u) → E_5
  119. Translate(E'''_1, u) → F_5
  120. Translate(J_3, u) → G_5
  121. Translate(B'''_1, u) → H_5
  122. Translate(K_3, u) → I_5
  123. Translate(L_3, u) → J_5
  124. Translate(M_3, u) → K_5
  125. Translate(T_4, w) → L_5
  126. Translate(U_4, w) → M_5
  127. Translate(V_4, w) → N_5
  128. Translate(W_4, w) → O_5
  129. Translate(Z_4, w) → P_5
  130. Translate(A_5, w) → Q_5
  131. Translate(B_5, w) → R_5
  132. Translate(C_5, w) → S_5
  133. Translate(D_5, w) → T_5
  134. Translate(E_5, w) → U_5
  135. Translate(F_5, w) → V_5
  136. Translate(G_5, w) → W_5
  137. Translate(H_5, w) → Z_5
  138. Translate(I_5, w) → A_6
  139. Translate(J_5, w) → B_6
  140. Translate(K_5, w) → C_6
  141. Translate(C'', w) → C'''_1
  142. Translate(H_2, w) → D_6
  143. Translate(I_2, w) → E_6
  144. Translate(J_2, w) → F_6
  145. Translate(A'', w) → A'''_1
  146. Translate(K_2, w) → G_6
  147. Translate(L_2, w) → H_6
  148. Translate(M_2, w) → I_6
  149. Translate(N_2, w) → J_6
  150. Translate(F''', w) → K_6
  151. Translate(E''', w) → L_6
  152. Translate(O_2, w) → M_6
  153. Translate(B''', w) → N_6
  154. Translate(P_2, w) → O_6
  155. Translate(Q_2, w) → P_6
  156. Translate(R_2, w) → Q_6
  157. Translate(C''', w) → R_6
  158. Translate(N_3, w) → S_6
  159. Translate(O_3, w) → T_6
  160. Translate(P_3, w) → U_6
  161. Translate(A''', w) → V_6
  162. Translate(Q_3, w) → W_6
  163. Translate(R_3, w) → Z_6
  164. Translate(S_3, w) → A_7
  165. Translate(T_3, w) → B_7
  166. Translate(U_3, w) → C_7
  167. Translate(V_3, w) → D_7
  168. Translate(W_3, w) → E_7
  169. Translate(Z_3, w) → F_7
  170. Translate(A_4, w) → G_7
  171. Translate(B_4, w) → H_7
  172. Translate(C_4, w) → I_7
  173. Translate(L_5, w) → J_7
  174. Translate(M_5, w) → K_7
  175. Translate(N_5, w) → L_7
  176. Translate(O_5, w) → M_7
  177. Translate(P_5, w) → N_7
  178. Translate(Q_5, w) → O_7
  179. Translate(R_5, w) → P_7
  180. Translate(S_5, w) → Q_7
  181. Translate(T_5, w) → R_7
  182. Translate(U_5, w) → S_7
  183. Translate(V_5, w) → T_7
  184. Translate(W_5, w) → U_7
  185. Translate(Z_5, w) → V_7
  186. Translate(A_6, w) → W_7
  187. Translate(B_6, w) → Z_7
  188. Translate(C_6, w) → A_8
  189. Vector(A, B_8) → z
  190. Translate(C, z) → C'_2
  191. Translate(G_1, z) → C_8
  192. Translate(E, z) → E'_3
  193. Translate(F, z) → F'_3
  194. Translate(A, z) → A'_2
  195. Translate(D_1, z) → D_8
  196. Translate(E_1, z) → E_8
  197. Translate(F_1, z) → F_8
  198. Translate(B, z) → B'_3
  199. Translate(F', z) → F''_2
  200. Translate(E', z) → E''_2
  201. Translate(H_1, z) → G_8
  202. Translate(B', z) → B''_2
  203. Translate(W_1, z) → H_8
  204. Translate(V_1, z) → I_8
  205. Translate(U_1, z) → J_8
  206. Polygon(C'_2, C_8, E''_2, G_8, B''_2, H_8, I_8, J_8, E'_3, F'_3, A'_2, D_8, E_8, F_8, B'_3, F''_2) → poly1', c'_2, f''_2, e''_2, g_8, b''_2, h_8, i_8, j_8, c_8, e'_3, f'_3, a'_2, d_8, e_8, f_8, b'_3
  207. Translate(C'_2, w) → K_8
  208. Translate(C_8, w) → L_8
  209. Translate(E'_3, w) → M_8
  210. Translate(F'_3, w) → N_8
  211. Translate(A'_2, w) → O_8
  212. Translate(D_8, w) → P_8
  213. Translate(E_8, w) → Q_8
  214. Translate(F_8, w) → R_8
  215. Translate(B'_3, w) → S_8
  216. Translate(F''_2, w) → T_8
  217. Translate(E''_2, w) → U_8
  218. Translate(G_8, w) → V_8
  219. Translate(B''_2, w) → W_8
  220. Translate(H_8, w) → Z_8
  221. Translate(I_8, w) → A_9
  222. Translate(J_8, w) → B_9
  223. Polygon(K_8, L_8, U_8, V_8, W_8, Z_8, A_9, B_9, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8) → poly1'', k_8, t_8, u_8, v_8, w_8, z_8, a_9, b_9, l_8, m_8, n_8, o_8, p_8, q_8, r_8, s_8
  224. Translate(C'_2, u) → C_9
  225. Translate(C_8, u) → D_9
  226. Translate(E'_3, u) → E_9
  227. Translate(F'_3, u) → F_9
  228. Translate(A'_2, u) → G_9
  229. Translate(D_8, u) → H_9
  230. Translate(E_8, u) → I_9
  231. Translate(F_8, u) → J_9
  232. Translate(B'_3, u) → K_9
  233. Translate(F''_2, u) → L_9
  234. Translate(E''_2, u) → M_9
  235. Translate(G_8, u) → N_9
  236. Translate(B''_2, u) → O_9
  237. Translate(H_8, u) → P_9
  238. Translate(I_8, u) → Q_9
  239. Translate(J_8, u) → R_9
  240. Polygon(C_9, D_9, M_9, N_9, O_9, P_9, Q_9, R_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9) → poly1''_1, c_9, l_9, m_9, n_9, o_9, p_9, q_9, r_9, d_9, e_9, f_9, g_9, h_9, i_9, j_9, k_9
  241. Translate(K_8, w) → S_9
  242. Translate(L_8, w) → T_9
  243. Translate(M_8, w) → U_9
  244. Translate(N_8, w) → V_9
  245. Translate(O_8, w) → W_9
  246. Translate(P_8, w) → Z_9
  247. Translate(Q_8, w) → A_{10}
  248. Translate(R_8, w) → B_{10}
  249. Translate(S_8, w) → C_{10}
  250. Translate(T_8, w) → D_{10}
  251. Translate(U_8, w) → E_{10}
  252. Translate(V_8, w) → F_{10}
  253. Translate(W_8, w) → G_{10}
  254. Translate(Z_8, w) → H_{10}
  255. Translate(A_9, w) → I_{10}
  256. Translate(B_9, w) → J_{10}
  257. Polygon(S_9, T_9, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}) → poly1''', s_9, d_{10}, e_{10}, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, t_9, u_9, v_9, w_9, z_9, a_{10}, b_{10}, c_{10}
  258. Translate(C_9, w) → K_{10}
  259. Translate(D_9, w) → L_{10}
  260. Translate(E_9, w) → M_{10}
  261. Translate(F_9, w) → N_{10}
  262. Translate(G_9, w) → O_{10}
  263. Translate(H_9, w) → P_{10}
  264. Translate(I_9, w) → Q_{10}
  265. Translate(J_9, w) → R_{10}
  266. Translate(K_9, w) → S_{10}
  267. Translate(L_9, w) → T_{10}
  268. Translate(M_9, w) → U_{10}
  269. Translate(N_9, w) → V_{10}
  270. Translate(O_9, w) → W_{10}
  271. Translate(P_9, w) → Z_{10}
  272. Translate(Q_9, w) → A_{11}
  273. Translate(R_9, w) → B_{11}
  274. Polygon(K_{10}, L_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}) → poly2, k_{10}, t_{10}, u_{10}, v_{10}, w_{10}, z_{10}, a_{11}, b_{11}, l_{10}, m_{10}, n_{10}, o_{10}, p_{10}, q_{10}, r_{10}, s_{10}
  275. Translate(K_{10}, w) → C_{11}
  276. Translate(L_{10}, w) → D_{11}
  277. Translate(M_{10}, w) → E_{11}
  278. Translate(N_{10}, w) → F_{11}
  279. Translate(O_{10}, w) → G_{11}
  280. Translate(P_{10}, w) → H_{11}
  281. Translate(Q_{10}, w) → I_{11}
  282. Translate(R_{10}, w) → J_{11}
  283. Translate(S_{10}, w) → K_{11}
  284. Translate(T_{10}, w) → L_{11}
  285. Translate(U_{10}, w) → M_{11}
  286. Translate(V_{10}, w) → N_{11}
  287. Translate(W_{10}, w) → O_{11}
  288. Translate(Z_{10}, w) → P_{11}
  289. Translate(A_{11}, w) → Q_{11}
  290. Translate(B_{11}, w) → R_{11}
  291. Polygon(C_{11}, D_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}) → poly2', c_{11}, l_{11}, m_{11}, n_{11}, o_{11}, p_{11}, q_{11}, r_{11}, d_{11}, e_{11}, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}
  292. Translate(S_9, w) → S_{11}
  293. Translate(T_9, w) → T_{11}
  294. Translate(U_9, w) → U_{11}
  295. Translate(V_9, w) → V_{11}
  296. Translate(W_9, w) → W_{11}
  297. Translate(Z_9, w) → Z_{11}
  298. Translate(A_{10}, w) → A_{12}
  299. Translate(B_{10}, w) → B_{12}
  300. Translate(C_{10}, w) → C_{12}
  301. Translate(D_{10}, w) → D_{12}
  302. Translate(E_{10}, w) → E_{12}
  303. Translate(F_{10}, w) → F_{12}
  304. Translate(G_{10}, w) → G_{12}
  305. Translate(H_{10}, w) → H_{12}
  306. Translate(I_{10}, w) → I_{12}
  307. Translate(J_{10}, w) → J_{12}
  308. Polygon(S_{11}, T_{11}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}) → poly3, s_{11}, d_{12}, e_{12}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, t_{11}, u_{11}, v_{11}, w_{11}, z_{11}, a_{12}, b_{12}, c_{12}
  309. Translate(C_{11}, w) → K_{12}
  310. Translate(D_{11}, w) → L_{12}
  311. Translate(E_{11}, w) → M_{12}
  312. Translate(F_{11}, w) → N_{12}
  313. Translate(G_{11}, w) → O_{12}
  314. Translate(H_{11}, w) → P_{12}
  315. Translate(I_{11}, w) → Q_{12}
  316. Translate(J_{11}, w) → R_{12}
  317. Translate(K_{11}, w) → S_{12}
  318. Translate(L_{11}, w) → T_{12}
  319. Translate(M_{11}, w) → U_{12}
  320. Translate(N_{11}, w) → V_{12}
  321. Translate(O_{11}, w) → W_{12}
  322. Translate(P_{11}, w) → Z_{12}
  323. Translate(Q_{11}, w) → A_{13}
  324. Translate(R_{11}, w) → B_{13}
  325. Polygon(K_{12}, L_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}) → poly2'', k_{12}, t_{12}, u_{12}, v_{12}, w_{12}, z_{12}, a_{13}, b_{13}, l_{12}, m_{12}, n_{12}, o_{12}, p_{12}, q_{12}, r_{12}, s_{12}
  326. Translate(K_{12}, u) → C_{13}
  327. Translate(L_{12}, u) → D_{13}
  328. Translate(M_{12}, u) → E_{13}
  329. Translate(N_{12}, u) → F_{13}
  330. Translate(O_{12}, u) → G_{13}
  331. Translate(P_{12}, u) → H_{13}
  332. Translate(Q_{12}, u) → I_{13}
  333. Translate(R_{12}, u) → J_{13}
  334. Translate(S_{12}, u) → K_{13}
  335. Translate(T_{12}, u) → L_{13}
  336. Translate(U_{12}, u) → M_{13}
  337. Translate(V_{12}, u) → N_{13}
  338. Translate(W_{12}, u) → O_{13}
  339. Translate(Z_{12}, u) → P_{13}
  340. Translate(A_{13}, u) → Q_{13}
  341. Translate(B_{13}, u) → R_{13}
  342. Polygon(C_{13}, D_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, L_{13}) → poly2''', c_{13}, l_{13}, m_{13}, n_{13}, o_{13}, p_{13}, q_{13}, r_{13}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}
  343. Translate(C_{11}, u) → S_{13}
  344. Translate(D_{11}, u) → T_{13}
  345. Translate(E_{11}, u) → U_{13}
  346. Translate(F_{11}, u) → V_{13}
  347. Translate(G_{11}, u) → W_{13}
  348. Translate(H_{11}, u) → Z_{13}
  349. Translate(I_{11}, u) → A_{14}
  350. Translate(J_{11}, u) → B_{14}
  351. Translate(K_{11}, u) → C_{14}
  352. Translate(L_{11}, u) → D_{14}
  353. Translate(M_{11}, u) → E_{14}
  354. Translate(N_{11}, u) → F_{14}
  355. Translate(O_{11}, u) → G_{14}
  356. Translate(P_{11}, u) → H_{14}
  357. Translate(Q_{11}, u) → I_{14}
  358. Translate(R_{11}, u) → J_{14}
  359. Polygon(S_{13}, T_{13}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}, J_{14}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}) → poly2''_1, s_{13}, d_{14}, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, t_{13}, u_{13}, v_{13}, w_{13}, z_{13}, a_{14}, b_{14}, c_{14}
  360. Translate(K_{10}, u) → K_{14}
  361. Translate(L_{10}, u) → L_{14}
  362. Translate(M_{10}, u) → M_{14}
  363. Translate(N_{10}, u) → N_{14}
  364. Translate(O_{10}, u) → O_{14}
  365. Translate(P_{10}, u) → P_{14}
  366. Translate(Q_{10}, u) → Q_{14}
  367. Translate(R_{10}, u) → R_{14}
  368. Translate(S_{10}, u) → S_{14}
  369. Translate(T_{10}, u) → T_{14}
  370. Translate(U_{10}, u) → U_{14}
  371. Translate(V_{10}, u) → V_{14}
  372. Translate(W_{10}, u) → W_{14}
  373. Translate(Z_{10}, u) → Z_{14}
  374. Translate(A_{11}, u) → A_{15}
  375. Translate(B_{11}, u) → B_{15}
  376. Polygon(K_{14}, L_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}) → poly2'_1, k_{14}, t_{14}, u_{14}, v_{14}, w_{14}, z_{14}, a_{15}, b_{15}, l_{14}, m_{14}, n_{14}, o_{14}, p_{14}, q_{14}, r_{14}, s_{14}
  377. Translate(C_9, u) → C_{15}
  378. Translate(D_9, u) → D_{15}
  379. Translate(E_9, u) → E_{15}
  380. Translate(F_9, u) → F_{15}
  381. Translate(G_9, u) → G_{15}
  382. Translate(H_9, u) → H_{15}
  383. Translate(I_9, u) → I_{15}
  384. Translate(J_9, u) → J_{15}
  385. Translate(K_9, u) → K_{15}
  386. Translate(L_9, u) → L_{15}
  387. Translate(M_9, u) → M_{15}
  388. Translate(N_9, u) → N_{15}
  389. Translate(O_9, u) → O_{15}
  390. Translate(P_9, u) → P_{15}
  391. Translate(Q_9, u) → Q_{15}
  392. Translate(R_9, u) → R_{15}
  393. Polygon(C_{15}, D_{15}, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}) → poly4, c_{15}, l_{15}, m_{15}, n_{15}, o_{15}, p_{15}, q_{15}, r_{15}, d_{15}, e_{15}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}
  394. Translate(C_{15}, u) → S_{15}
  395. Translate(D_{15}, u) → T_{15}
  396. Translate(E_{15}, u) → U_{15}
  397. Translate(F_{15}, u) → V_{15}
  398. Translate(G_{15}, u) → W_{15}
  399. Translate(H_{15}, u) → Z_{15}
  400. Translate(I_{15}, u) → A_{16}
  401. Translate(J_{15}, u) → B_{16}
  402. Translate(K_{15}, u) → C_{16}
  403. Translate(L_{15}, u) → D_{16}
  404. Translate(M_{15}, u) → E_{16}
  405. Translate(N_{15}, u) → F_{16}
  406. Translate(O_{15}, u) → G_{16}
  407. Translate(P_{15}, u) → H_{16}
  408. Translate(Q_{15}, u) → I_{16}
  409. Translate(R_{15}, u) → J_{16}
  410. Polygon(S_{15}, T_{15}, E_{16}, F_{16}, G_{16}, H_{16}, I_{16}, J_{16}, U_{15}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}) → poly4', s_{15}, d_{16}, e_{16}, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, t_{15}, u_{15}, v_{15}, w_{15}, z_{15}, a_{16}, b_{16}, c_{16}
  411. Translate(K_{14}, u) → K_{16}
  412. Translate(L_{14}, u) → L_{16}
  413. Translate(M_{14}, u) → M_{16}
  414. Translate(N_{14}, u) → N_{16}
  415. Translate(O_{14}, u) → O_{16}
  416. Translate(P_{14}, u) → P_{16}
  417. Translate(Q_{14}, u) → Q_{16}
  418. Translate(R_{14}, u) → R_{16}
  419. Translate(S_{14}, u) → S_{16}
  420. Translate(T_{14}, u) → T_{16}
  421. Translate(U_{14}, u) → U_{16}
  422. Translate(V_{14}, u) → V_{16}
  423. Translate(W_{14}, u) → W_{16}
  424. Translate(Z_{14}, u) → Z_{16}
  425. Translate(A_{15}, u) → A_{17}
  426. Translate(B_{15}, u) → B_{17}
  427. Polygon(K_{16}, L_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}, B_{17}, M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, R_{16}, S_{16}, T_{16}) → poly5, k_{16}, t_{16}, u_{16}, v_{16}, w_{16}, z_{16}, a_{17}, b_{17}, l_{16}, m_{16}, n_{16}, o_{16}, p_{16}, q_{16}, r_{16}, s_{16}
  428. Translate(S_{13}, u) → C_{17}
  429. Translate(T_{13}, u) → D_{17}
  430. Translate(U_{13}, u) → E_{17}
  431. Translate(V_{13}, u) → F_{17}
  432. Translate(W_{13}, u) → G_{17}
  433. Translate(Z_{13}, u) → H_{17}
  434. Translate(A_{14}, u) → I_{17}
  435. Translate(B_{14}, u) → J_{17}
  436. Translate(C_{14}, u) → K_{17}
  437. Translate(D_{14}, u) → L_{17}
  438. Translate(E_{14}, u) → M_{17}
  439. Translate(F_{14}, u) → N_{17}
  440. Translate(G_{14}, u) → O_{17}
  441. Translate(H_{14}, u) → P_{17}
  442. Translate(I_{14}, u) → Q_{17}
  443. Translate(J_{14}, u) → R_{17}
  444. Polygon(C_{17}, D_{17}, M_{17}, N_{17}, O_{17}, P_{17}, Q_{17}, R_{17}, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}, J_{17}, K_{17}, L_{17}) → poly6, c_{17}, l_{17}, m_{17}, n_{17}, o_{17}, p_{17}, q_{17}, r_{17}, d_{17}, e_{17}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, k_{17}
  445. Translate(C_{13}, u) → S_{17}
  446. Translate(D_{13}, u) → T_{17}
  447. Translate(E_{13}, u) → U_{17}
  448. Translate(F_{13}, u) → V_{17}
  449. Translate(G_{13}, u) → W_{17}
  450. Translate(H_{13}, u) → Z_{17}
  451. Translate(I_{13}, u) → A_{18}
  452. Translate(J_{13}, u) → B_{18}
  453. Translate(K_{13}, u) → C_{18}
  454. Translate(L_{13}, u) → D_{18}
  455. Translate(M_{13}, u) → E_{18}
  456. Translate(N_{13}, u) → F_{18}
  457. Translate(O_{13}, u) → G_{18}
  458. Translate(P_{13}, u) → H_{18}
  459. Translate(Q_{13}, u) → I_{18}
  460. Translate(R_{13}, u) → J_{18}
  461. Polygon(S_{17}, T_{17}, E_{18}, F_{18}, G_{18}, H_{18}, I_{18}, J_{18}, U_{17}, V_{17}, W_{17}, Z_{17}, A_{18}, B_{18}, C_{18}, D_{18}) → poly7, s_{17}, d_{18}, e_{18}, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, t_{17}, u_{17}, v_{17}, w_{17}, z_{17}, a_{18}, b_{18}, c_{18}
  462. Translate(S_{11}, w) → K_{18}
  463. Translate(T_{11}, w) → L_{18}
  464. Translate(U_{11}, w) → M_{18}
  465. Translate(V_{11}, w) → N_{18}
  466. Translate(W_{11}, w) → O_{18}
  467. Translate(Z_{11}, w) → P_{18}
  468. Translate(A_{12}, w) → Q_{18}
  469. Translate(B_{12}, w) → R_{18}
  470. Translate(C_{12}, w) → S_{18}
  471. Translate(D_{12}, w) → T_{18}
  472. Translate(E_{12}, w) → U_{18}
  473. Translate(F_{12}, w) → V_{18}
  474. Translate(G_{12}, w) → W_{18}
  475. Translate(H_{12}, w) → Z_{18}
  476. Translate(I_{12}, w) → A_{19}
  477. Translate(J_{12}, w) → B_{19}
  478. Polygon(K_{18}, L_{18}, U_{18}, V_{18}, W_{18}, Z_{18}, A_{19}, B_{19}, M_{18}, N_{18}, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}) → poly3', k_{18}, t_{18}, u_{18}, v_{18}, w_{18}, z_{18}, a_{19}, b_{19}, l_{18}, m_{18}, n_{18}, o_{18}, p_{18}, q_{18}, r_{18}, s_{18}
  479. Translate(K_{18}, u) → C_{19}
  480. Translate(L_{18}, u) → D_{19}
  481. Translate(M_{18}, u) → E_{19}
  482. Translate(N_{18}, u) → F_{19}
  483. Translate(O_{18}, u) → G_{19}
  484. Translate(P_{18}, u) → H_{19}
  485. Translate(Q_{18}, u) → I_{19}
  486. Translate(R_{18}, u) → J_{19}
  487. Translate(S_{18}, u) → K_{19}
  488. Translate(T_{18}, u) → L_{19}
  489. Translate(U_{18}, u) → M_{19}
  490. Translate(V_{18}, u) → N_{19}
  491. Translate(W_{18}, u) → O_{19}
  492. Translate(Z_{18}, u) → P_{19}
  493. Translate(A_{19}, u) → Q_{19}
  494. Translate(B_{19}, u) → R_{19}
  495. Polygon(C_{19}, D_{19}, M_{19}, N_{19}, O_{19}, P_{19}, Q_{19}, R_{19}, E_{19}, F_{19}, G_{19}, H_{19}, I_{19}, J_{19}, K_{19}, L_{19}) → poly3'', c_{19}, l_{19}, m_{19}, n_{19}, o_{19}, p_{19}, q_{19}, r_{19}, d_{19}, e_{19}, f_{19}, g_{19}, h_{19}, i_{19}, j_{19}, k_{19}
  496. Translate(C_{19}, u) → S_{19}
  497. Translate(D_{19}, u) → T_{19}
  498. Translate(E_{19}, u) → U_{19}
  499. Translate(F_{19}, u) → V_{19}
  500. Translate(G_{19}, u) → W_{19}
  501. Translate(H_{19}, u) → Z_{19}
  502. Translate(I_{19}, u) → A_{20}
  503. Translate(J_{19}, u) → B_{20}
  504. Translate(K_{19}, u) → C_{20}
  505. Translate(L_{19}, u) → D_{20}
  506. Translate(M_{19}, u) → E_{20}
  507. Translate(N_{19}, u) → F_{20}
  508. Translate(O_{19}, u) → G_{20}
  509. Translate(P_{19}, u) → H_{20}
  510. Translate(Q_{19}, u) → I_{20}
  511. Translate(R_{19}, u) → J_{20}
  512. Polygon(S_{19}, T_{19}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, B_{20}, C_{20}, D_{20}) → poly3''', s_{19}, d_{20}, e_{20}, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, t_{19}, u_{19}, v_{19}, w_{19}, z_{19}, a_{20}, b_{20}, c_{20}
  513. Translate(S_{19}, u) → K_{20}
  514. Translate(T_{19}, u) → L_{20}
  515. Translate(U_{19}, u) → M_{20}
  516. Translate(V_{19}, u) → N_{20}
  517. Translate(W_{19}, u) → O_{20}
  518. Translate(Z_{19}, u) → P_{20}
  519. Translate(A_{20}, u) → Q_{20}
  520. Translate(B_{20}, u) → R_{20}
  521. Translate(C_{20}, u) → S_{20}
  522. Translate(D_{20}, u) → T_{20}
  523. Translate(E_{20}, u) → U_{20}
  524. Translate(F_{20}, u) → V_{20}
  525. Translate(G_{20}, u) → W_{20}
  526. Translate(H_{20}, u) → Z_{20}
  527. Translate(I_{20}, u) → A_{21}
  528. Translate(J_{20}, u) → B_{21}
  529. Polygon(K_{20}, L_{20}, U_{20}, V_{20}, W_{20}, Z_{20}, A_{21}, B_{21}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}) → poly8, k_{20}, t_{20}, u_{20}, v_{20}, w_{20}, z_{20}, a_{21}, b_{21}, l_{20}, m_{20}, n_{20}, o_{20}, p_{20}, q_{20}, r_{20}, s_{20}
  530. Polygon(C, B', B, A) → poly9, c_2, b'_1, b_2, a_2
  531. Vector(B_8, C'_2) → d
  532. Vector(B_8, B'_3) → g

AI Drawing Prompt Reference

Draw a geometric figure consisting of a grid of squares with integer-coordinate vertices. Start with a base square, then translate it repeatedly along its two adjacent side directions to create multiple rows and columns of squares. All vertices lie on integer lattice points, forming a neat rectangular array. The figure shows many translated copies of the original square, connected edge-to-edge, emphasizing the relationship between squares and integer points.
The prompt above was compiled from the original drawing commands and is for reference only.