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Natural Numbers and Polygon Construction

Natural Numbers and Polygon Construction
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2018-04-29 02:57
PolygonFunctionCoordinate Geometry
This example demonstrates polygon construction and related phenomena using GeoGebra; core math concepts include polygons, segments, function graphs, special points, correlation, and expected value; construction highlights involve commands like Polygon and Segment from the GeoGebra summary; suitable for high school mathematics teaching or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Polygon(B, C, 4) → poly2, i, j, k, l, D, E
  3. Polygon(B, C, 5) → poly3, m, n, p, q, r, H, I, J
  4. Polygon(B, C, 6) → poly4, s, L, t, a, b, c, d, F, G, K
  5. Polygon(B, C, 7) → poly5, e, O, P, Q, f_1, g_1, h_1, i_1, j_1, k_1, M, N
  6. Polygon(B, C, 8) → poly6, l_1, S, T, U, V, W, m_1, n_1, p_1, q_1, r_1, s_1, t_1, R
  7. Polygon(B, C, 9) → poly7, a_1, Z, A_1, B_1, C_1, D_1, E_1, F_1, b_1, c_1, d_1, e_1, f_2, g_2, h_2, i_2
  8. Segment(B, C) → j_2
  9. Segment(I, C) → k_2
  10. Segment(I, A) → l_2
  11. Segment(I, D) → m_2
  12. Segment(I, E) → n_2
  13. Segment(I, B) → p_2
  14. Segment(E, J) → q_2
  15. Segment(D, H) → r_2
  16. Segment(G, H) → s_2
  17. Segment(H, F) → t_2
  18. Segment(G, K) → a_2
  19. Segment(G, I) → b_2
  20. Segment(K, I) → c_2
  21. Segment(K, L) → d_2
  22. Segment(L, J) → e_2
  23. Segment(K, J) → f_3
  24. Segment(P, L) → g_3
  25. Segment(L, Q) → h_3
  26. Segment(K, P) → i_3
  27. Segment(K, O) → j_3
  28. Segment(G, O) → k_3
  29. Segment(N, G) → l_3
  30. Segment(F, N) → m_3
  31. Segment(M, F) → n_3
  32. Segment(W, Q) → p_3
  33. Segment(Q, V) → q_3
  34. Segment(V, P) → r_3
  35. Segment(F_1, W) → s_3
  36. Segment(W, E_1) → t_3
  37. Segment(E_1, V) → a_3
  38. Segment(D_1, V) → b_3
  39. Segment(D_1, U) → c_3
  40. Segment(U, C_1) → d_3
  41. Segment(C_1, T) → e_3
  42. Segment(T, B_1) → f_4
  43. Segment(B_1, S) → g_4
  44. Segment(S, A_1) → h_4
  45. Segment(S, N) → i_4
  46. Segment(N, T) → j_4
  47. Segment(T, O) → k_4
  48. Segment(O, U) → l_4
  49. Segment(U, P) → m_4
  50. Segment(M, R) → n_4
  51. Segment(R, Z) → p_4
  52. Segment(E, B) → q_4
  53. Segment(J, B) → r_4
  54. Segment(I, J) → s_4
  55. Segment(E, D) → t_4
  56. Segment(D, C) → a_4
  57. Segment(A, C) → b_4
  58. Segment(A, B) → c_4
  59. Segment(B, Q) → d_4
  60. Segment(B, W) → e_4
  61. Segment(C, R) → f_5
  62. Segment(C, H) → g_5
  63. Segment(C, F) → h_5
  64. Segment(C, M) → i_5
  65. Segment(C, Z) → j_5
  66. Segment(Z, A_1) → k_5
  67. Segment(R, S) → l_5
  68. Segment(M, N) → m_5
  69. Segment(F, G) → n_5
  70. Segment(Q, P) → p_5
  71. Segment(P, O) → q_5
  72. Segment(N, O) → r_5
  73. Segment(S, T) → s_5
  74. Segment(A_1, B_1) → t_5
  75. Segment(B_1, C_1) → a_5
  76. Segment(C_1, D_1) → b_5
  77. Segment(D_1, E_1) → c_5
  78. Segment(F_1, E_1) → d_5
  79. Segment(B, F_1) → e_5
  80. Segment(I, H) → f_6
  81. Segment(U, V) → g_6
  82. Segment(V, W) → h_6
  83. Segment(U, T) → i_6
  84. Segment(L, B) → j_6
  85. Polygon(A_2, B_2, 3) → poly1_1, f_{13}, g_{13}, h_{13}, C_2
  86. Polygon(B_2, C_2, 4) → poly2_1, i_{13}, j_{13}, k_{11}, l_{11}, D_2, E_2
  87. Polygon(B_2, C_2, 5) → poly3_1, m_{11}, n_{11}, p_{11}, q_{11}, r_{11}, H_1, I_1, J_1
  88. Polygon(B_2, C_2, 6) → poly4_1, s_{11}, L_1, t_{11}, a_{11}, b_{11}, c_{11}, d_{11}, F_2, G_1, K_1
  89. Polygon(B_2, C_2, 7) → poly5_1, e_{11}, O_1, P_1, Q_1, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, k_{10}, M_1, N_1
  90. Polygon(B_2, C_2, 8) → poly6_1, l_{10}, S_1, T_1, U_1, V_1, W_1, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, R_1
  91. Polygon(B_2, C_2, 9) → poly7_1, a_{10}, Z_1, A_3, B_3, C_3, D_3, E_3, F_3, b_{10}, c_{10}, d_{10}, e_{10}, f_{11}, g_{11}, h_{11}, i_{11}
  92. Segment(B_2, C_2) → j_7
  93. Segment(I_1, C_2) → k_6
  94. Segment(I_1, A_2) → l_6
  95. Segment(I_1, D_2) → m_6
  96. Segment(I_1, E_2) → n_6
  97. Segment(I_1, B_2) → p_6
  98. Segment(E_2, J_1) → q_6
  99. Segment(D_2, H_1) → r_6
  100. Segment(G_1, H_1) → s_6
  101. Segment(H_1, F_2) → t_6
  102. Segment(G_1, K_1) → a_6
  103. Segment(G_1, I_1) → b_6
  104. Segment(K_1, I_1) → c_6
  105. Segment(K_1, L_1) → d_6
  106. Segment(L_1, J_1) → e_6
  107. Segment(K_1, J_1) → f_7
  108. Segment(P_1, L_1) → g_7
  109. Segment(L_1, Q_1) → h_7
  110. Segment(K_1, P_1) → i_7
  111. Segment(K_1, O_1) → j_8
  112. Segment(G_1, O_1) → k_7
  113. Segment(N_1, G_1) → l_7
  114. Segment(F_2, N_1) → m_7
  115. Segment(M_1, F_2) → n_7
  116. Segment(W_1, Q_1) → p_7
  117. Segment(Q_1, V_1) → q_7
  118. Segment(V_1, P_1) → r_7
  119. Segment(F_3, W_1) → s_7
  120. Segment(W_1, E_3) → t_7
  121. Segment(E_3, V_1) → a_7
  122. Segment(D_3, V_1) → b_7
  123. Segment(D_3, U_1) → c_7
  124. Segment(U_1, C_3) → d_7
  125. Segment(C_3, T_1) → e_7
  126. Segment(T_1, B_3) → f_8
  127. Segment(B_3, S_1) → g_8
  128. Segment(S_1, A_3) → h_8
  129. Segment(S_1, N_1) → i_8
  130. Segment(N_1, T_1) → j_9
  131. Segment(T_1, O_1) → k_8
  132. Segment(O_1, U_1) → l_8
  133. Segment(U_1, P_1) → m_8
  134. Segment(M_1, R_1) → n_8
  135. Segment(R_1, Z_1) → p_8
  136. Segment(E_2, B_2) → q_8
  137. Segment(J_1, B_2) → r_8
  138. Segment(I_1, J_1) → s_8
  139. Segment(E_2, D_2) → t_8
  140. Segment(D_2, C_2) → a_8
  141. Segment(A_2, C_2) → b_8
  142. Segment(A_2, B_2) → c_8
  143. Segment(B_2, Q_1) → d_8
  144. Segment(B_2, W_1) → e_8
  145. Segment(C_2, R_1) → f_9
  146. Segment(C_2, H_1) → g_9
  147. Segment(C_2, F_2) → h_9
  148. Segment(C_2, M_1) → i_9
  149. Segment(C_2, Z_1) → j_{10}
  150. Segment(Z_1, A_3) → k_9
  151. Segment(R_1, S_1) → l_9
  152. Segment(M_1, N_1) → m_9
  153. Segment(F_2, G_1) → n_9
  154. Segment(Q_1, P_1) → p_9
  155. Segment(P_1, O_1) → q_9
  156. Segment(N_1, O_1) → r_9
  157. Segment(S_1, T_1) → s_9
  158. Segment(A_3, B_3) → t_9
  159. Segment(B_3, C_3) → a_9
  160. Segment(C_3, D_3) → b_9
  161. Segment(D_3, E_3) → c_9
  162. Segment(F_3, E_3) → d_9
  163. Segment(B_2, F_3) → e_9
  164. Segment(I_1, H_1) → f_{10}
  165. Segment(U_1, V_1) → g_{10}
  166. Segment(V_1, W_1) → h_{10}
  167. Segment(U_1, T_1) → i_{10}
  168. Segment(L_1, B_2) → j_{11}
  169. Polygon(A_4, B_4, 3) → poly1_2, f_{27}, g_{27}, h_{27}, C_4
  170. Polygon(B_4, C_4, 4) → poly2_2, i_{27}, j_{27}, k_{23}, l_{23}, D_4, E_4
  171. Polygon(B_4, C_4, 5) → poly3_2, m_{23}, n_{23}, p_{23}, q_{23}, r_{23}, H_2, I_2, J_2
  172. Polygon(B_4, C_4, 6) → poly4_2, s_{23}, L_2, t_{23}, a_{23}, b_{23}, c_{23}, d_{23}, F_4, G_2, K_2
  173. Polygon(B_4, C_4, 7) → poly5_2, e_{23}, O_2, P_2, Q_2, f_{26}, g_{26}, h_{26}, i_{26}, j_{26}, k_{22}, M_2, N_2
  174. Polygon(B_4, C_4, 8) → poly6_2, l_{22}, S_2, T_2, U_2, V_2, W_2, m_{22}, n_{22}, p_{22}, q_{22}, r_{22}, s_{22}, t_{22}, R_2
  175. Polygon(B_4, C_4, 9) → poly7_2, a_{22}, Z_2, A_5, B_5, C_5, D_5, E_5, F_5, b_{22}, c_{22}, d_{22}, e_{22}, f_{25}, g_{25}, h_{25}, i_{25}
  176. Segment(B_4, C_4) → j_{14}
  177. Segment(I_2, C_4) → k_{12}
  178. Segment(I_2, A_4) → l_{12}
  179. Segment(I_2, D_4) → m_{12}
  180. Segment(I_2, E_4) → n_{12}
  181. Segment(I_2, B_4) → p_{12}
  182. Segment(E_4, J_2) → q_{12}
  183. Segment(D_4, H_2) → r_{12}
  184. Segment(G_2, H_2) → s_{12}
  185. Segment(H_2, F_4) → t_{12}
  186. Segment(G_2, K_2) → a_{12}
  187. Segment(G_2, I_2) → b_{12}
  188. Segment(K_2, I_2) → c_{12}
  189. Segment(K_2, L_2) → d_{12}
  190. Segment(L_2, J_2) → e_{12}
  191. Segment(K_2, J_2) → f_{14}
  192. Segment(P_2, L_2) → g_{14}
  193. Segment(L_2, Q_2) → h_{14}
  194. Segment(K_2, P_2) → i_{14}
  195. Segment(K_2, O_2) → j_{15}
  196. Segment(G_2, O_2) → k_{13}
  197. Segment(N_2, G_2) → l_{13}
  198. Segment(F_4, N_2) → m_{13}
  199. Segment(M_2, F_4) → n_{13}
  200. Segment(W_2, Q_2) → p_{13}
  201. Segment(Q_2, V_2) → q_{13}
  202. Segment(V_2, P_2) → r_{13}
  203. Segment(F_5, W_2) → s_{13}
  204. Segment(W_2, E_5) → t_{13}
  205. Segment(E_5, V_2) → a_{13}
  206. Segment(D_5, V_2) → b_{13}
  207. Segment(D_5, U_2) → c_{13}
  208. Segment(U_2, C_5) → d_{13}
  209. Segment(C_5, T_2) → e_{13}
  210. Segment(T_2, B_5) → f_{15}
  211. Segment(B_5, S_2) → g_{15}
  212. Segment(S_2, A_5) → h_{15}
  213. Segment(S_2, N_2) → i_{15}
  214. Segment(N_2, T_2) → j_{16}
  215. Segment(T_2, O_2) → k_{14}
  216. Segment(O_2, U_2) → l_{14}
  217. Segment(U_2, P_2) → m_{14}
  218. Segment(M_2, R_2) → n_{14}
  219. Segment(R_2, Z_2) → p_{14}
  220. Segment(E_4, B_4) → q_{14}
  221. Segment(J_2, B_4) → r_{14}
  222. Segment(I_2, J_2) → s_{14}
  223. Segment(E_4, D_4) → t_{14}
  224. Segment(D_4, C_4) → a_{14}
  225. Segment(A_4, C_4) → b_{14}
  226. Segment(A_4, B_4) → c_{14}
  227. Segment(B_4, Q_2) → d_{14}
  228. Segment(B_4, W_2) → e_{14}
  229. Segment(C_4, R_2) → f_{16}
  230. Segment(C_4, H_2) → g_{16}
  231. Segment(C_4, F_4) → h_{16}
  232. Segment(C_4, M_2) → i_{16}
  233. Segment(C_4, Z_2) → j_{17}
  234. Segment(Z_2, A_5) → k_{15}
  235. Segment(R_2, S_2) → l_{15}
  236. Segment(M_2, N_2) → m_{15}
  237. Segment(F_4, G_2) → n_{15}
  238. Segment(Q_2, P_2) → p_{15}
  239. Segment(P_2, O_2) → q_{15}
  240. Segment(N_2, O_2) → r_{15}
  241. Segment(S_2, T_2) → s_{15}
  242. Segment(A_5, B_5) → t_{15}
  243. Segment(B_5, C_5) → a_{15}
  244. Segment(C_5, D_5) → b_{15}
  245. Segment(D_5, E_5) → c_{15}
  246. Segment(F_5, E_5) → d_{15}
  247. Segment(B_4, F_5) → e_{15}
  248. Segment(I_2, H_2) → f_{17}
  249. Segment(U_2, V_2) → g_{17}
  250. Segment(V_2, W_2) → h_{17}
  251. Segment(U_2, T_2) → i_{17}
  252. Segment(L_2, B_4) → j_{18}
  253. Polygon(A_6, B_6, 3) → poly1_3, f_{24}, g_{24}, h_{24}, C_6
  254. Polygon(B_6, C_6, 4) → poly2_3, i_{24}, j_{25}, k_{21}, l_{21}, D_6, E_6
  255. Polygon(B_6, C_6, 5) → poly3_3, m_{21}, n_{21}, p_{21}, q_{21}, r_{21}, H_3, I_3, J_3
  256. Polygon(B_6, C_6, 6) → poly4_3, s_{21}, L_3, t_{21}, a_{21}, b_{21}, c_{21}, d_{21}, F_6, G_3, K_3
  257. Polygon(B_6, C_6, 7) → poly5_3, e_{21}, O_3, P_3, Q_3, f_{23}, g_{23}, h_{23}, i_{23}, j_{24}, k_{20}, M_3, N_3
  258. Polygon(B_6, C_6, 8) → poly6_3, l_{20}, S_3, T_3, U_3, V_3, W_3, m_{20}, n_{20}, p_{20}, q_{20}, r_{20}, s_{20}, t_{20}, R_3
  259. Polygon(B_6, C_6, 9) → poly7_3, a_{20}, Z_3, A_7, B_7, C_7, D_7, E_7, F_7, b_{20}, c_{20}, d_{20}, e_{20}, f_{22}, g_{22}, h_{22}, i_{22}
  260. Segment(B_6, C_6) → j_{19}
  261. Segment(I_3, C_6) → k_{16}
  262. Segment(I_3, A_6) → l_{16}
  263. Segment(I_3, D_6) → m_{16}
  264. Segment(I_3, E_6) → n_{16}
  265. Segment(I_3, B_6) → p_{16}
  266. Segment(E_6, J_3) → q_{16}
  267. Segment(D_6, H_3) → r_{16}
  268. Segment(G_3, H_3) → s_{16}
  269. Segment(H_3, F_6) → t_{16}
  270. Segment(G_3, K_3) → a_{16}
  271. Segment(G_3, I_3) → b_{16}
  272. Segment(K_3, I_3) → c_{16}
  273. Segment(K_3, L_3) → d_{16}
  274. Segment(L_3, J_3) → e_{16}
  275. Segment(K_3, J_3) → f_{18}
  276. Segment(P_3, L_3) → g_{18}
  277. Segment(L_3, Q_3) → h_{18}
  278. Segment(K_3, P_3) → i_{18}
  279. Segment(K_3, O_3) → j_{20}
  280. Segment(G_3, O_3) → k_{17}
  281. Segment(N_3, G_3) → l_{17}
  282. Segment(F_6, N_3) → m_{17}
  283. Segment(M_3, F_6) → n_{17}
  284. Segment(W_3, Q_3) → p_{17}
  285. Segment(Q_3, V_3) → q_{17}
  286. Segment(V_3, P_3) → r_{17}
  287. Segment(F_7, W_3) → s_{17}
  288. Segment(W_3, E_7) → t_{17}
  289. Segment(E_7, V_3) → a_{17}
  290. Segment(D_7, V_3) → b_{17}
  291. Segment(D_7, U_3) → c_{17}
  292. Segment(U_3, C_7) → d_{17}
  293. Segment(C_7, T_3) → e_{17}
  294. Segment(T_3, B_7) → f_{19}
  295. Segment(B_7, S_3) → g_{19}
  296. Segment(S_3, A_7) → h_{19}
  297. Segment(S_3, N_3) → i_{19}
  298. Segment(N_3, T_3) → j_{21}
  299. Segment(T_3, O_3) → k_{18}
  300. Segment(O_3, U_3) → l_{18}
  301. Segment(U_3, P_3) → m_{18}
  302. Segment(M_3, R_3) → n_{18}
  303. Segment(R_3, Z_3) → p_{18}
  304. Segment(E_6, B_6) → q_{18}
  305. Segment(J_3, B_6) → r_{18}
  306. Segment(I_3, J_3) → s_{18}
  307. Segment(E_6, D_6) → t_{18}
  308. Segment(D_6, C_6) → a_{18}
  309. Segment(A_6, C_6) → b_{18}
  310. Segment(A_6, B_6) → c_{18}
  311. Segment(B_6, Q_3) → d_{18}
  312. Segment(B_6, W_3) → e_{18}
  313. Segment(C_6, R_3) → f_{20}
  314. Segment(C_6, H_3) → g_{20}
  315. Segment(C_6, F_6) → h_{20}
  316. Segment(C_6, M_3) → i_{20}
  317. Segment(C_6, Z_3) → j_{22}
  318. Segment(Z_3, A_7) → k_{19}
  319. Segment(R_3, S_3) → l_{19}
  320. Segment(M_3, N_3) → m_{19}
  321. Segment(F_6, G_3) → n_{19}
  322. Segment(Q_3, P_3) → p_{19}
  323. Segment(P_3, O_3) → q_{19}
  324. Segment(N_3, O_3) → r_{19}
  325. Segment(S_3, T_3) → s_{19}
  326. Segment(A_7, B_7) → t_{19}
  327. Segment(B_7, C_7) → a_{19}
  328. Segment(C_7, D_7) → b_{19}
  329. Segment(D_7, E_7) → c_{19}
  330. Segment(F_7, E_7) → d_{19}
  331. Segment(B_6, F_7) → e_{19}
  332. Segment(I_3, H_3) → f_{21}
  333. Segment(U_3, V_3) → g_{21}
  334. Segment(V_3, W_3) → h_{21}
  335. Segment(U_3, T_3) → i_{21}
  336. Segment(L_3, B_6) → j_{23}
  337. Polygon(A_8, B_8, 3) → poly1_4, f_{55}, g_{55}, h_{55}, C_8
  338. Polygon(B_8, C_8, 4) → poly2_4, i_{55}, j_{55}, k_{47}, l_{47}, D_8, E_8
  339. Polygon(B_8, C_8, 5) → poly3_4, m_{47}, n_{47}, p_{47}, q_{47}, r_{47}, H_4, I_4, J_4
  340. Polygon(B_8, C_8, 6) → poly4_4, s_{47}, L_4, t_{47}, a_{47}, b_{47}, c_{47}, d_{47}, F_8, G_4, K_4
  341. Polygon(B_8, C_8, 7) → poly5_4, e_{47}, O_4, P_4, Q_4, f_{54}, g_{54}, h_{54}, i_{54}, j_{54}, k_{46}, M_4, N_4
  342. Polygon(B_8, C_8, 8) → poly6_4, l_{46}, S_4, T_4, U_4, V_4, W_4, m_{46}, n_{46}, p_{46}, q_{46}, r_{46}, s_{46}, t_{46}, R_4
  343. Polygon(B_8, C_8, 9) → poly7_4, a_{46}, Z_4, A_9, B_9, C_9, D_9, E_9, F_9, b_{46}, c_{46}, d_{46}, e_{46}, f_{53}, g_{53}, h_{53}, i_{53}
  344. Segment(B_8, C_8) → j_{28}
  345. Segment(I_4, C_8) → k_{24}
  346. Segment(I_4, A_8) → l_{24}
  347. Segment(I_4, D_8) → m_{24}
  348. Segment(I_4, E_8) → n_{24}
  349. Segment(I_4, B_8) → p_{24}
  350. Segment(E_8, J_4) → q_{24}
  351. Segment(D_8, H_4) → r_{24}
  352. Segment(G_4, H_4) → s_{24}
  353. Segment(H_4, F_8) → t_{24}
  354. Segment(G_4, K_4) → a_{24}
  355. Segment(G_4, I_4) → b_{24}
  356. Segment(K_4, I_4) → c_{24}
  357. Segment(K_4, L_4) → d_{24}
  358. Segment(L_4, J_4) → e_{24}
  359. Segment(K_4, J_4) → f_{28}
  360. Segment(P_4, L_4) → g_{28}
  361. Segment(L_4, Q_4) → h_{28}
  362. Segment(K_4, P_4) → i_{28}
  363. Segment(K_4, O_4) → j_{29}
  364. Segment(G_4, O_4) → k_{25}
  365. Segment(N_4, G_4) → l_{25}
  366. Segment(F_8, N_4) → m_{25}
  367. Segment(M_4, F_8) → n_{25}
  368. Segment(W_4, Q_4) → p_{25}
  369. Segment(Q_4, V_4) → q_{25}
  370. Segment(V_4, P_4) → r_{25}
  371. Segment(F_9, W_4) → s_{25}
  372. Segment(W_4, E_9) → t_{25}
  373. Segment(E_9, V_4) → a_{25}
  374. Segment(D_9, V_4) → b_{25}
  375. Segment(D_9, U_4) → c_{25}
  376. Segment(U_4, C_9) → d_{25}
  377. Segment(C_9, T_4) → e_{25}
  378. Segment(T_4, B_9) → f_{29}
  379. Segment(B_9, S_4) → g_{29}
  380. Segment(S_4, A_9) → h_{29}
  381. Segment(S_4, N_4) → i_{29}
  382. Segment(N_4, T_4) → j_{30}
  383. Segment(T_4, O_4) → k_{26}
  384. Segment(O_4, U_4) → l_{26}
  385. Segment(U_4, P_4) → m_{26}
  386. Segment(M_4, R_4) → n_{26}
  387. Segment(R_4, Z_4) → p_{26}
  388. Segment(E_8, B_8) → q_{26}
  389. Segment(J_4, B_8) → r_{26}
  390. Segment(I_4, J_4) → s_{26}
  391. Segment(E_8, D_8) → t_{26}
  392. Segment(D_8, C_8) → a_{26}
  393. Segment(A_8, C_8) → b_{26}
  394. Segment(A_8, B_8) → c_{26}
  395. Segment(B_8, Q_4) → d_{26}
  396. Segment(B_8, W_4) → e_{26}
  397. Segment(C_8, R_4) → f_{30}
  398. Segment(C_8, H_4) → g_{30}
  399. Segment(C_8, F_8) → h_{30}
  400. Segment(C_8, M_4) → i_{30}
  401. Segment(C_8, Z_4) → j_{31}
  402. Segment(Z_4, A_9) → k_{27}
  403. Segment(R_4, S_4) → l_{27}
  404. Segment(M_4, N_4) → m_{27}
  405. Segment(F_8, G_4) → n_{27}
  406. Segment(Q_4, P_4) → p_{27}
  407. Segment(P_4, O_4) → q_{27}
  408. Segment(N_4, O_4) → r_{27}
  409. Segment(S_4, T_4) → s_{27}
  410. Segment(A_9, B_9) → t_{27}
  411. Segment(B_9, C_9) → a_{27}
  412. Segment(C_9, D_9) → b_{27}
  413. Segment(D_9, E_9) → c_{27}
  414. Segment(F_9, E_9) → d_{27}
  415. Segment(B_8, F_9) → e_{27}
  416. Segment(I_4, H_4) → f_{31}
  417. Segment(U_4, V_4) → g_{31}
  418. Segment(V_4, W_4) → h_{31}
  419. Segment(U_4, T_4) → i_{31}
  420. Segment(L_4, B_8) → j_{32}
  421. Polygon(A_{10}, B_{10}, 3) → poly1_5, f_{52}, g_{52}, h_{52}, C_{10}
  422. Polygon(B_{10}, C_{10}, 4) → poly2_5, i_{52}, j_{53}, k_{45}, l_{45}, D_{10}, E_{10}
  423. Polygon(B_{10}, C_{10}, 5) → poly3_5, m_{45}, n_{45}, p_{45}, q_{45}, r_{45}, H_5, I_5, J_5
  424. Polygon(B_{10}, C_{10}, 6) → poly4_5, s_{45}, L_5, t_{45}, a_{45}, b_{45}, c_{45}, d_{45}, F_{10}, G_5, K_5
  425. Polygon(B_{10}, C_{10}, 7) → poly5_5, e_{45}, O_5, P_5, Q_5, f_{51}, g_{51}, h_{51}, i_{51}, j_{52}, k_{44}, M_5, N_5
  426. Polygon(B_{10}, C_{10}, 8) → poly6_5, l_{44}, S_5, T_5, U_5, V_5, W_5, m_{44}, n_{44}, p_{44}, q_{44}, r_{44}, s_{44}, t_{44}, R_5
  427. Polygon(B_{10}, C_{10}, 9) → poly7_5, a_{44}, Z_5, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, b_{44}, c_{44}, d_{44}, e_{44}, f_{50}, g_{50}, h_{50}, i_{50}
  428. Segment(B_{10}, C_{10}) → j_{33}
  429. Segment(I_5, C_{10}) → k_{28}
  430. Segment(I_5, A_{10}) → l_{28}
  431. Segment(I_5, D_{10}) → m_{28}
  432. Segment(I_5, E_{10}) → n_{28}
  433. Segment(I_5, B_{10}) → p_{28}
  434. Segment(E_{10}, J_5) → q_{28}
  435. Segment(D_{10}, H_5) → r_{28}
  436. Segment(G_5, H_5) → s_{28}
  437. Segment(H_5, F_{10}) → t_{28}
  438. Segment(G_5, K_5) → a_{28}
  439. Segment(G_5, I_5) → b_{28}
  440. Segment(K_5, I_5) → c_{28}
  441. Segment(K_5, L_5) → d_{28}
  442. Segment(L_5, J_5) → e_{28}
  443. Segment(K_5, J_5) → f_{32}
  444. Segment(P_5, L_5) → g_{32}
  445. Segment(L_5, Q_5) → h_{32}
  446. Segment(K_5, P_5) → i_{32}
  447. Segment(K_5, O_5) → j_{34}
  448. Segment(G_5, O_5) → k_{29}
  449. Segment(N_5, G_5) → l_{29}
  450. Segment(F_{10}, N_5) → m_{29}
  451. Segment(M_5, F_{10}) → n_{29}
  452. Segment(W_5, Q_5) → p_{29}
  453. Segment(Q_5, V_5) → q_{29}
  454. Segment(V_5, P_5) → r_{29}
  455. Segment(F_{11}, W_5) → s_{29}
  456. Segment(W_5, E_{11}) → t_{29}
  457. Segment(E_{11}, V_5) → a_{29}
  458. Segment(D_{11}, V_5) → b_{29}
  459. Segment(D_{11}, U_5) → c_{29}
  460. Segment(U_5, C_{11}) → d_{29}
  461. Segment(C_{11}, T_5) → e_{29}
  462. Segment(T_5, B_{11}) → f_{33}
  463. Segment(B_{11}, S_5) → g_{33}
  464. Segment(S_5, A_{11}) → h_{33}
  465. Segment(S_5, N_5) → i_{33}
  466. Segment(N_5, T_5) → j_{35}
  467. Segment(T_5, O_5) → k_{30}
  468. Segment(O_5, U_5) → l_{30}
  469. Segment(U_5, P_5) → m_{30}
  470. Segment(M_5, R_5) → n_{30}
  471. Segment(R_5, Z_5) → p_{30}
  472. Segment(E_{10}, B_{10}) → q_{30}
  473. Segment(J_5, B_{10}) → r_{30}
  474. Segment(I_5, J_5) → s_{30}
  475. Segment(E_{10}, D_{10}) → t_{30}
  476. Segment(D_{10}, C_{10}) → a_{30}
  477. Segment(A_{10}, C_{10}) → b_{30}
  478. Segment(A_{10}, B_{10}) → c_{30}
  479. Segment(B_{10}, Q_5) → d_{30}
  480. Segment(B_{10}, W_5) → e_{30}
  481. Segment(C_{10}, R_5) → f_{34}
  482. Segment(C_{10}, H_5) → g_{34}
  483. Segment(C_{10}, F_{10}) → h_{34}
  484. Segment(C_{10}, M_5) → i_{34}
  485. Segment(C_{10}, Z_5) → j_{36}
  486. Segment(Z_5, A_{11}) → k_{31}
  487. Segment(R_5, S_5) → l_{31}
  488. Segment(M_5, N_5) → m_{31}
  489. Segment(F_{10}, G_5) → n_{31}
  490. Segment(Q_5, P_5) → p_{31}
  491. Segment(P_5, O_5) → q_{31}
  492. Segment(N_5, O_5) → r_{31}
  493. Segment(S_5, T_5) → s_{31}
  494. Segment(A_{11}, B_{11}) → t_{31}
  495. Segment(B_{11}, C_{11}) → a_{31}
  496. Segment(C_{11}, D_{11}) → b_{31}
  497. Segment(D_{11}, E_{11}) → c_{31}
  498. Segment(F_{11}, E_{11}) → d_{31}
  499. Segment(B_{10}, F_{11}) → e_{31}
  500. Segment(I_5, H_5) → f_{35}
  501. Segment(U_5, V_5) → g_{35}
  502. Segment(V_5, W_5) → h_{35}
  503. Segment(U_5, T_5) → i_{35}
  504. Segment(L_5, B_{10}) → j_{37}
  505. Polygon(A_{12}, B_{12}, 3) → poly1_6, f_{49}, g_{49}, h_{49}, C_{12}
  506. Polygon(B_{12}, C_{12}, 4) → poly2_6, i_{49}, j_{51}, k_{43}, l_{43}, D_{12}, E_{12}
  507. Polygon(B_{12}, C_{12}, 5) → poly3_6, m_{43}, n_{43}, p_{43}, q_{43}, r_{43}, H_6, I_6, J_6
  508. Polygon(B_{12}, C_{12}, 6) → poly4_6, s_{43}, L_6, t_{43}, a_{43}, b_{43}, c_{43}, d_{43}, F_{12}, G_6, K_6
  509. Polygon(B_{12}, C_{12}, 7) → poly5_6, e_{43}, O_6, P_6, Q_6, f_{48}, g_{48}, h_{48}, i_{48}, j_{50}, k_{42}, M_6, N_6
  510. Polygon(B_{12}, C_{12}, 8) → poly6_6, l_{42}, S_6, T_6, U_6, V_6, W_6, m_{42}, n_{42}, p_{42}, q_{42}, r_{42}, s_{42}, t_{42}, R_6
  511. Polygon(B_{12}, C_{12}, 9) → poly7_6, a_{42}, Z_6, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, b_{42}, c_{42}, d_{42}, e_{42}, f_{47}, g_{47}, h_{47}, i_{47}
  512. Segment(B_{12}, C_{12}) → j_{38}
  513. Segment(I_6, C_{12}) → k_{32}
  514. Segment(I_6, A_{12}) → l_{32}
  515. Segment(I_6, D_{12}) → m_{32}
  516. Segment(I_6, E_{12}) → n_{32}
  517. Segment(I_6, B_{12}) → p_{32}
  518. Segment(E_{12}, J_6) → q_{32}
  519. Segment(D_{12}, H_6) → r_{32}
  520. Segment(G_6, H_6) → s_{32}
  521. Segment(H_6, F_{12}) → t_{32}
  522. Segment(G_6, K_6) → a_{32}
  523. Segment(G_6, I_6) → b_{32}
  524. Segment(K_6, I_6) → c_{32}
  525. Segment(K_6, L_6) → d_{32}
  526. Segment(L_6, J_6) → e_{32}
  527. Segment(K_6, J_6) → f_{36}
  528. Segment(P_6, L_6) → g_{36}
  529. Segment(L_6, Q_6) → h_{36}
  530. Segment(K_6, P_6) → i_{36}
  531. Segment(K_6, O_6) → j_{39}
  532. Segment(G_6, O_6) → k_{33}
  533. Segment(N_6, G_6) → l_{33}
  534. Segment(F_{12}, N_6) → m_{33}
  535. Segment(M_6, F_{12}) → n_{33}
  536. Segment(W_6, Q_6) → p_{33}
  537. Segment(Q_6, V_6) → q_{33}
  538. Segment(V_6, P_6) → r_{33}
  539. Segment(F_{13}, W_6) → s_{33}
  540. Segment(W_6, E_{13}) → t_{33}
  541. Segment(E_{13}, V_6) → a_{33}
  542. Segment(D_{13}, V_6) → b_{33}
  543. Segment(D_{13}, U_6) → c_{33}
  544. Segment(U_6, C_{13}) → d_{33}
  545. Segment(C_{13}, T_6) → e_{33}
  546. Segment(T_6, B_{13}) → f_{37}
  547. Segment(B_{13}, S_6) → g_{37}
  548. Segment(S_6, A_{13}) → h_{37}
  549. Segment(S_6, N_6) → i_{37}
  550. Segment(N_6, T_6) → j_{40}
  551. Segment(T_6, O_6) → k_{34}
  552. Segment(O_6, U_6) → l_{34}
  553. Segment(U_6, P_6) → m_{34}
  554. Segment(M_6, R_6) → n_{34}
  555. Segment(R_6, Z_6) → p_{34}
  556. Segment(E_{12}, B_{12}) → q_{34}
  557. Segment(J_6, B_{12}) → r_{34}
  558. Segment(I_6, J_6) → s_{34}
  559. Segment(E_{12}, D_{12}) → t_{34}
  560. Segment(D_{12}, C_{12}) → a_{34}
  561. Segment(A_{12}, C_{12}) → b_{34}
  562. Segment(A_{12}, B_{12}) → c_{34}
  563. Segment(B_{12}, Q_6) → d_{34}
  564. Segment(B_{12}, W_6) → e_{34}
  565. Segment(C_{12}, R_6) → f_{38}
  566. Segment(C_{12}, H_6) → g_{38}
  567. Segment(C_{12}, F_{12}) → h_{38}
  568. Segment(C_{12}, M_6) → i_{38}
  569. Segment(C_{12}, Z_6) → j_{41}
  570. Segment(Z_6, A_{13}) → k_{35}
  571. Segment(R_6, S_6) → l_{35}
  572. Segment(M_6, N_6) → m_{35}
  573. Segment(F_{12}, G_6) → n_{35}
  574. Segment(Q_6, P_6) → p_{35}
  575. Segment(P_6, O_6) → q_{35}
  576. Segment(N_6, O_6) → r_{35}
  577. Segment(S_6, T_6) → s_{35}
  578. Segment(A_{13}, B_{13}) → t_{35}
  579. Segment(B_{13}, C_{13}) → a_{35}
  580. Segment(C_{13}, D_{13}) → b_{35}
  581. Segment(D_{13}, E_{13}) → c_{35}
  582. Segment(F_{13}, E_{13}) → d_{35}
  583. Segment(B_{12}, F_{13}) → e_{35}
  584. Segment(I_6, H_6) → f_{39}
  585. Segment(U_6, V_6) → g_{39}
  586. Segment(V_6, W_6) → h_{39}
  587. Segment(U_6, T_6) → i_{39}
  588. Segment(L_6, B_{12}) → j_{42}
  589. Polygon(A_{14}, B_{14}, 3) → poly1_7, f_{46}, g_{46}, h_{46}, C_{14}
  590. Polygon(B_{14}, C_{14}, 4) → poly2_7, i_{46}, j_{49}, k_{41}, l_{41}, D_{14}, E_{14}
  591. Polygon(B_{14}, C_{14}, 5) → poly3_7, m_{41}, n_{41}, p_{41}, q_{41}, r_{41}, H_7, I_7, J_7
  592. Polygon(B_{14}, C_{14}, 6) → poly4_7, s_{41}, L_7, t_{41}, a_{41}, b_{41}, c_{41}, d_{41}, F_{14}, G_7, K_7
  593. Polygon(B_{14}, C_{14}, 7) → poly5_7, e_{41}, O_7, P_7, Q_7, f_{45}, g_{45}, h_{45}, i_{45}, j_{48}, k_{40}, M_7, N_7
  594. Polygon(B_{14}, C_{14}, 8) → poly6_7, l_{40}, S_7, T_7, U_7, V_7, W_7, m_{40}, n_{40}, p_{40}, q_{40}, r_{40}, s_{40}, t_{40}, R_7
  595. Polygon(B_{14}, C_{14}, 9) → poly7_7, a_{40}, Z_7, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}, b_{40}, c_{40}, d_{40}, e_{40}, f_{44}, g_{44}, h_{44}, i_{44}
  596. Segment(B_{14}, C_{14}) → j_{43}
  597. Segment(I_7, C_{14}) → k_{36}
  598. Segment(I_7, A_{14}) → l_{36}
  599. Segment(I_7, D_{14}) → m_{36}
  600. Segment(I_7, E_{14}) → n_{36}
  601. Segment(I_7, B_{14}) → p_{36}
  602. Segment(E_{14}, J_7) → q_{36}
  603. Segment(D_{14}, H_7) → r_{36}
  604. Segment(G_7, H_7) → s_{36}
  605. Segment(H_7, F_{14}) → t_{36}
  606. Segment(G_7, K_7) → a_{36}
  607. Segment(G_7, I_7) → b_{36}
  608. Segment(K_7, I_7) → c_{36}
  609. Segment(K_7, L_7) → d_{36}
  610. Segment(L_7, J_7) → e_{36}
  611. Segment(K_7, J_7) → f_{40}
  612. Segment(P_7, L_7) → g_{40}
  613. Segment(L_7, Q_7) → h_{40}
  614. Segment(K_7, P_7) → i_{40}
  615. Segment(K_7, O_7) → j_{44}
  616. Segment(G_7, O_7) → k_{37}
  617. Segment(N_7, G_7) → l_{37}
  618. Segment(F_{14}, N_7) → m_{37}
  619. Segment(M_7, F_{14}) → n_{37}
  620. Segment(W_7, Q_7) → p_{37}
  621. Segment(Q_7, V_7) → q_{37}
  622. Segment(V_7, P_7) → r_{37}
  623. Segment(F_{15}, W_7) → s_{37}
  624. Segment(W_7, E_{15}) → t_{37}
  625. Segment(E_{15}, V_7) → a_{37}
  626. Segment(D_{15}, V_7) → b_{37}
  627. Segment(D_{15}, U_7) → c_{37}
  628. Segment(U_7, C_{15}) → d_{37}
  629. Segment(C_{15}, T_7) → e_{37}
  630. Segment(T_7, B_{15}) → f_{41}
  631. Segment(B_{15}, S_7) → g_{41}
  632. Segment(S_7, A_{15}) → h_{41}
  633. Segment(S_7, N_7) → i_{41}
  634. Segment(N_7, T_7) → j_{45}
  635. Segment(T_7, O_7) → k_{38}
  636. Segment(O_7, U_7) → l_{38}
  637. Segment(U_7, P_7) → m_{38}
  638. Segment(M_7, R_7) → n_{38}
  639. Segment(R_7, Z_7) → p_{38}
  640. Segment(E_{14}, B_{14}) → q_{38}
  641. Segment(J_7, B_{14}) → r_{38}
  642. Segment(I_7, J_7) → s_{38}
  643. Segment(E_{14}, D_{14}) → t_{38}
  644. Segment(D_{14}, C_{14}) → a_{38}
  645. Segment(A_{14}, C_{14}) → b_{38}
  646. Segment(A_{14}, B_{14}) → c_{38}
  647. Segment(B_{14}, Q_7) → d_{38}
  648. Segment(B_{14}, W_7) → e_{38}
  649. Segment(C_{14}, R_7) → f_{42}
  650. Segment(C_{14}, H_7) → g_{42}
  651. Segment(C_{14}, F_{14}) → h_{42}
  652. Segment(C_{14}, M_7) → i_{42}
  653. Segment(C_{14}, Z_7) → j_{46}
  654. Segment(Z_7, A_{15}) → k_{39}
  655. Segment(R_7, S_7) → l_{39}
  656. Segment(M_7, N_7) → m_{39}
  657. Segment(F_{14}, G_7) → n_{39}
  658. Segment(Q_7, P_7) → p_{39}
  659. Segment(P_7, O_7) → q_{39}
  660. Segment(N_7, O_7) → r_{39}
  661. Segment(S_7, T_7) → s_{39}
  662. Segment(A_{15}, B_{15}) → t_{39}
  663. Segment(B_{15}, C_{15}) → a_{39}
  664. Segment(C_{15}, D_{15}) → b_{39}
  665. Segment(D_{15}, E_{15}) → c_{39}
  666. Segment(F_{15}, E_{15}) → d_{39}
  667. Segment(B_{14}, F_{15}) → e_{39}
  668. Segment(I_7, H_7) → f_{43}
  669. Segment(U_7, V_7) → g_{43}
  670. Segment(V_7, W_7) → h_{43}
  671. Segment(U_7, T_7) → i_{43}
  672. Segment(L_7, B_{14}) → j_{47}
  673. Segment(G_8, H_8) → k_{48}
  674. Segment(I_8, H_8) → l_{48}
  675. Segment(I_8, G_8) → m_{48}
  676. Segment(G_8, N_8) → n_{48}
  677. Segment(N_8, I_8) → p_{48}
  678. Segment(M_8, I_8) → q_{48}
  679. Segment(N_8, M_8) → r_{48}
  680. Segment(L_8, M_8) → s_{48}
  681. Segment(M_8, K_8) → t_{48}
  682. Segment(J_8, M_8) → a_{48}
  683. Segment(J_8, I_8) → b_{48}
  684. Segment(K_8, J_8) → c_{48}
  685. Segment(K_8, L_8) → d_{48}

AI Drawing Prompt Reference

Draw a point B and point C, then construct heptagons with vertices B and C having 3, 4, 5, 6, 7, 8, and 9 sides respectively. Connect the midpoints of these polygons and their sides to form nested polygons and line segments, illustrating the relationship between polygon construction and function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.