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Pythagorean Tessellation: Geometric Construction and Principles

Pythagorean Tessellation: Geometric Construction and Principles
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2015-01-11 05:01
TriangleCirclePolygonGeometric Construction
This example demonstrates the construction of a Pythagorean tiling based on the Pythagorean theorem. Key mathematical concepts include the Pythagorean theorem, geometric construction, trigonometric functions, and expected value in probability statistics. The construction involves GeoGebra commands such as Line, OrthogonalLine, Point, Intersect, Semicircle, Segment, and Polygon to create triangles, circles, and polygons. Suitable for middle school and above, this example helps students understand geometric transformations and area calculations, useful for classroom teaching or self-study.

GeoGebra Commands & Parameters

  1. Line(B, C) → a
  2. OrthogonalLine(C, a) → b
  3. Point(b) → D
  4. Line(D, E) → c
  5. Line(E, B) → d
  6. Point(a) → F
  7. OrthogonalLine(F, a) → e
  8. Point(a) → G
  9. OrthogonalLine(G, a) → f
  10. Point(a) → H
  11. OrthogonalLine(H, a) → g
  12. Point(a) → I
  13. Point(c) → J
  14. Line(I, J) → h
  15. Point(a) → K
  16. OrthogonalLine(K, a) → i
  17. Point(a) → L
  18. OrthogonalLine(L, a) → j
  19. Point(a) → M
  20. OrthogonalLine(M, a) → k
  21. Point(a) → N
  22. OrthogonalLine(N, a) → l
  23. Point(a) → O
  24. OrthogonalLine(O, a) → m
  25. Point(a) → P
  26. OrthogonalLine(P, a) → n
  27. Point(n) → Q
  28. OrthogonalLine(Q, n) → p
  29. Point(n) → R
  30. OrthogonalLine(R, n) → q
  31. Point(n) → S
  32. OrthogonalLine(S, n) → r
  33. Point(n) → T
  34. OrthogonalLine(T, n) → s
  35. Point(n) → U
  36. OrthogonalLine(U, n) → t
  37. Point(n) → V
  38. OrthogonalLine(V, n) → a_1
  39. Intersect(k, t) → W
  40. Intersect(l, t) → Z
  41. Semicircle(W, Z) → c_1
  42. Segment(Z, A_1) → b_1
  43. Segment(A_1, W) → d_1
  44. Segment(Z, B_1) → e_1
  45. Segment(B_1, W) → f_1
  46. Intersect(k, s) → C_1
  47. Segment(C_1, D_1) → g_1
  48. Segment(D_1, W) → h_1
  49. Segment(C_1, E_1) → i_1
  50. Segment(E_1, W) → j_1
  51. Intersect(j, t) → F_1
  52. Segment(F_1, G_1) → k_1
  53. Segment(G_1, W) → l_1
  54. Segment(W, H_1) → m_1
  55. Segment(H_1, F_1) → n_1
  56. Segment(W, I_1) → p_1
  57. Intersect(k, a_1) → J_1
  58. Segment(I_1, J_1) → q_1
  59. Segment(J_1, K_1) → r_1
  60. Segment(K_1, W) → s_1
  61. Segment(Z, L_1) → t_1
  62. Intersect(m, t) → M_1
  63. Segment(L_1, M_1) → a_2
  64. Segment(Z, N_1) → b_2
  65. Segment(N_1, M_1) → c_2
  66. Segment(M_1, O_1) → d_2
  67. Segment(O_1, U) → e_2
  68. Segment(U, P_1) → f_2
  69. Segment(P_1, M_1) → g_2
  70. Intersect(m, s) → Q_1
  71. Segment(Q_1, R_1) → h_2
  72. Segment(R_1, M_1) → i_2
  73. Segment(Q_1, S_1) → j_2
  74. Segment(S_1, M_1) → k_2
  75. Segment(M_1, T_1) → l_2
  76. Intersect(m, a_1) → U_1
  77. Segment(T_1, U_1) → m_2
  78. Segment(U_1, V_1) → n_2
  79. Segment(V_1, M_1) → p_2
  80. Segment(C_1, W_1) → q_2
  81. Intersect(k, r) → Z_1
  82. Segment(W_1, Z_1) → r_2
  83. Segment(Z_1, A_2) → s_2
  84. Segment(A_2, C_1) → t_2
  85. Intersect(l, r) → C_2
  86. Segment(B_2, C_2) → a_3
  87. Segment(C_2, D_2) → b_3
  88. Segment(D_2, Z_1) → c_3
  89. Segment(Z_1, B_2) → d_3
  90. Segment(C_2, E_2) → e_3
  91. Intersect(m, r) → F_2
  92. Segment(E_2, F_2) → f_3
  93. Segment(F_2, G_2) → g_3
  94. Segment(G_2, C_2) → h_3
  95. Segment(H_2, F_2) → i_3
  96. Segment(Q_1, H_2) → j_3
  97. Segment(F_2, I_2) → k_3
  98. Segment(I_2, Q_1) → l_3
  99. Segment(B_2, N_1) → m_3
  100. Segment(A_1, G_2) → n_3
  101. Segment(A_2, R_1) → p_3
  102. Segment(D_1, H_2) → q_3
  103. Intersect(k, q) → K_2
  104. Segment(J_2, K_2) → r_3
  105. Segment(K_2, L_2) → s_3
  106. Segment(L_2, Z_1) → t_3
  107. Segment(Z_1, J_2) → a_4
  108. Intersect(j, r) → M_2
  109. Segment(M_2, N_2) → b_4
  110. Segment(N_2, Z_1) → c_4
  111. Segment(Z_1, O_2) → d_4
  112. Segment(O_2, M_2) → e_4
  113. Segment(K_2, P_2) → f_4
  114. Segment(K_2, Q_2) → g_4
  115. Intersect(k, p) → R_2
  116. Segment(P_2, R_2) → h_4
  117. Segment(R_2, Q_2) → i_4
  118. Intersect(l, p) → T_2
  119. Segment(S_2, T_2) → j_4
  120. Segment(T_2, U_2) → k_4
  121. Segment(U_2, R_2) → l_4
  122. Segment(R_2, S_2) → m_4
  123. Segment(R_2, V_2) → n_4
  124. Intersect(j, p) → W_2
  125. Segment(V_2, W_2) → p_4
  126. Segment(W_2, Z_2) → q_4
  127. Segment(Z_2, R_2) → r_4
  128. Intersect(c, k) → A_3
  129. Segment(A_3, B_3) → s_4
  130. Segment(B_3, R_2) → t_4
  131. Segment(R_2, C_3) → a_5
  132. Segment(C_3, A_3) → b_5
  133. Segment(D_3, T_2) → c_5
  134. Segment(T_2, E_3) → d_5
  135. Intersect(m, p) → F_3
  136. Segment(F_3, E_3) → e_5
  137. Segment(F_3, D_3) → f_5
  138. Segment(F_3, G_3) → g_5
  139. Segment(G_3, Q) → h_5
  140. Segment(Q, H_3) → i_5
  141. Segment(H_3, F_3) → j_5
  142. Segment(I_3, F_3) → k_5
  143. Segment(F_3, J_3) → l_5
  144. Intersect(m, q) → K_3
  145. Segment(J_3, K_3) → m_5
  146. Segment(K_3, I_3) → n_5
  147. Segment(L_3, K_3) → p_5
  148. Segment(K_3, M_3) → q_5
  149. Segment(M_3, F_2) → r_5
  150. Segment(F_2, L_3) → s_5
  151. Segment(U_2, E_2) → t_5
  152. Segment(E_3, D_2) → a_6
  153. Segment(Q_2, L_3) → b_6
  154. Segment(L_2, I_3) → c_6
  155. Segment(N_3, W_2) → d_6
  156. Segment(W_2, O_3) → e_6
  157. Intersect(i, p) → P_3
  158. Segment(O_3, P_3) → f_6
  159. Segment(P_3, N_3) → g_6
  160. Segment(Q_3, S) → h_6
  161. Segment(S, R_3) → i_6
  162. Segment(R_3, F_2) → j_6
  163. Segment(F_2, Q_3) → k_6
  164. Intersect(c, m) → T_3
  165. Segment(S_3, T_3) → l_6
  166. Segment(T_3, U_3) → m_6
  167. Segment(U_3, F_3) → n_6
  168. Segment(F_3, S_3) → p_6
  169. Segment(V_3, A_3) → q_6
  170. Segment(V_3, M) → r_6
  171. Segment(M, W_3) → s_6
  172. Segment(W_3, A_3) → t_6
  173. Segment(Z_3, T_3) → a_7
  174. Segment(T_3, A_4) → b_7
  175. Segment(A_4, O) → c_7
  176. Segment(O, Z_3) → d_7
  177. Segment(W_3, S_3) → e_7
  178. Segment(C_3, Z_3) → f_7
  179. Segment(B_4, N) → g_7
  180. Segment(N, C_4) → h_7
  181. Segment(C_4, M) → i_7
  182. Segment(M, B_4) → j_7
  183. Segment(D_4, N) → k_7
  184. Segment(N, E_4) → l_7
  185. Segment(E_4, O) → m_7
  186. Segment(O, D_4) → n_7
  187. Segment(C_4, D_3) → p_7
  188. Segment(S_2, E_4) → q_7
  189. Segment(F_4, P_3) → r_7
  190. Segment(P_3, G_4) → s_7
  191. Intersect(i, q) → H_4
  192. Segment(G_4, H_4) → t_7
  193. Segment(H_4, F_4) → a_8
  194. Intersect(i, r) → I_4
  195. Segment(I_4, J_4) → b_8
  196. Segment(J_4, H_4) → c_8
  197. Segment(H_4, K_4) → d_8
  198. Segment(K_4, L_4) → e_8
  199. Segment(M_4, M_2) → f_8
  200. Segment(N_4, M_2) → g_8
  201. Segment(N_4, L_4) → h_8
  202. Segment(L_4, M_4) → i_8
  203. Segment(M_4, Z_2) → j_8
  204. Segment(O_3, N_2) → k_8
  205. Segment(G_4, J_2) → l_8
  206. Segment(J_4, P_2) → m_8
  207. Intersect(i, s) → O_4
  208. Segment(O_4, P_4) → n_8
  209. Segment(P_4, L_4) → p_8
  210. Segment(L_4, Q_4) → q_8
  211. Segment(Q_4, O_4) → r_8
  212. Intersect(h, r) → R_4
  213. Segment(R_4, S_4) → s_8
  214. Segment(S_4, L_4) → t_8
  215. Segment(L_4, T_4) → a_9
  216. Segment(T_4, R_4) → b_9
  217. Segment(O_4, U_4) → c_9
  218. Intersect(i, t) → V_4
  219. Segment(U_4, V_4) → d_9
  220. Segment(V_4, W_4) → e_9
  221. Segment(W_4, O_4) → f_9
  222. Segment(V_4, Z_4) → g_9
  223. Segment(Z_4, F_1) → h_9
  224. Segment(F_1, A_5) → i_9
  225. Segment(A_5, V_4) → j_9
  226. Segment(N_4, G_1) → k_9
  227. Segment(Z_4, O_2) → l_9
  228. Segment(P_4, E_1) → m_9
  229. Segment(W_4, W_1) → n_9
  230. Intersect(l, a_1) → B_5
  231. Segment(B_1, B_5) → p_9
  232. Segment(B_5, L_1) → q_9
  233. Segment(T_1, B_5) → r_9
  234. Segment(B_5, K_1) → s_9
  235. Intersect(j, a_1) → C_5
  236. Segment(C_5, H_1) → t_9
  237. Segment(C_5, A_5) → a_{10}
  238. Segment(V_4, D_5) → b_{10}
  239. Point(i) → E_5
  240. Segment(D_5, E_5) → c_{10}
  241. Segment(E_5, F_5) → d_{10}
  242. Segment(F_5, V_4) → e_{10}
  243. Segment(V_4, G_5) → f_{10}
  244. Intersect(h, t) → H_5
  245. Segment(G_5, H_5) → g_{10}
  246. Segment(H_5, I_5) → h_{10}
  247. Segment(I_5, V_4) → i_{10}
  248. Segment(D_5, C_5) → j_{10}
  249. Segment(C_5, I_1) → k_{10}
  250. Segment(J_5, L) → l_{10}
  251. Segment(L, K_5) → m_{10}
  252. Segment(K_5, M) → n_{10}
  253. Segment(M, J_5) → p_{10}
  254. Segment(L, L_5) → q_{10}
  255. Segment(L_5, K) → r_{10}
  256. Segment(K, M_5) → s_{10}
  257. Segment(M_5, L) → t_{10}
  258. Segment(K, N_5) → a_{11}
  259. Intersect(c, i) → O_5
  260. Segment(N_5, O_5) → b_{11}
  261. Segment(O_5, P_5) → c_{11}
  262. Point(i) → Q_5
  263. Segment(P_5, Q_5) → d_{11}
  264. Segment(R_5, O_5) → e_{11}
  265. Segment(O_5, S_5) → f_{11}
  266. Segment(S_5, P_3) → g_{11}
  267. Segment(R_5, P_3) → h_{11}
  268. Segment(R_5, V_3) → i_{11}
  269. Segment(N_5, B_3) → j_{11}
  270. Segment(N_3, K_5) → k_{11}
  271. Segment(L_5, V_2) → l_{11}
  272. Segment(M_3, R) → m_{11}
  273. Segment(R, J_3) → n_{11}
  274. Segment(R, Q_3) → p_{11}
  275. Segment(R, H_3) → q_{11}
  276. Segment(R_3, T) → r_{11}
  277. Segment(T, I_2) → s_{11}
  278. Segment(T, S_1) → t_{11}
  279. Segment(T, O_1) → a_{12}
  280. Segment(P_1, V) → b_{12}
  281. Segment(V, V_1) → c_{12}
  282. Segment(T_5, H_5) → d_{12}
  283. Segment(H_5, U_5) → e_{12}
  284. Intersect(g, t) → V_5
  285. Segment(U_5, V_5) → f_{12}
  286. Segment(V_5, W_5) → g_{12}
  287. Intersect(f, t) → Z_5
  288. Segment(W_5, Z_5) → h_{12}
  289. Segment(Z_5, A_6) → i_{12}
  290. Segment(A_6, T_5) → j_{12}
  291. Intersect(g, s) → B_6
  292. Segment(B_6, C_6) → k_{12}
  293. Segment(C_6, D_6) → l_{12}
  294. Intersect(g, a_1) → E_6
  295. Segment(D_6, E_6) → m_{12}
  296. Segment(E_6, F_6) → n_{12}
  297. Segment(F_6, G_6) → p_{12}
  298. Segment(G_6, B_6) → q_{12}
  299. Intersect(h, a_1) → H_6
  300. Segment(U_5, H_6) → r_{12}
  301. Segment(H_6, G_5) → s_{12}
  302. Segment(H_6, F_5) → t_{12}
  303. Segment(H_6, D_6) → a_{13}
  304. Segment(I_6, B_6) → b_{13}
  305. Segment(B_6, J_6) → c_{13}
  306. Intersect(g, r) → K_6
  307. Segment(J_6, K_6) → d_{13}
  308. Segment(K_6, I_6) → e_{13}
  309. Segment(K_6, L_6) → f_{13}
  310. Segment(L_6, R_4) → g_{13}
  311. Segment(R_4, M_6) → h_{13}
  312. Segment(M_6, K_6) → i_{13}
  313. Segment(L_6, I_5) → j_{13}
  314. Segment(T_5, T_4) → k_{13}
  315. Segment(J_6, U_4) → l_{13}
  316. Segment(G_6, Q_4) → m_{13}
  317. Intersect(g, q) → N_6
  318. Segment(N_6, O_6) → n_{13}
  319. Segment(K_6, O_6) → p_{13}
  320. Segment(N_6, P_6) → q_{13}
  321. Segment(P_6, K_6) → r_{13}
  322. Segment(K_6, Q_6) → s_{13}
  323. Intersect(f, r) → R_6
  324. Segment(Q_6, R_6) → t_{13}
  325. Segment(R_6, S_6) → a_{14}
  326. Segment(S_6, K_6) → b_{14}
  327. Segment(N_6, T_6) → c_{14}
  328. Segment(N_6, U_6) → d_{14}
  329. Intersect(g, p) → V_6
  330. Segment(T_6, V_6) → e_{14}
  331. Segment(U_6, V_6) → f_{14}
  332. Segment(V_6, W_6) → g_{14}
  333. Intersect(h, p) → Z_6
  334. Segment(W_6, Z_6) → h_{14}
  335. Segment(Z_6, A_7) → i_{14}
  336. Segment(A_7, V_6) → j_{14}
  337. Segment(Z_6, B_7) → k_{14}
  338. Segment(B_7, P_3) → l_{14}
  339. Segment(P_3, C_7) → m_{14}
  340. Segment(C_7, Z_6) → n_{14}
  341. Segment(C_7, M_6) → p_{14}
  342. Segment(W_6, S_4) → q_{14}
  343. Segment(P_6, F_4) → r_{14}
  344. Segment(T_6, K_4) → s_{14}
  345. Segment(D_7, V_6) → t_{14}
  346. Segment(V_6, E_7) → a_{15}
  347. Segment(E_7, F_7) → b_{15}
  348. Segment(D_7, G_7) → c_{15}
  349. Segment(G_7, H) → d_{15}
  350. Segment(F_7, H) → e_{15}
  351. Segment(H, H_7) → f_{15}
  352. Segment(H_7, I) → g_{15}
  353. Segment(I, I_7) → h_{15}
  354. Segment(I_7, H) → i_{15}
  355. Segment(I, J_7) → j_{15}
  356. Segment(J_7, Q_5) → k_{15}
  357. Segment(I, K_7) → l_{15}
  358. Segment(K_7, Q_5) → m_{15}
  359. Segment(H_7, B_7) → n_{15}
  360. Segment(A_7, K_7) → p_{15}
  361. Segment(F_7, S_5) → q_{15}
  362. Segment(D_7, P_5) → r_{15}
  363. Segment(R_6, L_7) → s_{15}
  364. Intersect(e, r) → M_7
  365. Segment(L_7, M_7) → t_{15}
  366. Segment(M_7, N_7) → a_{16}
  367. Segment(N_7, R_6) → b_{16}
  368. Segment(M_7, O_7) → c_{16}
  369. Segment(O_7, P_7) → d_{16}
  370. Segment(M_7, Q_7) → e_{16}
  371. Segment(Q_7, R_7) → f_{16}
  372. Segment(S_7, R_7) → g_{16}
  373. Segment(P_7, T_7) → h_{16}
  374. Intersect(e, a_1) → U_7
  375. Segment(T_7, U_7) → i_{16}
  376. Segment(U_7, S_7) → j_{16}
  377. Segment(V_7, W_7) → k_{16}
  378. Segment(W_7, Z_5) → l_{16}
  379. Segment(Z_5, Z_7) → m_{16}
  380. Segment(Z_7, A_8) → n_{16}
  381. Intersect(b, t) → B_8
  382. Segment(A_8, B_8) → p_{16}
  383. Segment(B_8, V_7) → q_{16}
  384. Segment(N_7, W_5) → r_{16}
  385. Segment(R_7, I_6) → s_{16}
  386. Segment(O_7, C_6) → t_{16}
  387. Segment(W_7, S_6) → a_{17}
  388. Intersect(f, a_1) → C_8
  389. Segment(A_6, C_8) → b_{17}
  390. Segment(C_8, F_6) → c_{17}
  391. Segment(C_8, T_7) → d_{17}
  392. Segment(C_8, Z_7) → e_{17}
  393. Segment(D_8, E_8) → f_{17}
  394. Segment(F_8, G_8) → g_{17}
  395. Segment(G_8, M_7) → h_{17}
  396. Segment(M_7, D_8) → i_{17}
  397. Intersect(e, p) → H_8
  398. Segment(F_8, H_8) → j_{17}
  399. Segment(E_8, H_8) → k_{17}
  400. Segment(H_8, I_8) → l_{17}
  401. Segment(I_8, J_8) → m_{17}
  402. Segment(K_8, L_8) → n_{17}
  403. Segment(L_8, V_6) → p_{17}
  404. Segment(J_8, V_6) → q_{17}
  405. Segment(L_8, L_7) → r_{17}
  406. Segment(F_8, O_6) → s_{17}
  407. Segment(D_8, U_6) → t_{17}
  408. Segment(I_8, Q_6) → a_{18}
  409. Segment(K_8, H_8) → b_{18}
  410. Segment(H_8, N_8) → c_{18}
  411. Intersect(b, p) → O_8
  412. Segment(N_8, O_8) → d_{18}
  413. Segment(O_8, P_8) → e_{18}
  414. Segment(P_8, H_8) → f_{18}
  415. Intersect(c, e) → R_8
  416. Segment(Q_8, R_8) → g_{18}
  417. Segment(R_8, S_8) → h_{18}
  418. Segment(S_8, H_8) → i_{18}
  419. Segment(H_8, Q_8) → j_{18}
  420. Segment(R_8, T_8) → k_{18}
  421. Segment(R_8, U_8) → l_{18}
  422. Segment(U_8, F) → m_{18}
  423. Segment(F, T_8) → n_{18}
  424. Segment(V_8, G) → p_{18}
  425. Segment(G, W_8) → q_{18}
  426. Segment(Z_8, A_9) → r_{18}
  427. Segment(V_8, F) → s_{18}
  428. Segment(Z_8, F) → t_{18}
  429. Segment(W_8, H) → a_{19}
  430. Segment(A_9, H) → b_{19}
  431. Segment(V_8, J_8) → c_{19}
  432. Segment(K_8, A_9) → d_{19}
  433. Segment(S_8, G_7) → e_{19}
  434. Segment(T_8, E_7) → f_{19}
  435. Segment(B_9, B_8) → g_{19}
  436. Segment(C_9, B_8) → h_{19}
  437. Intersect(d, t) → D_9
  438. Segment(C_9, D_9) → i_{19}
  439. Segment(D_9, B_9) → j_{19}
  440. Segment(D_9, E_9) → k_{19}
  441. Intersect(d, a_1) → F_9
  442. Segment(E_9, F_9) → l_{19}
  443. Segment(F_9, G_9) → m_{19}
  444. Segment(G_9, D_9) → n_{19}
  445. Intersect(b, a_1) → H_9
  446. Segment(E_9, H_9) → p_{19}
  447. Segment(H_9, S_7) → q_{19}
  448. Segment(V_7, H_9) → r_{19}
  449. Segment(H_9, C_9) → s_{19}
  450. Intersect(d, s) → J_9
  451. Segment(I_9, J_9) → t_{19}
  452. Segment(J_9, K_9) → a_{20}
  453. Segment(K_9, D_9) → b_{20}
  454. Segment(D_9, I_9) → c_{20}
  455. Segment(L_9, J_9) → d_{20}
  456. Segment(J_9, M_9) → e_{20}
  457. Intersect(d, r) → N_9
  458. Segment(M_9, N_9) → f_{20}
  459. Segment(N_9, L_9) → g_{20}
  460. Intersect(b, r) → P_9
  461. Segment(O_9, P_9) → h_{20}
  462. Segment(P_9, Q_9) → i_{20}
  463. Segment(Q_9, N_9) → j_{20}
  464. Segment(N_9, O_9) → k_{20}
  465. Segment(R_9, M_7) → l_{20}
  466. Segment(M_7, S_9) → m_{20}
  467. Segment(S_9, P_9) → n_{20}
  468. Segment(P_9, R_9) → p_{20}
  469. Segment(B_9, S_9) → q_{20}
  470. Segment(O_9, A_8) → r_{20}
  471. Segment(K_9, Q_7) → s_{20}
  472. Segment(M_9, P_7) → t_{20}
  473. Segment(T_9, U_9) → a_{21}
  474. Segment(U_9, N_9) → b_{21}
  475. Segment(N_9, V_9) → c_{21}
  476. Segment(V_9, W_9) → d_{21}
  477. Intersect(d, p) → Z_9
  478. Segment(W_9, Z_9) → e_{21}
  479. Segment(Z_9, T_9) → f_{21}
  480. Segment(Z_9, A_{10}) → g_{21}
  481. Segment(A_{10}, O_8) → h_{21}
  482. Segment(O_8, B_{10}) → i_{21}
  483. Segment(B_{10}, Z_9) → j_{21}
  484. Segment(A_{10}, R_9) → k_{21}
  485. Segment(Q_9, N_8) → l_{21}
  486. Segment(U_9, E_8) → m_{21}
  487. Segment(W_9, G_8) → n_{21}
  488. Segment(C_{10}, Z_9) → p_{21}
  489. Segment(Z_9, D_{10}) → q_{21}
  490. Segment(D_{10}, E_{10}) → r_{21}
  491. Segment(C_{10}, F_{10}) → s_{21}
  492. Segment(F_{10}, B) → t_{21}
  493. Segment(E_{10}, B) → a_{22}
  494. Segment(B, G_{10}) → b_{22}
  495. Segment(G_{10}, H_{10}) → c_{22}
  496. Segment(I_{10}, J_{10}) → d_{22}
  497. Segment(I_{10}, B) → e_{22}
  498. Segment(J_{10}, F) → f_{22}
  499. Segment(F, H_{10}) → g_{22}
  500. Segment(G_{10}, P_8) → h_{22}
  501. Segment(B_{10}, J_{10}) → i_{22}
  502. Segment(E_{10}, Q_8) → j_{22}
  503. Segment(C_{10}, U_8) → k_{22}
  504. Point(q_{13}) → K_{10}
  505. Intersect(d_{13}, e_{13}) → L_{10}
  506. Intersect(f_{13}, g_{13}) → M_{10}
  507. Intersect(s_8, t_8) → N_{10}
  508. Intersect(g_{14}, h_{14}) → O_{10}
  509. Intersect(k_{14}, l_{14}) → P_{10}
  510. Intersect(f_6, g_6) → Q_{10}
  511. Intersect(r_7, a_8) → R_{10}
  512. Polygon(K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}) → poly1, k_{23}, l_{22}, m_{22}, n_{22}, o_{10}, p_{22}, q_{22}, r_{22}
  513. Intersect(e_{14}, f_{14}) → S_{10}
  514. Intersect(d_{14}, f_{14}) → T_{10}
  515. Intersect(b_8, c_8) → U_{10}
  516. Point(b_8) → V_{10}
  517. Polygon(S_{10}, T_{10}, K_{10}, R_{10}, U_{10}, V_{10}, N_{10}, O_{10}) → poly2, s_{22}, t_{22}, k_{24}, r_{23}, u_{10}, v_{10}, n_{23}, o_1
  518. Intersect(j_4, m_4) → W_{10}
  519. Intersect(q_4, r_4) → Z_{10}
  520. Segment(W_{10}, Z_{10}) → a_{23}
  521. Intersect(f_8, i_8) → A_{11}
  522. Segment(Z_{10}, A_{11}) → b_{23}
  523. Intersect(d_4, e_4) → B_{11}
  524. Segment(A_{11}, B_{11}) → c_{23}
  525. Intersect(b_3, c_3) → C_{11}
  526. Segment(B_{11}, C_{11}) → d_{23}
  527. Intersect(d_5, e_5) → D_{11}
  528. Segment(C_{11}, D_{11}) → e_{23}
  529. Segment(D_{11}, W_{10}) → f_{23}
  530. Intersect(d_{21}, e_{21}) → E_{11}
  531. Intersect(e_{21}, f_{21}) → F_{11}
  532. Intersect(i_{21}, j_{21}) → G_{11}
  533. Intersect(c_{18}, d_{18}) → H_{11}
  534. Intersect(i_{20}, j_{20}) → I_{11}
  535. Intersect(m_{20}, n_{20}) → J_{11}
  536. Intersect(t_{15}, a_{16}) → K_{11}
  537. Intersect(g_{17}, h_{17}) → L_{11}
  538. Polygon(E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}) → poly3, e_{24}, f_{24}, g_{23}, h_{23}, i_{23}, j_{23}, k_{25}, l_{23}
  539. Intersect(j_{17}, k_{17}) → M_{11}
  540. Intersect(f_{20}, g_{20}) → N_{11}
  541. Intersect(c_{21}, d_{21}) → O_{11}
  542. Intersect(g_{17}, j_{17}) → P_{11}
  543. Polygon(M_{11}, H_{11}, I_{11}, N_{11}, O_{11}, E_{11}, L_{11}, P_{11}) → poly4, m_{23}, h_{24}, i_{24}, n_{24}, o_{11}, e_{25}, l_{24}, p_{23}
  544. Intersect(m_4, n_4) → Q_{11}
  545. Segment(Q_{11}, Z_{10}) → q_{23}
  546. Segment(Z_{10}, A_{11}) → s_{23}
  547. Segment(B_{11}, A_{11}) → t_{23}
  548. Intersect(r_2, s_2) → R_{11}
  549. Segment(B_{11}, R_{11}) → a_{24}
  550. Segment(C_{11}, D_{11}) → b_{24}
  551. Point(k_4) → S_{11}
  552. Segment(S_{11}, W_{10}) → c_{24}
  553. Intersect(t_{15}, a_{16}) → T_{11}
  554. Intersect(c_{16}, d_{16}) → U_{11}
  555. Intersect(d_{16}, t_{20}) → V_{11}
  556. Intersect(g_{16}, h_{16}) → W_{11}
  557. Intersect(k_{16}, q_{16}) → Z_{11}
  558. Intersect(g_{19}, j_{19}) → A_{12}
  559. Intersect(i_{19}, j_{19}) → B_{12}
  560. Intersect(t_{19}, c_{20}) → C_{12}
  561. Intersect(e_{20}, f_{20}) → D_{12}
  562. Intersect(f_{20}, g_{20}) → E_{12}
  563. Intersect(i_{20}, j_{20}) → F_{12}
  564. Polygon(T_{11}, U_{11}, F_{12}, J_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}) → poly5, t_{24}, e_{26}, f_{25}, j_{24}, u_{11}, v_{11}, w_{11}, z_{11}, a_{25}, b_{25}, c_{25}, d_{24}
  565. Polygon(F_{12}, E_{12}, T_{11}, J_{11}, D_{12}, C_{12}, B_{12}, A_{12}, Z_{11}, W_{11}, V_{11}, U_{11}) → poly6, f_{26}, u_1, t_{25}, j_{25}, e_{27}, d_{25}, c_{26}, b_{26}, a_{26}, z_1, w_1, v_1
  566. Intersect(d_{13}, e_{13}) → G_{12}
  567. Intersect(b_{13}, e_{13}) → H_{12}
  568. Intersect(p_{12}, q_{12}) → I_{12}
  569. Point(f_{12}) → J_{12}
  570. Intersect(e_{12}, f_{12}) → K_{12}
  571. Intersect(h_{10}, i_{10}) → L_{12}
  572. Intersect(d_9, e_9) → M_{12}
  573. Intersect(e_9, f_9) → N_{12}
  574. Intersect(q_8, r_8) → O_{12}
  575. Point(b_8) → P_{12}
  576. Intersect(s_8, t_8) → Q_{12}
  577. Intersect(f_{13}, g_{13}) → R_{12}
  578. Polygon(G_{12}, H_{12}, Q_{12}, R_{12}, I_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}) → poly7, g_{24}, p_{24}, q_{24}, r_{24}, h_{25}, i_{25}, j_{26}, k_{26}, l_{25}, m_{24}, n_{25}, o_{12}
  579. Intersect(m_{18}, n_{18}) → S_{12}
  580. Intersect(c_{22}, g_{22}) → T_{12}
  581. Intersect(b_{22}, c_{22}) → U_{12}
  582. Intersect(t_{21}, a_{22}) → V_{12}
  583. Intersect(s_{21}, t_{21}) → W_{12}
  584. Point(i_{22}) → Z_{12}
  585. Intersect(d_{18}, h_{23}) → A_{13}
  586. Intersect(j_{17}, k_{17}) → B_{13}
  587. Intersect(g_{18}, j_{18}) → C_{13}
  588. Intersect(k_{18}, n_{18}) → D_{13}
  589. Intersect(m_{18}, n_{18}) → E_{13}
  590. Intersect(d_{22}, f_{22}) → F_{13}
  591. Intersect(d_{22}, e_{22}) → G_{13}
  592. Intersect(t_{21}, a_{22}) → H_{13}
  593. Intersect(r_{21}, a_{22}) → I_{13}
  594. Intersect(q_{21}, r_{21}) → J_{13}
  595. Intersect(e_{21}, f_{21}) → K_{13}
  596. Polygon(Z_{12}, A_{13}, J_{13}, K_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}) → poly8, z_{12}, i_{26}, j_{27}, k_{27}, a_{27}, b_{27}, c_{27}, d_{26}, e_{28}, f_{27}, g_{25}, h_{26}
  597. Point(c_{15}) → L_{13}
  598. Intersect(t_{14}, a_{15}) → M_{13}
  599. Intersect(g_{14}, h_{14}) → N_{13}
  600. Intersect(k_{14}, l_{14}) → O_{13}
  601. Intersect(f_6, g_6) → P_{13}
  602. Intersect(e_{11}, h_{11}) → Q_{13}
  603. Intersect(c_{11}, d_{11}) → R_{13}
  604. Intersect(r_{10}, s_{10}) → S_{13}
  605. Intersect(j_{15}, k_{15}) → T_{13}
  606. Intersect(f_{15}, g_{15}) → U_{13}
  607. Intersect(d_{15}, e_{15}) → V_{13}
  608. Point(d_{15}) → W_{13}
  609. Polygon(L_{13}, M_{13}, V_{13}, W_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}) → poly9, l_{26}, u_{13}, v_{13}, w_{13}, m_{25}, n_{26}, o_{13}, p_{25}, q_{25}, r_{25}, s_{24}, t_{26}
  610. Intersect(e_3, f_3) → Z_{13}
  611. Intersect(a_3, d_3) → A_{14}
  612. Intersect(r_2, s_2) → B_{14}
  613. Point(r_2) → C_{14}
  614. Intersect(g_1, h_1) → D_{14}
  615. Intersect(d_1, f_1) → E_{14}
  616. Intersect(e_1, f_1) → F_{14}
  617. Intersect(b_2, c_2) → G_{14}
  618. Intersect(a_2, c_2) → H_{14}
  619. Intersect(j_2, k_2) → I_{14}
  620. Intersect(i_3, j_3) → J_{14}
  621. Polygon(Z_{13}, A_{14}, J_{14}, F_2, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}) → poly10, z_{13}, i_{27}, j_{28}, f_{29}, a_{28}, b_{28}, c_{28}, d_{27}, e_{29}, f_{28}, g_{26}, h_{27}
  622. Intersect(q_5, r_5) → K_{14}
  623. Intersect(k_5, n_5) → L_{14}
  624. Intersect(e_5, f_5) → M_{14}
  625. Intersect(c_5, f_5) → N_{14}
  626. Intersect(k_4, l_4) → O_{14}
  627. Intersect(h_4, i_4) → P_{14}
  628. Intersect(f_4, h_4) → Q_{14}
  629. Intersect(s_3, t_3) → R_{14}
  630. Polygon(Z_{13}, F_2, B_{14}, A_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}) → poly11, z_2, r_{26}, b_{29}, a_{29}, f_{30}, k_{28}, l_{27}, m_{26}, n_{27}, o_{14}, p_{26}, q_{26}
  631. Intersect(b_3, c_3) → S_{14}
  632. Intersect(g_3, h_3) → T_{14}
  633. Intersect(k_3, l_3) → U_{14}
  634. Intersect(h_2, i_2) → V_{14}
  635. Intersect(b_1, d_1) → Z_{14}
  636. Intersect(i_1, j_1) → A_{15}
  637. Intersect(s_2, t_2) → B_{15}
  638. Polygon(B_{14}, S_{14}, A_{15}, B_{15}, T_{14}, F_2, U_{14}, V_{14}, H_{14}, W_{14}, Z_{14}, E_{14}) → poly12, b_{30}, e_{30}, a_{30}, b_{31}, s_{25}, t_{27}, f_{31}, u_{14}, v_{14}, h_{28}, w_{14}, z_{14}
  639. Intersect(p_5, s_5) → C_{15}
  640. Intersect(l_5, m_5) → D_{15}
  641. Intersect(d_5, e_5) → E_{15}
  642. Intersect(m_4, q_7) → F_{15}
  643. Intersect(g_4, i_4) → G_{15}
  644. Intersect(r_3, a_4) → H_{15}
  645. Polygon(S_{14}, T_{14}, H_{15}, B_{14}, F_2, C_{15}, D_{15}, M_{14}, E_{15}, F_{15}, P_{14}, G_{15}) → poly13, s_{26}, g_{27}, h_{29}, b_{32}, t_{28}, f_{32}, c_{29}, d_{28}, m_{27}, e_{31}, f_{33}, p_{27}
  646. Intersect(b_7, c_7) → I_{15}
  647. Intersect(c_7, d_7) → J_{15}
  648. Intersect(l_7, m_7) → K_{15}
  649. Intersect(g_7, j_7) → L_{15}
  650. Intersect(r_6, s_6) → M_{15}
  651. Intersect(s_6, t_6) → N_{15}
  652. Intersect(s_4, t_4) → O_{15}
  653. Polygon(F_{15}, E_{15}, O_{15}, P_{14}, M_{14}, S_3, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}) → poly14, f_{34}, n_{28}, o_{15}, p_{28}, e_{32}, m_{28}, s_{27}, i_{28}, j_{29}, k_{29}, l_{28}, m_{29}
  654. Intersect(g_9, h_9) → P_{15}
  655. Intersect(t_{23}, a_{24}) → Q_{15}
  656. Polygon(M_{12}, P_{15}, Q_{15}, B_{14}, C_{14}, N_{12}) → poly15, m_{30}, p_{29}, q_{27}, b_{33}, c_{30}, n_{29}
  657. Intersect(g_8, h_8) → R_{15}
  658. Intersect(k_1, l_1) → S_{15}
  659. Point(p_8) → T_{15}
  660. Polygon(P_{12}, R_{15}, S_{15}, E_{14}, A_{15}, T_{15}) → poly16, p_{30}, r_{27}, s_{28}, e_{33}, a_{31}, t_{29}
  661. Intersect(b_4, g_8) → U_{15}
  662. Intersect(k_1, h_9) → V_{15}
  663. Polygon(U_{15}, R_{15}, S_{15}, V_{15}, P_{15}, Q_{15}) → poly17, u_{15}, r_{28}, s_{29}, v_{15}, p_{31}, q_{28}
  664. Intersect(g_1, i_1) → W_{15}
  665. Intersect(n_8, r_8) → Z_{15}
  666. Polygon(W_{15}, A_{15}, T_{15}, Z_{15}, N_{12}, C_{14}) → poly18, w_{15}, a_{32}, t_{30}, z_{15}, n_{30}, c_{31}
  667. Intersect(p_4, q_4) → A_{16}
  668. Intersect(e_6, f_6) → B_{16}
  669. Intersect(b_4, c_4) → C_{16}
  670. Intersect(i_8, s_{23}) → D_{16}
  671. Point(q_4) → E_{16}
  672. Polygon(A_{16}, B_{16}, C_{16}, U_{15}, D_{16}, E_{16}) → poly19, a_{33}, b_{34}, c_{32}, u_2, d_{29}, e_{34}
  673. Intersect(r_3, s_3) → F_{16}
  674. Intersect(b_8, c_8) → G_{16}
  675. Intersect(t_7, a_8) → H_{16}
  676. Intersect(s_7, t_7) → I_{16}
  677. Polygon(F_{16}, Q_{14}, G_{16}, H_{16}, I_{16}, H_{15}) → poly20, f_{35}, q_{29}, g_{28}, h_{30}, i_{29}, h_{31}
  678. Polygon(P_{14}, E_{16}, D_{16}, P_{12}, G_{16}, Q_{14}) → poly21, p_{32}, e_{35}, d_{30}, p_{33}, g_{29}, q_{30}
  679. Polygon(P_{13}, I_{16}, H_{15}, B_{14}, C_{16}, B_{16}) → poly22, p_{34}, i_{30}, h_{32}, b_{35}, c_{33}, b_{36}
  680. Intersect(l_{10}, m_{10}) → J_{16}
  681. Intersect(q_{10}, r_{10}) → K_{16}
  682. Intersect(n_4, p_4) → L_{16}
  683. Intersect(d_6, g_6) → M_{16}
  684. Intersect(m_{10}, n_{10}) → N_{16}
  685. Polygon(J_{16}, K_{16}, L_{16}, A_{16}, M_{16}, N_{16}) → poly23, j_{30}, k_{30}, l_{29}, a_{34}, m_{31}, n_{31}
  686. Intersect(s_4, b_5) → O_{16}
  687. Intersect(q_6, r_6) → P_{16}
  688. Intersect(b_{11}, c_{11}) → Q_{16}
  689. Intersect(a_{11}, b_{11}) → R_{16}
  690. Polygon(O_{16}, P_{16}, Q_{13}, Q_{16}, R_{16}, O_{15}) → poly24, o_{16}, p_{35}, q_{31}, q_{32}, r_{29}, o_2
  691. Polygon(M_{15}, N_{16}, M_{16}, P_{13}, Q_{13}, P_{16}) → poly25, m_{32}, n_{32}, m_{33}, p_{36}, q_{33}, p_{37}
  692. Polygon(S_{13}, R_{16}, O_{15}, P_{14}, L_{16}, K_{16}) → poly26, s_{30}, r_{30}, o_3, p_{38}, l_{30}, k_{31}
  693. Intersect(a_{15}, b_{15}) → T_{16}
  694. Intersect(m_{17}, q_{17}) → U_{16}
  695. Intersect(p_{18}, s_{18}) → V_{16}
  696. Polygon(E_{13}, D_{13}, T_{16}, M_{13}, U_{16}, V_{16}) → poly27, e_{36}, d_{31}, t_{31}, m_{34}, u_{16}, v_{16}
  697. Intersect(n_{17}, b_{18}) → W_{16}
  698. Point(r_{18}) → Z_{16}
  699. Intersect(h_{18}, i_{18}) → A_{17}
  700. Polygon(B_{13}, W_{16}, Z_{16}, V_{13}, W_{13}, A_{17}) → poly28, b_{37}, w_{16}, z_{16}, v_2, w_2, a_{35}
  701. Point(p_{18}) → B_{17}
  702. Intersect(m_{17}, n_{17}) → C_{17}
  703. Polygon(B_{17}, V_{16}, U_{16}, C_{17}, W_{16}, Z_{16}) → poly29, b_{38}, v_3, u_3, c_{34}, w_3, z_3
  704. Intersect(b_{15}, c_{15}) → D_{17}
  705. Intersect(g_{18}, h_{18}) → E_{17}
  706. Polygon(D_{17}, W_{13}, A_{17}, E_{17}, D_{13}, T_{16}) → poly30, d_{32}, w_4, a_{36}, e_{37}, d_{33}, t_{32}
  707. Intersect(d_{14}, f_{14}) → F_{17}
  708. Intersect(f_{17}, i_{17}) → G_{17}
  709. Intersect(s_{15}, t_{15}) → H_{17}
  710. Intersect(n_{17}, p_{17}) → I_{17}
  711. Polygon(M_{13}, F_{17}, G_{17}, T_{11}, H_{17}, I_{17}) → poly31, m_{35}, f_{36}, g_{30}, t_{33}, h_{33}, i_{31}
  712. Intersect(g_{17}, j_{17}) → J_{17}
  713. Intersect(n_{13}, p_{13}) → K_{17}
  714. Intersect(s_{13}, t_{13}) → L_{17}
  715. Intersect(l_{17}, m_{17}) → M_{17}
  716. Polygon(B_{13}, J_{17}, K_{17}, G_{12}, L_{17}, M_{17}) → poly32, b_{39}, j_{31}, k_{32}, g_{31}, l_{31}, m_{36}
  717. Intersect(t_{13}, a_{14}) → N_{17}
  718. Polygon(C_{17}, M_{17}, L_{17}, N_{17}, H_{17}, I_{17}) → poly33, c_{35}, m_{37}, l_{32}, n_{33}, h_{34}, i_{32}
  719. Intersect(n_{13}, q_{13}) → O_{17}
  720. Intersect(f_{17}, g_{17}) → P_{17}
  721. Polygon(O_{17}, K_{17}, J_{17}, P_{17}, G_{17}, F_{17}) → poly34, o_{17}, k_{33}, j_{32}, p_{39}, g_{32}, f_{37}
  722. Intersect(a_{16}, b_{16}) → Q_{17}
  723. Intersect(g_{12}, h_{12}) → R_{17}
  724. Intersect(h_{12}, i_{12}) → S_{17}
  725. Intersect(k_{16}, l_{16}) → T_{17}
  726. Intersect(a_{14}, b_{14}) → U_{17}
  727. Polygon(N_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, U_{17}) → poly35, n_{34}, q_{34}, r_{31}, s_{31}, t_{34}, u_{17}
  728. Intersect(k_{12}, q_{12}) → V_{17}
  729. Intersect(f_{16}, g_{16}) → W_{17}
  730. Intersect(d_{16}, f_{16}) → Z_{17}
  731. Intersect(k_{12}, l_{12}) → A_{18}
  732. Polygon(V_{17}, H_{12}, W_{17}, Z_{17}, U_{11}, A_{18}) → poly36, v_{17}, h_{35}, w_{17}, z_{17}, u_4, a_{37}
  733. Polygon(W_{11}, T_{17}, U_{17}, G_{12}, H_{12}, W_{17}) → poly37, w_5, t_{35}, u_5, g_{33}, h_{36}, w_6
  734. Polygon(J_{12}, R_{17}, Q_{17}, T_{11}, U_{11}, A_{18}) → poly38, j_{33}, r_{32}, q_{35}, t_{36}, u_6, a_{38}
  735. Intersect(k_{19}, l_{19}) → B_{18}
  736. Intersect(p_{19}, q_{19}) → C_{18}
  737. Polygon(A_{12}, B_{12}, B_{18}, C_{18}, Z_{11}) → poly39, a_{39}, b_{40}, b_{41}, c_{36}, z_4
  738. Intersect(i_{16}, d_{17}) → D_{18}
  739. Intersect(i_{16}, j_{16}) → E_{18}
  740. Intersect(g_{16}, j_{16}) → F_{18}
  741. Polygon(C_{18}, Z_{11}, W_{11}, D_{18}, E_{18}, F_{18}) → poly40, c_{37}, z_5, w_7, d_{34}, e_{38}, f_{38}
  742. Intersect(n_{12}, p_{12}) → G_{18}
  743. Intersect(m_{12}, n_{12}) → H_{18}
  744. Intersect(l_{12}, m_{12}) → I_{18}
  745. Intersect(r_{12}, s_{12}) → J_{18}
  746. Intersect(f_{10}, g_{10}) → K_{18}
  747. Intersect(d_{10}, e_{10}) → L_{18}
  748. Polygon(L_{18}, M_{12}, L_{12}, K_{12}, J_{12}, G_{18}, H_{18}, I_{18}, J_{18}) → poly41, l_{33}, m_{38}, l_{34}, k_{34}, j_{34}, g_{34}, h_{37}, i_{33}, j_{35}
  749. Intersect(r_1, s_1) → M_{18}
  750. Intersect(p_9, q_9) → N_{18}
  751. Intersect(l_2, m_2) → O_{18}
  752. Polygon(Z_{14}, E_{14}, M_{18}, N_{18}, O_{18}, H_{14}, W_{14}) → poly42, z_6, e_{39}, m_{39}, n_{35}, o_{18}, h_{38}, w_8
  753. Intersect(n_2, p_2) → P_{18}
  754. Intersect(m_2, n_2) → Q_{18}
  755. Polygon(H_{14}, P_{18}, Q_{18}, O_{18}) → poly43, h_{39}, p_{40}, q_{36}, o_4
  756. Intersect(m_{11}, n_{11}) → R_{18}
  757. Intersect(m_5, n_5) → S_{18}
  758. Intersect(h_6, k_6) → T_{18}
  759. Polygon(R_{18}, D_{15}, S_{18}, K_{14}, F_2, T_{18}) → poly44, r_{33}, d_{35}, s_{32}, k_{35}, f_{39}, t_{37}
  760. Intersect(i_5, j_5) → U_{18}
  761. Polygon(R_{18}, D_{15}, M_{14}, U_{18}) → poly45, r_{34}, d_{36}, m_{40}, u_{18}
  762. Intersect(r_{11}, s_{11}) → V_{18}
  763. Intersect(d_2, e_2) → W_{18}
  764. Polygon(V_{18}, I_{14}, H_{14}, W_{18}) → poly46, v_{18}, i_{34}, h_{40}, w_{18}
  765. Intersect(h_2, j_2) → Z_{18}
  766. Intersect(i_6, j_6) → A_{19}
  767. Polygon(V_{18}, I_{14}, Z_{18}, U_{14}, F_2, A_{19}) → poly47, v_4, i_{35}, z_{18}, u_7, f_{40}, a_{40}
  768. Intersect(b_{12}, c_{12}) → B_{19}
  769. Intersect(f_2, g_2) → C_{19}
  770. Polygon(H_{14}, P_{18}, B_{19}, C_{19}) → poly48, h_{41}, p_{41}, b_{42}, c_{38}
  771. Intersect(p_1, q_1) → D_{19}
  772. Intersect(t_9, a_{10}) → E_{19}
  773. Intersect(b_{10}, c_{10}) → F_{19}
  774. Intersect(i_9, j_9) → G_{19}
  775. Intersect(m_1, n_1) → H_{19}
  776. Polygon(E_{14}, D_{19}, E_{19}, F_{19}, M_{12}, G_{19}, V_{15}, H_{19}) → poly49, e_{40}, d_{37}, e_{41}, f_{41}, m_{41}, g_{35}, v_5, h_{42}
  777. Intersect(b_{17}, d_{17}) → I_{19}
  778. Intersect(m_{16}, n_{16}) → J_{19}
  779. Intersect(i_{12}, j_{12}) → K_{19}
  780. Polygon(J_{12}, G_{18}, I_{19}, D_{18}, W_{11}, J_{19}, S_{17}, K_{19}) → poly50, j_{36}, g_{36}, i_{36}, d_{38}, w_9, j_{37}, s_{33}, k_{36}
  781. Intersect(g_{18}, h_{18}) → L_{19}
  782. Intersect(g_{18}, j_{18}) → M_{19}
  783. Intersect(b_{18}, f_{18}) → N_{19}
  784. Intersect(l_{17}, m_{17}) → O_{19}
  785. Intersect(m_{17}, n_{17}) → P_{19}
  786. Intersect(n_{17}, p_{17}) → Q_{19}
  787. Intersect(e_{14}, f_{14}) → R_{19}
  788. Intersect(t_{14}, c_{15}) → S_{19}
  789. Intersect(b_{15}, c_{15}) → T_{19}
  790. Intersect(a_{15}, b_{15}) → U_{19}
  791. Intersect(m_{17}, q_{17}) → V_{19}
  792. Intersect(m_{17}, q_{17}) → W_{19}
  793. Intersect(n_{17}, b_{18}) → Z_{19}
  794. Intersect(h_{18}, i_{18}) → B_{20}
  795. Polygon(L_{19}, M_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, B_{20}, N_{19}, O_{19}, P_{19}, Q_{19}, R_{19}, S_{19}, T_{19}, U_{19}) → poly51, l_{35}, u_{19}, v_{19}, w_{19}, z_{19}, a_{41}, b_{43}, m_{42}, n_{36}, o_{19}, p_{42}, q_{37}, r_{35}, s_{34}, t_{38}
  796. Polygon(L_{19}, M_{19}, A_{20}, O_{19}, P_{19}, Z_{19}, N_{19}, B_{20}) → poly52, l_{36}, m_{43}, a_{42}, o_5, p_{43}, z_7, n_{37}, b_{44}
  797. Polygon(T_{19}, U_{19}, R_{19}, W_{19}, P_{19}, Q_{19}, V_{19}, S_{19}) → poly53, t_{39}, u_8, r_{36}, w_{10}, p_{44}, q_{38}, v_6, s_{35}
  798. Intersect(f_{17}, g_{17}) → C_{20}
  799. Intersect(g_{17}, h_{17}) → D_{20}
  800. Intersect(t_{15}, a_{16}) → E_{20}
  801. Intersect(a_{16}, b_{16}) → F_{20}
  802. Intersect(a_{14}, b_{16}) → G_{20}
  803. Intersect(s_{15}, t_{15}) → H_{20}
  804. Intersect(f_{17}, i_{17}) → J_{20}
  805. Polygon(C_{20}, D_{20}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}) → poly54, c_{39}, d_{39}, e_{42}, f_{42}, g_{37}, h_{43}, i_{37}, j_{38}
  806. Intersect(n_{13}, q_{13}) → K_{20}
  807. Point(n_{13}) → L_{20}
  808. Intersect(p_{13}, s_{13}) → M_{20}
  809. Intersect(s_{13}, t_{13}) → N_{20}
  810. Point(a_{14}) → O_{20}
  811. Point(r_{13}) → Q_{20}
  812. Polygon(K_{20}, L_{20}, M_{20}, N_{20}, G_{20}, O_{20}, P_{20}, Q_{20}) → poly55, k_{37}, l_{37}, m_{44}, n_{38}, g_{38}, o_{20}, p_{45}, q_{39}
  813. Intersect(d_{16}, f_{16}) → R_{20}
  814. Intersect(d_{16}, h_{16}) → S_{20}
  815. Intersect(h_{16}, n_{16}) → T_{20}
  816. Intersect(m_{16}, n_{16}) → U_{20}
  817. Intersect(h_{12}, i_{12}) → V_{20}
  818. Intersect(k_{16}, l_{16}) → W_{20}
  819. Intersect(f_{16}, g_{16}) → A_{21}
  820. Polygon(R_{20}, S_{20}, T_{20}, U_{20}, V_{20}, W_{20}, Z_{20}, A_{21}) → poly56, r_{37}, s_{36}, t_{40}, u_{20}, v_{20}, w_{20}, z_{20}, a_{43}
  821. Intersect(i_{12}, j_{12}) → B_{21}
  822. Point(f_{12}) → C_{21}
  823. Point(q_{12}) → D_{21}
  824. Intersect(k_{12}, q_{12}) → E_{21}
  825. Intersect(k_{12}, l_{12}) → F_{21}
  826. Intersect(g_{12}, h_{12}) → H_{21}
  827. Polygon(V_{20}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}, H_{21}) → poly57, v_7, b_{45}, c_{40}, d_{40}, e_{43}, f_{43}, g_{39}, h_{44}
  828. Intersect(t_7, a_8) → I_{21}
  829. Intersect(r_7, a_8) → J_{21}
  830. Intersect(f_6, g_6) → K_{21}
  831. Intersect(d_6, g_6) → L_{21}
  832. Intersect(p_4, q_4) → M_{21}
  833. Intersect(e_6, f_6) → N_{21}
  834. Intersect(s_7, t_7) → P_{21}
  835. Polygon(I_{21}, J_{21}, K_{21}, L_{21}, M_{21}, N_{21}, O_{21}, P_{21}) → poly58, i_{38}, j_{39}, k_{38}, l_{38}, m_{45}, n_{39}, o_{21}, p_{46}
  836. Intersect(q_4, q_{23}) → Q_{21}
  837. Intersect(h_4, i_4) → R_{21}
  838. Intersect(f_4, h_4) → S_{21}
  839. Intersect(r_3, s_3) → T_{21}
  840. Intersect(g_4, i_4) → U_{21}
  841. Point(l_{11}) → W_{21}
  842. Polygon(M_{21}, Q_{21}, R_{21}, S_{21}, T_{21}, U_{21}, V_{21}, W_{21}) → poly59, m_{46}, q_{40}, r_{38}, s_{37}, t_{41}, u_{21}, v_{21}, w_{21}
  843. Intersect(n_8, r_8) → Z_{21}
  844. Intersect(q_8, r_8) → A_{22}
  845. Point(b_8) → B_{22}
  846. Intersect(i_8, s_{23}) → C_{22}
  847. Intersect(g_8, t_{23}) → D_{22}
  848. Intersect(g_8, h_8) → E_{22}
  849. Intersect(n_8, p_8) → G_{22}
  850. Polygon(Z_{21}, A_{22}, B_{22}, C_{22}, D_{22}, E_{22}, F_{22}, G_{22}) → poly60, z_{21}, a_{44}, b_{46}, c_{41}, d_{41}, e_{44}, f_{44}, g_{40}
  851. Intersect(l_9, t_{23}) → H_{22}
  852. Intersect(a_4, c_4) → I_{22}
  853. Intersect(q_2, r_2) → J_{22}
  854. Intersect(q_2, t_2) → K_{22}
  855. Intersect(s_2, t_2) → L_{22}
  856. Intersect(b_4, c_4) → N_{22}
  857. Polygon(D_{22}, H_{22}, I_{22}, J_{22}, K_{22}, L_{22}, M_{22}, N_{22}) → poly61, d_{42}, h_{45}, i_{39}, j_{40}, k_{39}, l_{39}, m_{47}, n_{40}
  858. Intersect(d_{10}, e_{10}) → O_{22}
  859. Intersect(d_9, e_9) → P_{22}
  860. Intersect(g_9, h_9) → Q_{22}
  861. Intersect(k_1, n_1) → R_{22}
  862. Intersect(i_9, j_9) → S_{22}
  863. Intersect(c_{10}, d_{10}) → V_{22}
  864. Polygon(O_{22}, P_{22}, Q_{22}, R_{22}, S_{22}, T_{22}, U_{22}, V_{22}) → poly62, o_{22}, p_{47}, q_{41}, r_{39}, s_{38}, t_{42}, u_{22}, v_{22}
  865. Intersect(k_1, l_1) → W_{22}
  866. Intersect(d_1, f_1) → Z_{22}
  867. Point(s_1) → A_{23}
  868. Intersect(q_1, r_1) → B_{23}
  869. Intersect(p_1, q_1) → C_{23}
  870. Intersect(m_1, n_1) → E_{23}
  871. Polygon(R_{22}, W_{22}, Z_{22}, A_{23}, B_{23}, C_{23}, D_{23}, E_{23}) → poly63, r_{40}, w_{22}, z_{22}, a_{45}, b_{47}, c_{42}, d_{43}, e_{45}
  872. Intersect(h_2, j_2) → F_{23}
  873. Intersect(h_2, p_3) → G_{23}
  874. Intersect(a_2, c_2) → H_{23}
  875. Intersect(j_2, k_2) → I_{23}
  876. Polygon(F_{23}, G_{23}, H_{23}, I_{23}) → poly64, f_{45}, g_{41}, h_{46}, i_{40}
  877. Intersect(f_2, g_2) → J_{23}
  878. Intersect(e_2, f_2) → K_{23}
  879. Intersect(d_2, e_2) → L_{23}
  880. Polygon(H_{23}, J_{23}, K_{23}, L_{23}) → poly65, h_{47}, j_{41}, k_{40}, l_{40}
  881. Intersect(m_5, n_5) → M_{23}
  882. Intersect(p_5, s_5) → N_{23}
  883. Intersect(f_3, r_5) → O_{23}
  884. Intersect(i_6, j_6) → P_{23}
  885. Intersect(h_6, i_6) → Q_{23}
  886. Intersect(h_6, k_6) → R_{23}
  887. Intersect(q_5, r_5) → T_{23}
  888. Polygon(M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}, S_{23}, T_{23}) → poly66, m_{48}, n_{41}, o_{23}, p_{48}, q_{42}, r_{41}, s_{39}, t_{43}
  889. Intersect(l_6, m_6) → U_{23}
  890. Intersect(l_6, p_6) → V_{23}
  891. Intersect(f_5, n_6) → W_{23}
  892. Intersect(i_5, j_5) → Z_{23}
  893. Intersect(h_5, i_5) → A_{24}
  894. Intersect(g_5, h_5) → B_{24}
  895. Polygon(U_{23}, V_{23}, W_{23}, Z_{23}, A_{24}, B_{24}, C_{24}, D_{24}) → poly67, u_{23}, v_{23}, w_{23}, z_{23}, a_{46}, b_{48}, c_{43}, d_{44}
  896. Intersect(g_7, h_7) → E_{24}
  897. Intersect(l_7, m_7) → F_{24}
  898. Intersect(c_7, d_7) → G_{24}
  899. Point(k_7) → H_{24}
  900. Polygon(E_{24}, F_{24}, G_{24}, H_{24}) → poly68, e_{46}, f_{46}, g_{42}, h_{48}
  901. Intersect(r_6, s_6) → I_{24}
  902. Intersect(q_6, r_6) → J_{24}
  903. Intersect(s_4, b_5) → K_{24}
  904. Intersect(s_6, t_6) → L_{24}
  905. Polygon(I_{24}, J_{24}, K_{24}, L_{24}) → poly69, i_{41}, j_{42}, k_{41}, l_{41}
  906. Intersect(m_{10}, n_{10}) → M_{24}
  907. Intersect(s_{10}, t_{10}) → N_{24}
  908. Intersect(r_{10}, s_{10}) → O_{24}
  909. Point(r_{10}) → P_{24}
  910. Intersect(l_{10}, p_{10}) → Q_{24}
  911. Polygon(I_{24}, M_{24}, N_{24}, O_{24}, P_{24}, Q_{24}) → poly70, i_{42}, m_{49}, n_{42}, o_{24}, p_{49}, q_{43}
  912. Intersect(c_{11}, d_{11}) → R_{24}
  913. Intersect(b_{11}, c_{11}) → S_{24}
  914. Intersect(a_{11}, b_{11}) → T_{24}
  915. Polygon(O_{24}, R_{24}, S_{24}, T_{24}) → poly71, o_6, r_{42}, s_{40}, t_{44}
  916. Intersect(g_{15}, h_{15}) → U_{24}
  917. Intersect(f_{15}, g_{15}) → V_{24}
  918. Intersect(q_{18}, a_{19}) → W_{24}
  919. Point(p_{18}) → Z_{24}
  920. Intersect(c_{22}, g_{22}) → A_{25}
  921. Intersect(c_{22}, d_{22}) → B_{25}
  922. Intersect(d_{22}, f_{22}) → C_{25}
  923. Intersect(r_{18}, t_{18}) → D_{25}
  924. Intersect(r_{18}, b_{19}) → E_{25}
  925. Intersect(h_{15}, i_{15}) → F_{25}
  926. Polygon(U_{24}, V_{24}, W_{24}, Z_{24}, A_{25}, B_{25}, C_{25}, D_{25}, E_{25}, F_{25}) → poly72, u_{24}, f_{47}, v_{24}, w_{24}, z_{24}, a_{47}, b_{49}, c_{44}, d_{45}, e_{47}
  927. Intersect(t_{21}, a_{22}) → G_{25}
  928. Point(a_{22}) → H_{25}
  929. Intersect(r_{21}, s_{21}) → I_{25}
  930. Point(t_{21}) → J_{25}
  931. Polygon(G_{25}, H_{25}, I_{25}, J_{25}) → poly73, g_{43}, h_{49}, i_{43}, j_{43}
  932. Intersect(e_{21}, f_{21}) → K_{25}
  933. Point(f_{21}) → L_{25}
  934. Intersect(a_{21}, d_{21}) → M_{25}
  935. Intersect(d_{21}, e_{21}) → N_{25}
  936. Polygon(K_{25}, L_{25}, M_{25}, N_{25}) → poly74, k_{42}, l_{42}, m_{50}, n_{43}
  937. Intersect(f_{20}, g_{20}) → O_{25}
  938. Intersect(d_{20}, g_{20}) → P_{25}
  939. Intersect(d_{20}, e_{20}) → Q_{25}
  940. Point(f_{20}) → R_{25}
  941. Polygon(O_{25}, P_{25}, Q_{25}, R_{25}) → poly75, o_{25}, p_{50}, q_{44}, r_{43}
  942. Intersect(i_{19}, j_{19}) → S_{25}
  943. Intersect(k_{19}, l_{19}) → T_{25}
  944. Point(m_{19}) → U_{25}
  945. Point(n_{19}) → V_{25}
  946. Polygon(S_{25}, T_{25}, U_{25}, V_{25}) → poly76, s_{41}, t_{45}, u_{25}, v_{25}
  947. Intersect(b_{15}, c_{15}) → W_{25}
  948. Intersect(a_{15}, b_{15}) → Z_{25}
  949. Intersect(e_{14}, f_{14}) → A_{26}
  950. Intersect(c_{15}, w_{13}) → B_{26}
  951. Polygon(W_{25}, Z_{25}, A_{26}, B_{26}) → poly77, w_{25}, z_{25}, a_{48}, b_{50}
  952. Intersect(m_{17}, q_{17}) → C_{26}
  953. Intersect(m_{17}, n_{17}) → D_{26}
  954. Intersect(n_{17}, p_{17}) → E_{26}
  955. Polygon(A_{26}, C_{26}, D_{26}, E_{26}) → poly78, a_{49}, c_{45}, d_{46}, e_{48}
  956. Intersect(t_{14}, r_{15}) → G_{26}
  957. Intersect(d_{15}, w_{13}) → H_{26}
  958. Segment(G_{26}, H_{26}) → s_{42}
  959. Intersect(n_{17}, b_{18}) → I_{26}
  960. Intersect(r_{18}, b_{19}) → J_{26}
  961. Segment(I_{26}, J_{26}) → k_{43}
  962. Intersect(h_{18}, i_{18}) → K_{26}
  963. Intersect(d_{15}, e_{19}) → L_{26}
  964. Segment(K_{26}, L_{26}) → l_{43}
  965. Intersect(p_{18}, s_{18}) → M_{26}
  966. Intersect(m_{17}, q_{17}) → N_{26}
  967. Segment(M_{26}, N_{26}) → s_{43}
  968. Intersect(k_{18}, n_{18}) → O_{26}
  969. Intersect(a_{15}, b_{15}) → P_{26}
  970. Segment(O_{26}, P_{26}) → g_{44}
  971. Intersect(s_{15}, t_{15}) → Q_{26}
  972. Intersect(n_{17}, p_{17}) → R_{26}
  973. Segment(Q_{26}, R_{26}) → i_{44}
  974. Intersect(g_{17}, j_{17}) → S_{26}
  975. Intersect(n_{13}, p_{13}) → T_{26}
  976. Segment(S_{26}, T_{26}) → j_{44}
  977. Intersect(d_{14}, f_{14}) → U_{26}
  978. Intersect(f_{17}, i_{17}) → V_{26}
  979. Segment(U_{26}, V_{26}) → k_{44}
  980. Intersect(s_{13}, t_{13}) → W_{26}
  981. Point(m_{17}) → Z_{26}
  982. Segment(W_{26}, Z_{26}) → l_{44}
  983. Intersect(a_{14}, b_{14}) → A_{27}
  984. Intersect(k_{16}, l_{16}) → B_{27}
  985. Segment(A_{27}, B_{27}) → n_{44}
  986. Intersect(c_{16}, d_{16}) → C_{27}
  987. Intersect(k_{12}, l_{12}) → D_{27}
  988. Segment(C_{27}, D_{27}) → r_{44}
  989. Intersect(b_{13}, e_{13}) → E_{27}
  990. Intersect(f_{16}, g_{16}) → F_{27}
  991. Segment(E_{27}, F_{27}) → s_{44}
  992. Intersect(g_{12}, h_{12}) → G_{27}
  993. Intersect(a_{16}, b_{16}) → H_{27}
  994. Segment(G_{27}, H_{27}) → g_{45}
  995. Intersect(g_{14}, h_{14}) → I_{27}
  996. Intersect(s_8, t_8) → J_{27}
  997. Segment(I_{27}, J_{27}) → i_{45}
  998. Intersect(q_{13}, r_{13}) → K_{27}
  999. Point(r_7) → L_{27}
  1000. Segment(K_{27}, L_{27}) → j_{45}
  1001. Intersect(e_6, f_6) → M_{27}
  1002. Intersect(b_4, c_4) → N_{27}
  1003. Segment(M_{27}, N_{27}) → k_{45}
  1004. Point(c_8) → O_{27}
  1005. Intersect(f_4, h_4) → P_{27}
  1006. Segment(O_{27}, P_{27}) → l_{45}
  1007. Intersect(s_7, t_7) → Q_{27}
  1008. Intersect(r_3, a_4) → R_{27}
  1009. Segment(Q_{27}, R_{27}) → n_{45}
  1010. Intersect(i_8, s_{23}) → S_{27}
  1011. Intersect(q_4, q_{23}) → T_{27}
  1012. Segment(S_{27}, T_{27}) → q_{45}
  1013. Intersect(l_9, t_{23}) → U_{27}
  1014. Point(l_9) → V_{27}
  1015. Segment(U_{27}, V_{27}) → r_{45}
  1016. Intersect(k_1, l_1) → W_{27}
  1017. Intersect(h_8, p_{30}) → Z_{27}
  1018. Segment(W_{27}, Z_{27}) → s_{45}
  1019. Intersect(p_8, t_{29}) → A_{28}
  1020. Intersect(i_1, j_1) → B_{28}
  1021. Segment(A_{28}, B_{28}) → c_{46}
  1022. Intersect(e_9, f_9) → C_{28}
  1023. Intersect(q_2, r_2) → D_{28}
  1024. Segment(C_{28}, D_{28}) → g_{46}
  1025. Intersect(m_{10}, n_{10}) → E_{28}
  1026. Intersect(d_6, g_6) → F_{28}
  1027. Segment(E_{28}, F_{28}) → i_{46}
  1028. Point(r_{10}) → G_{28}
  1029. Intersect(n_4, p_4) → H_{28}
  1030. Segment(G_{28}, H_{28}) → j_{46}
  1031. Intersect(a_{11}, b_{11}) → I_{28}
  1032. Intersect(s_4, t_4) → J_{28}
  1033. Segment(I_{28}, J_{28}) → k_{46}
  1034. Intersect(e_{11}, h_{11}) → K_{28}
  1035. Intersect(q_6, r_6) → L_{28}
  1036. Segment(K_{28}, L_{28}) → l_{46}
  1037. Intersect(m_6, n_6) → M_{28}
  1038. Intersect(l_6, m_6) → N_{28}
  1039. Intersect(l_6, p_6) → O_{28}
  1040. Intersect(e_5, f_5) → P_{28}
  1041. Polygon(M_{28}, N_{28}, O_{28}, P_{28}) → poly79, m_{51}, n_{46}, o_{28}, p_{51}
  1042. Intersect(f_3, g_3) → Q_{28}
  1043. Intersect(q_5, r_5) → R_{28}
  1044. Intersect(p_5, q_5) → S_{28}
  1045. Intersect(p_5, s_5) → T_{28}
  1046. Polygon(Q_{28}, R_{28}, S_{28}, T_{28}) → poly80, q_{46}, r_{46}, s_{46}, t_{46}

AI Drawing Prompt Reference

Draw a geometric pattern based on the Pythagorean theorem, including multiple triangles, circles, and polygons. Start by constructing a right triangle, then draw perpendicular lines on its sides to find intersection points. Next, draw semicircles centered at these points and connect relevant points to form new polygons. The final design should showcase a complex geometric pattern illustrating the Pythagorean theorem and construction principles.
The prompt above was compiled from the original drawing commands and is for reference only.