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Geometric Tiling: Pythagorean Theorem and Circle Intersection

Geometric Tiling: Pythagorean Theorem and Circle Intersection
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2015-01-11 04:34
TriangleCircleGeometric Construction
This example demonstrates the Pythagorean theorem and circle intersection through geometric tiling. Key mathematical concepts include the Pythagorean theorem, circle equations, and geometric construction techniques. Construction involves using GeoGebra commands like Line, Point, OrthogonalLine, Semicircle to create rhombus, circles, and intersection points. Suitable for middle school students learning geometry fundamentals or for math teaching demonstrations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. OrthogonalLine(B, a) → b
  4. OrthogonalLine(A, a) → c
  5. Point(b) → D
  6. OrthogonalLine(D, b) → d
  7. Point(c) → E
  8. OrthogonalLine(E, c) → e
  9. Point(a) → F
  10. OrthogonalLine(F, a) → f
  11. Point(b) → G
  12. OrthogonalLine(G, b) → g
  13. Point(b) → H
  14. OrthogonalLine(H, b) → h
  15. Point(h) → I
  16. OrthogonalLine(I, h) → i
  17. Point(b) → J
  18. OrthogonalLine(J, b) → j
  19. Point(i) → K
  20. OrthogonalLine(K, i) → k
  21. Point(g) → L
  22. OrthogonalLine(L, g) → l
  23. Point(g) → M
  24. OrthogonalLine(M, g) → m
  25. Semicircle(D, G) → p
  26. Point(p) → N
  27. Segment(N, G) → n
  28. Segment(N, O) → q
  29. Segment(P, O) → r
  30. Intersect(d, i) → Q
  31. Segment(Q, N) → s
  32. Segment(N, R) → t
  33. Segment(R, S) → a_1
  34. Intersect(g, i) → T
  35. Segment(T, N) → b_1
  36. Segment(N, U) → c_1
  37. Segment(U, V) → d_1
  38. Segment(D, N) → e_1
  39. Segment(N, W) → f_1
  40. Segment(W, Z) → g_1
  41. Segment(B_1, A_1) → h_1
  42. Segment(A_1, C_1) → i_1
  43. Segment(B_1, V) → j_1
  44. Segment(B_1, D_1) → k_1
  45. Segment(D_1, E_1) → l_1
  46. Segment(B_1, F_1) → m_1
  47. Segment(F_1, G_1) → n_1
  48. Segment(H_1, P) → p_1
  49. Segment(I_1, J_1) → q_1
  50. Segment(J_1, K_1) → r_1
  51. Segment(K_1, L_1) → s_1
  52. Segment(M_1, Z) → t_1
  53. Segment(N_1, M_1) → a_2
  54. Segment(O_1, I_1) → b_2
  55. Segment(P_1, Q_1) → c_2
  56. Segment(Q_1, R_1) → d_2
  57. Point(i) → S_1
  58. Segment(R_1, S_1) → e_2
  59. Segment(P_1, T_1) → f_2
  60. Segment(U_1, N_1) → g_2
  61. Segment(V_1, U_1) → h_2
  62. Segment(W_1, Z_1) → i_2
  63. Segment(Z_1, A_2) → j_2
  64. Segment(A_2, B_2) → k_2
  65. Segment(B_2, C_2) → l_2
  66. Segment(D_2, E_2) → m_2
  67. Segment(E_2, O_1) → n_2
  68. Segment(F_2, E_1) → p_2
  69. Segment(L_1, G_2) → q_2
  70. Segment(G_2, H_2) → r_2
  71. Segment(G_1, I_2) → s_2
  72. Segment(J_2, K_2) → t_2
  73. Segment(K_2, L_2) → a_3
  74. Segment(L_2, M_2) → b_3
  75. Segment(M_2, N_2) → c_3
  76. Segment(H_2, O_2) → d_3
  77. Point(i) → P_2
  78. Segment(J_2, P_2) → e_3
  79. Segment(I_2, Q_2) → f_3
  80. Segment(Q_2, R_2) → g_3
  81. Point(k) → S_2
  82. Segment(R_2, S_2) → h_3
  83. Segment(T_2, U_2) → i_3
  84. Point(i) → V_2
  85. Segment(U_2, V_2) → j_3
  86. Segment(T_2, W_2) → k_3
  87. Segment(W_2, Z_2) → l_3
  88. Segment(Z_2, A_3) → m_3
  89. Segment(O_2, B_3) → n_3
  90. Segment(B_3, C_3) → p_3
  91. Point(k) → D_3
  92. Segment(C_3, D_3) → q_3
  93. Segment(E_3, N_2) → r_3
  94. Segment(F_3, G_3) → s_3
  95. Segment(H_3, G_3) → t_3
  96. Segment(H_3, I_3) → a_4
  97. Point(k) → J_3
  98. Segment(I_3, J_3) → b_4
  99. Segment(A_3, K_3) → c_4
  100. Segment(K_3, L_3) → d_4
  101. Point(i) → M_3
  102. Segment(W_1, M_3) → e_4
  103. Point(e) → N_3
  104. Segment(N_3, D_2) → f_4
  105. Segment(O_3, P_3) → g_4
  106. Segment(Q_3, R_3) → h_4
  107. Segment(S_3, R_3) → i_4
  108. Segment(O_3, C_2) → j_4
  109. Point(e) → T_3
  110. Segment(Q_3, T_3) → k_4
  111. Segment(P_3, U_3) → l_4
  112. Segment(S_3, V_3) → m_4
  113. Segment(V_3, W_3) → n_4
  114. Segment(W_3, Z_3) → p_4
  115. Segment(Z_3, A_4) → q_4
  116. Segment(A_4, B_4) → r_4
  117. Segment(B_4, F_3) → s_4
  118. Segment(F_2, C_4) → t_4
  119. Segment(C_4, D_4) → a_5
  120. Segment(D_4, E_4) → b_5
  121. Segment(H_1, F_4) → c_5
  122. Segment(F_4, G_4) → d_5
  123. Segment(G_4, H_4) → e_5
  124. Segment(T_1, I_4) → f_5
  125. Segment(I_4, J_4) → g_5
  126. Segment(J_4, K_4) → h_5
  127. Segment(L_4, U_3) → i_5
  128. Segment(M_4, K_4) → j_5
  129. Segment(N_4, H_4) → k_5
  130. Segment(O_4, E_4) → l_5
  131. Segment(P_4, Q_4) → m_5
  132. Segment(E_3, Q_4) → n_5
  133. Segment(R_4, L_3) → p_5
  134. Segment(S_4, T_4) → q_5
  135. Point(k) → U_4
  136. Segment(T_4, U_4) → r_5
  137. Segment(R_4, V_4) → s_5
  138. Segment(W_4, S_4) → t_5
  139. Segment(W_4, Z_4) → a_6
  140. Segment(Z_4, A_5) → b_6
  141. Segment(A_5, B_5) → c_6
  142. Segment(B_5, C_5) → d_6
  143. Segment(C_5, D_5) → e_6
  144. Segment(N_4, E_5) → f_6
  145. Segment(F_5, O_4) → g_6
  146. Segment(G_5, P_4) → h_6
  147. Segment(H_5, D_5) → i_6
  148. Segment(I_5, M_4) → j_6
  149. Segment(H_5, J_5) → k_6
  150. Segment(J_5, K_5) → l_6
  151. Point(e) → L_5
  152. Segment(L_5, M_5) → m_6
  153. Segment(M_5, K_5) → n_6
  154. Segment(L_4, N_5) → p_6
  155. Segment(N_5, O_5) → q_6
  156. Point(m) → P_5
  157. Segment(O_5, P_5) → r_6
  158. Point(e) → Q_5
  159. Segment(Q_5, R_5) → s_6
  160. Segment(R_5, S_5) → t_6
  161. Segment(S_5, T_5) → a_7
  162. Segment(T_5, U_5) → b_7
  163. Point(m) → W_5
  164. Segment(V_5, W_5) → c_7
  165. Segment(V_5, I_5) → d_7
  166. Segment(Z_5, E_5) → e_7
  167. Point(m) → A_6
  168. Segment(A_6, Z_5) → f_7
  169. Segment(B_6, U_5) → g_7
  170. Segment(B_6, C_6) → h_7
  171. Segment(C_6, D_6) → i_7
  172. Segment(D_6, E_6) → j_7
  173. Segment(F_6, F_5) → k_7
  174. Point(m) → G_6
  175. Segment(F_6, G_6) → l_7
  176. Segment(E_6, H_6) → m_7
  177. Segment(H_6, I_6) → n_7
  178. Segment(J_6, G_5) → p_7
  179. Segment(K_6, I_6) → q_7
  180. Point(m) → L_6
  181. Segment(J_6, L_6) → r_7
  182. Segment(K_6, M_6) → s_7
  183. Point(k) → N_6
  184. Segment(M_6, N_6) → t_7
  185. Segment(O_6, V_4) → a_8
  186. Point(m) → P_6
  187. Segment(O_6, P_6) → b_8
  188. Intersect(c, g) → Q_6
  189. Intersect(g, q_4) → R_6
  190. Intersect(p_4, d_5) → S_6
  191. Intersect(c, c_5) → T_6
  192. Polygon(Q_6, R_6, Z_3, S_6, F_4, T_6) → poly1, q_8, r_8, z_3, s_8, f_8, t_8
  193. Intersect(g, s_1) → U_6
  194. Intersect(p_2, q_2) → V_6
  195. Intersect(c, t_4) → W_6
  196. Polygon(Q_6, U_6, L_1, V_6, F_2, W_6) → poly2, q_9, u_6, l_8, v_6, f_9, w_6
  197. Intersect(r_4, a_5) → Z_6
  198. Polygon(Q_6, R_6, A_4, Z_6, C_4, W_6) → poly3, q_{10}, r_9, a_9, z_6, c_8, w_1
  199. Intersect(p_1, r_1) → A_7
  200. Polygon(K_1, U_6, Q_6, T_6, H_1, A_7) → poly4, k_8, u_1, q_{11}, t_9, h_8, a_{10}
  201. Intersect(d, q_1) → B_7
  202. Intersect(c, d) → C_7
  203. Intersect(c, f_5) → D_7
  204. Intersect(b_2, f_2) → E_7
  205. Polygon(I_1, B_7, C_7, D_7, T_1, E_7) → poly5, i_8, b_9, c_9, d_8, t_{10}, e_8
  206. Intersect(a, n_2) → F_7
  207. Intersect(a, c) → G_7
  208. Intersect(k_2, m_2) → H_7
  209. Polygon(E_2, F_7, G_7, C_2, B_2, H_7) → poly6, e_9, f_{10}, g_8, c_{10}, b_{10}, h_9
  210. Intersect(h, r_2) → I_7
  211. Intersect(c, h) → J_7
  212. Polygon(G_2, I_7, J_7, W_6, F_2, V_6) → poly7, g_9, i_9, j_8, w_2, f_{11}, v_1
  213. Intersect(j, n_3) → K_7
  214. Intersect(c, j) → L_7
  215. Intersect(c, c_3) → M_7
  216. Intersect(b_3, d_3) → N_7
  217. Polygon(O_2, K_7, L_7, M_7, M_2, N_7) → poly8, o_2, k_9, l_9, m_8, m_9, n_8
  218. Intersect(k, q_3) → O_7
  219. Intersect(c, k) → P_7
  220. Intersect(c, m_3) → Q_7
  221. Intersect(l_3, p_3) → R_7
  222. Polygon(C_3, O_7, P_7, Q_7, Z_2, R_7) → poly9, c_{11}, o_7, p_8, q_{12}, z_2, r_{10}
  223. Intersect(a, i_4) → S_7
  224. Intersect(g_4, h_4) → T_7
  225. Polygon(G_7, S_7, R_3, T_7, O_3, C_2) → poly10, g_{10}, s_9, r_{11}, t_{11}, o_3, c_{12}
  226. Intersect(d, n_4) → U_7
  227. Intersect(m_4, g_5) → V_7
  228. Polygon(U_7, V_3, V_7, I_4, D_7, C_7) → poly11, u_7, v_3, v_7, i_{10}, d_9, c_{13}
  229. Intersect(h, s_4) → W_7
  230. Polygon(Z_6, C_4, W_6, J_7, W_7, B_4) → poly12, z_1, c_{14}, w_3, j_9, w_7, b_{11}
  231. Intersect(r_3, s_3) → Z_7
  232. Intersect(j, t_3) → A_8
  233. Polygon(Z_7, N_2, M_7, L_7, A_8, G_3) → poly13, z_7, n_9, m_{10}, l_{10}, a_{11}, g_{11}
  234. Intersect(a_4, c_4) → B_8
  235. Polygon(B_8, A_3, Q_7, P_7, J_3, I_3) → poly14, b_{12}, a_{12}, q_{13}, p_9, j_{10}, i_{11}
  236. Polygon(V_7, S_3, S_7, G_7, D_7, I_4) → poly15, v_2, s_{10}, s_{11}, g_{12}, d_{10}, i_{12}
  237. Polygon(C_7, U_7, W_3, S_6, F_4, T_6) → poly16, c_{15}, u_2, w_4, s_{12}, f_{12}, t_{12}
  238. Polygon(T_7, Q_3, T_3, E, C_2, O_3) → poly17, t_{13}, q_{14}, t_{14}, e_{10}, c_{16}, o_1
  239. Polygon(M_7, N_2, Z_7, F_3, W_7, J_7) → poly18, m_{11}, n_{10}, z_4, f_{13}, w_5, j_{11}
  240. Polygon(B_8, H_3, A_8, L_7, Q_7, A_3) → poly19, b_{13}, h_{10}, a_{13}, l_{11}, q_{15}, a_{14}
  241. Polygon(N_3, E, C_2, B_2, H_7, D_2) → poly20, n_{11}, e_{11}, c_{17}, b_{14}, h_{11}, d_{11}
  242. Polygon(F_7, G_7, D_7, T_1, E_7, O_1) → poly21, f_{14}, g_{13}, d_{12}, t_{15}, e_{12}, o_4
  243. Polygon(B_7, C_7, T_6, H_1, A_7, J_1) → poly22, b_{15}, c_{18}, t_{16}, h_{12}, a_{15}, j_{12}
  244. Polygon(I_7, J_7, M_7, M_2, N_7, H_2) → poly23, i_{13}, j_{13}, m_{12}, m_{13}, n_{12}, h_{13}
  245. Polygon(K_7, L_7, Q_7, Z_2, R_7, B_3) → poly24, k_{10}, l_{12}, q_{16}, z_5, r_{12}, b_{16}
  246. Intersect(e, f) → C_8
  247. Intersect(f, l_4) → D_8
  248. Polygon(T_3, C_8, D_8, P_3, T_7, Q_3) → poly25, t_{17}, c_{19}, d_{13}, p_{10}, t_{18}, q_{17}
  249. Intersect(f, h_5) → E_8
  250. Polygon(S_7, F, E_8, J_4, V_7, S_3) → poly26, s_{13}, f_{15}, e_{13}, j_{14}, v_4, s_{14}
  251. Intersect(d, f) → F_8
  252. Intersect(f, e_5) → G_8
  253. Polygon(U_7, F_8, G_8, G_4, S_6, W_3) → poly27, u_3, f_{16}, g_{14}, g_{15}, s_{15}, w_8
  254. Intersect(f, g) → H_8
  255. Intersect(f, b_5) → I_8
  256. Polygon(R_6, H_8, I_8, D_4, Z_6, A_4) → poly28, r_{13}, h_{14}, i_{14}, d_{14}, z_8, a_{16}
  257. Intersect(f, h) → J_8
  258. Intersect(f, n_5) → K_8
  259. Polygon(W_7, J_8, K_8, E_3, Z_7, F_3) → poly29, w_9, j_{15}, k_{11}, e_{14}, z_9, f_{17}
  260. Intersect(f, j) → L_8
  261. Intersect(f, d_4) → M_8
  262. Polygon(A_8, L_8, M_8, K_3, B_8, H_3) → poly30, a_{17}, l_{13}, m_{14}, k_{12}, b_{17}, h_{15}
  263. Intersect(i_5, n_6) → N_8
  264. Polygon(D_8, C_8, L_5, M_5, N_8, U_3) → poly31, d_{15}, c_{20}, l_{14}, m_{15}, n_{13}, u_4
  265. Intersect(a, l_6) → O_8
  266. Intersect(j_5, k_6) → P_8
  267. Polygon(E_8, F, O_8, J_5, P_8, K_4) → poly32, e_{15}, f_{18}, o_8, j_{16}, p_{11}, k_{13}
  268. Intersect(d, i_6) → Q_8
  269. Intersect(k_5, e_6) → R_8
  270. Polygon(G_8, F_8, Q_8, D_5, R_8, H_4) → poly33, g_{16}, f_{19}, q_{18}, d_{16}, r_{14}, h_{16}
  271. Intersect(l_5, c_6) → S_8
  272. Intersect(g, d_6) → T_8
  273. Polygon(S_8, B_5, T_8, H_8, I_8, E_4) → poly34, s_{16}, b_{18}, t_{19}, h_{17}, i_{15}, e_{16}
  274. Intersect(h, b_6) → U_8
  275. Intersect(m_5, a_6) → V_8
  276. Polygon(K_8, J_8, U_8, Z_4, V_8, Q_4) → poly35, k_{14}, j_{17}, u_8, z_{10}, v_8, q_{19}
  277. Intersect(j, t_5) → W_8
  278. Intersect(p_5, q_5) → Z_8
  279. Polygon(M_8, L_8, W_8, S_4, Z_8, L_3) → poly36, m_{16}, l_{15}, w_{10}, s_{17}, z_{11}, l_{16}
  280. Polygon(T_7, P_3, D_8, F, S_7, R_3) → poly37, t_{20}, p_{12}, d_{17}, f_{20}, s_{18}, r_{15}
  281. Polygon(V_3, V_7, J_4, E_8, F_8, U_7) → poly38, v_5, v_9, j_{18}, e_{17}, f_{21}, u_5
  282. Polygon(Z_3, S_6, G_4, G_8, H_8, R_6) → poly39, z_{12}, s_{19}, g_{17}, g_{18}, h_{18}, r_{16}
  283. Polygon(Z_6, D_4, I_8, J_8, W_7, B_4) → poly40, z_{13}, d_{18}, i_{16}, j_{19}, w_{11}, b_{19}
  284. Polygon(Z_7, E_3, K_8, L_8, A_8, G_3) → poly41, z_{14}, e_{18}, k_{15}, l_{17}, a_{18}, g_{19}
  285. Intersect(f, k) → A_9
  286. Polygon(I_3, B_8, K_3, M_8, A_9, J_3) → poly42, i_{17}, b_{20}, k_{16}, m_{17}, a_{19}, j_{20}
  287. Polygon(F, D_8, U_3, N_8, K_5, O_8) → poly43, f_{22}, d_{19}, u_9, n_{14}, k_{17}, o_5
  288. Polygon(F_8, E_8, K_4, P_8, H_5, Q_8) → poly44, f_{23}, e_{19}, k_{18}, p_{13}, h_{19}, q_{20}
  289. Polygon(H_8, G_8, H_4, R_8, C_5, T_8) → poly45, h_{20}, g_{20}, h_{21}, r_{17}, c_{21}, t_{21}
  290. Polygon(E_4, S_8, A_5, U_8, J_8, I_8) → poly46, e_{20}, s_{20}, a_{20}, u_{10}, j_{21}, i_{18}
  291. Polygon(W_8, L_8, K_8, Q_4, V_8, W_4) → poly47, w_{12}, l_{18}, k_{19}, q_{21}, v_{10}, w_{13}
  292. Polygon(U_4, A_9, M_8, L_3, Z_8, T_4) → poly48, u_{11}, a_{21}, m_{18}, l_{19}, z_{15}, t_{22}
  293. Intersect(a, l) → B_9
  294. Intersect(l, p_6) → C_9
  295. Polygon(K_5, O_8, B_9, C_9, L_4, N_8) → poly49, k_{20}, o_6, b_{21}, c_{22}, l_{20}, n_{15}
  296. Intersect(d, l) → D_9
  297. Intersect(l, j_6) → E_9
  298. Polygon(H_5, Q_8, D_9, E_9, M_4, P_8) → poly50, h_{22}, q_{22}, d_{20}, e_{21}, m_{19}, p_{14}
  299. Intersect(l, f_6) → F_9
  300. Polygon(R_8, C_5, T_8, L, F_9, N_4) → poly51, r_{18}, c_{23}, t_{23}, l_{21}, f_{24}, n_{16}
  301. Intersect(h, l) → G_9
  302. Intersect(l, g_6) → H_9
  303. Polygon(A_5, U_8, G_9, H_9, O_4, S_8) → poly52, a_{22}, u_{12}, g_{21}, h_{23}, o_9, s_{21}
  304. Intersect(j, l) → I_9
  305. Intersect(l, h_6) → J_9
  306. Polygon(W_4, W_8, I_9, J_9, P_4, V_8) → poly53, w_{14}, w_{15}, i_{19}, j_{22}, p_{15}, v_{11}
  307. Intersect(k, l) → K_9
  308. Intersect(l, s_5) → L_9
  309. Polygon(Z_8, T_4, U_4, K_9, L_9, R_4) → poly54, z_{16}, t_{24}, u_{13}, k_{21}, l_{22}, r_{19}
  310. Intersect(e, l) → M_9
  311. Polygon(N_8, L_4, C_9, M_9, L_5, M_5) → poly55, n_{17}, l_{23}, c_{24}, m_{20}, l_{24}, m_{21}
  312. Polygon(O_8, J_5, P_8, M_4, E_9, B_9) → poly56, o_{10}, j_{23}, p_{16}, m_{22}, e_{22}, b_{22}
  313. Polygon(Q_8, D_5, R_8, N_4, F_9, D_9) → poly57, q_{23}, d_{21}, r_{20}, n_{18}, f_{25}, d_{22}
  314. Polygon(T_8, B_5, S_8, O_4, H_9, L) → poly58, t_{25}, b_{23}, s_{22}, o_{11}, h_{24}, l_{25}
  315. Polygon(U_8, G_9, J_9, P_4, V_8, Z_4) → poly59, u_{14}, g_{22}, j_{24}, p_{17}, v_{12}, z_{17}
  316. Polygon(W_8, I_9, L_9, R_4, Z_8, S_4) → poly60, w_{16}, i_{20}, l_{26}, r_{21}, z_{18}, s_{23}
  317. Intersect(q_6, t_6) → N_9
  318. Intersect(a, a_7) → O_9
  319. Polygon(B_9, C_9, N_5, N_9, S_5, O_9) → poly61, b_{24}, c_{25}, n_{19}, n_{20}, s_{24}, o_{12}
  320. Intersect(b_7, d_7) → P_9
  321. Polygon(E_9, B_9, O_9, T_5, P_9, I_5) → poly62, e_{23}, b_{25}, o_{13}, t_{26}, p_{18}, i_{21}
  322. Intersect(d, g_7) → Q_9
  323. Intersect(e_7, h_7) → R_9
  324. Polygon(F_9, D_9, Q_9, B_6, R_9, E_5) → poly63, f_{26}, d_{23}, q_{24}, b_{26}, r_{22}, e_{24}
  325. Intersect(g, i_7) → S_9
  326. Intersect(j_7, k_7) → T_9
  327. Polygon(H_9, L, S_9, D_6, T_9, F_5) → poly64, h_{25}, l_{27}, s_{25}, d_{24}, t_{27}, f_{27}
  328. Intersect(h, m_7) → U_9
  329. Intersect(n_7, p_7) → V_9
  330. Polygon(J_9, G_9, U_9, H_6, V_9, G_5) → poly65, j_{25}, g_{23}, u_{15}, h_{26}, v_{13}, g_{24}
  331. Intersect(j, q_7) → W_9
  332. Intersect(s_7, a_8) → Z_9
  333. Polygon(L_9, I_9, W_9, K_6, Z_9, V_4) → poly66, l_{28}, i_{22}, w_{17}, k_{22}, z_{19}, v_{14}
  334. Polygon(Q_9, D_9, E_9, I_5, P_9, U_5) → poly67, q_{25}, d_{25}, e_{25}, i_{23}, p_{19}, u_{16}
  335. Polygon(E_5, R_9, C_6, S_9, L, F_9) → poly68, e_{26}, r_{23}, c_{26}, s_{26}, l_{29}, f_{28}
  336. Polygon(F_5, T_9, E_6, U_9, G_9, H_9) → poly69, f_{29}, t_{28}, e_{27}, u_{17}, g_{25}, h_{27}
  337. Polygon(G_5, V_9, I_6, W_9, I_9, J_9) → poly70, g_{26}, v_{15}, i_{24}, w_{18}, i_{25}, j_{26}
  338. Polygon(V_4, Z_9, M_6, N_6, K_9, L_9) → poly71, v_{16}, z_{20}, m_{23}, n_{21}, k_{23}, l_{30}
  339. Polygon(C_9, M_9, Q_5, R_5, N_9, N_5) → poly72, c_{27}, m_{24}, q_{26}, r_{24}, n_{22}, n_{23}
  340. Intersect(e, m) → A_{10}
  341. Polygon(Q_5, A_{10}, P_5, O_5, N_9, R_5) → poly73, q_{27}, a_{23}, p_{20}, o_{14}, n_{24}, r_{25}
  342. Intersect(a, m) → B_{10}
  343. Polygon(O_9, B_{10}, W_5, V_5, P_9, T_5) → poly74, o_{15}, b_{27}, w_{19}, v_{17}, p_{21}, t_{29}
  344. Intersect(d, m) → C_{10}
  345. Polygon(Q_9, C_{10}, A_6, Z_5, R_9, B_6) → poly75, q_{28}, c_{28}, a_{24}, z_{21}, r_{26}, b_{28}
  346. Polygon(S_9, M, G_6, F_6, T_9, D_6) → poly76, s_{27}, m_{25}, g_{27}, f_{30}, t_{30}, d_{26}
  347. Intersect(h, m) → D_{10}
  348. Polygon(U_9, D_{10}, L_6, J_6, V_9, H_6) → poly77, u_{18}, d_{27}, l_{31}, j_{27}, v_{18}, h_{28}
  349. Intersect(j, m) → E_{10}
  350. Polygon(W_9, E_{10}, P_6, O_6, Z_9, K_6) → poly78, w_{20}, e_{28}, p_{22}, o_{16}, z_{22}, k_{24}
  351. Polygon(S_5, N_9, O_5, P_5, B_{10}, O_9) → poly79, s_{28}, n_{25}, o_{17}, p_{23}, b_{29}, o_{18}
  352. Polygon(P_9, U_5, Q_9, C_{10}, W_5, V_5) → poly80, p_{24}, u_{19}, q_{29}, c_{29}, w_{21}, v_{19}
  353. Polygon(R_9, C_6, S_9, M, A_6, Z_5) → poly81, r_{27}, c_{30}, s_{29}, m_{26}, a_{25}, z_{23}
  354. Polygon(T_9, F_6, G_6, D_{10}, U_9, E_6) → poly82, t_{31}, f_{31}, g_{28}, d_{28}, u_{20}, e_{29}
  355. Polygon(V_9, J_6, L_6, E_{10}, W_9, I_6) → poly83, v_{20}, j_{28}, l_{32}, e_{30}, w_{22}, i_{26}
  356. Intersect(k, m) → G_{10}
  357. Polygon(Z_9, O_6, P_6, G_{10}, N_6, M_6) → poly84, z_{24}, o_{19}, p_{25}, g_{29}, n_{26}, m_{27}
  358. Intersect(b, j_2) → H_{10}
  359. Intersect(a, a_2) → I_{10}
  360. Intersect(g_2, i_2) → J_{10}
  361. Polygon(H_{10}, B, I_{10}, N_1, J_{10}, Z_1) → poly85, h_{29}, b_{30}, i_{27}, n_{27}, j_{29}, z_{25}
  362. Intersect(d, g_1) → K_{10}
  363. Intersect(b, c_2) → L_{10}
  364. Intersect(t_1, d_2) → M_{10}
  365. Polygon(Z, K_{10}, D, L_{10}, Q_1, M_{10}) → poly86, z, k_{25}, d_{29}, l_{33}, q_{30}, m_{28}
  366. Intersect(b, r) → N_{10}
  367. Intersect(g, d_1) → O_{10}
  368. Polygon(N, O, N_{10}, G, O_{10}, U) → poly87, n_{28}, o, n_{29}, g_{30}, o_{20}, u
  369. Intersect(h, n_1) → P_{10}
  370. Intersect(b, l_1) → Q_{10}
  371. Polygon(F_1, P_{10}, H, Q_{10}, D_1, B_1) → poly88, f_{32}, p_{26}, h_{30}, q_{31}, d_{30}, b_{31}
  372. Intersect(s_2, t_2) → R_{10}
  373. Intersect(b, a_3) → S_{10}
  374. Intersect(j, f_3) → T_{10}
  375. Polygon(R_{10}, K_2, S_{10}, J, T_{10}, I_2) → poly89, r_{28}, k_{26}, s_{30}, j_{30}, t_{32}, i_{28}
  376. Intersect(g_3, i_3) → U_{10}
  377. Intersect(b, k_3) → V_{10}
  378. Intersect(b, k) → W_{10}
  379. Polygon(U_{10}, T_2, V_{10}, W_{10}, S_2, R_2) → poly90, u_{21}, t_{33}, v_{21}, w_{23}, s_{31}, r_{29}
  380. Intersect(b, e) → Z_{10}
  381. Polygon(V_1, Z_{10}, H_{10}, Z_1, J_{10}, U_1) → poly91, v_{22}, z_{26}, h_{31}, z_{27}, j_{31}, u_{22}
  382. Polygon(I_{10}, B, L_{10}, Q_1, M_{10}, M_1) → poly92, i_{29}, b_{32}, l_{34}, q_{32}, m_{29}, m_{30}
  383. Polygon(K_{10}, D, N_{10}, O, N, W) → poly93, k_{27}, d_{31}, n_{30}, o_{21}, n_{31}, w
  384. Polygon(O_{10}, G, Q_{10}, D_1, B_1, V) → poly94, o_{22}, g_{31}, q_{33}, d_{32}, b_{33}, v
  385. Polygon(P_{10}, H, S_{10}, K_2, R_{10}, G_1) → poly95, p_{27}, h_{32}, s_{32}, k_{28}, r_{30}, g_{32}
  386. Polygon(T_{10}, J, V_{10}, T_2, U_{10}, Q_2) → poly96, t_{34}, j_{32}, v_{23}, t_{35}, u_{23}, q_{34}
  387. Polygon(B, H_{10}, A_2, H_7, E_2, F_7) → poly97, b_{34}, h_{33}, a_{26}, h_{34}, e_{31}, f_{33}
  388. Polygon(B_7, D, L_{10}, P_1, E_7, I_1) → poly98, b_{35}, d_{33}, l_{35}, p_{28}, e_{32}, i_{30}
  389. Polygon(U_6, G, N_{10}, P, A_7, K_1) → poly99, u_{24}, g_{33}, n_{32}, p_{29}, a_{27}, k_{29}
  390. Polygon(I_7, H, Q_{10}, E_1, V_6, G_2) → poly100, i_{31}, h_{35}, q_{35}, e_{33}, v_{24}, g_{34}
  391. Polygon(K_7, J, S_{10}, L_2, N_7, O_2) → poly101, k_{30}, j_{33}, s_{33}, l_{36}, n_{33}, o_{23}
  392. Polygon(O_7, W_{10}, V_{10}, W_2, R_7, C_3) → poly102, o_{24}, w_{24}, v_{25}, w_{25}, r_{31}, c_{31}
  393. Polygon(Z_{10}, N_3, D_2, H_7, A_2, H_{10}) → poly103, z_{28}, n_{34}, d_{34}, h_{36}, a_{28}, h_{37}
  394. Polygon(E_7, O_1, F_7, B, L_{10}, P_1) → poly104, e_{34}, o_{25}, f_{34}, b_{36}, l_{37}, p_{30}
  395. Polygon(D, B_7, J_1, A_7, P, N_{10}) → poly105, d_{35}, b_{37}, j_{34}, a_{29}, p_{31}, n_{35}
  396. Polygon(G, U_6, L_1, V_6, E_1, Q_{10}) → poly106, g_{35}, u_{25}, l_{38}, v_{26}, e_{35}, q_{36}
  397. Polygon(S_{10}, H, I_7, H_2, N_7, L_2) → poly107, s_{34}, h_{38}, i_{32}, h_{39}, n_{36}, l_{39}
  398. Polygon(V_{10}, J, K_7, B_3, R_7, W_2) → poly108, v_{27}, j_{35}, k_{31}, b_{38}, r_{32}, w_{26}
  399. Intersect(e, i) → A_{11}
  400. Polygon(M_3, A_{11}, V_1, U_1, J_{10}, W_1) → poly109, m_{31}, a_{30}, v_{28}, u_{26}, j_{36}, w_{27}
  401. Intersect(a, i) → B_{11}
  402. Polygon(B_{11}, M_3, W_1, J_{10}, N_1, I_{10}) → poly110, b_{39}, m_{32}, w_{28}, j_{37}, n_{37}, i_{33}
  403. Polygon(K_{10}, Q, S_1, R_1, M_{10}, Z) → poly111, k_{32}, q_{37}, s_{35}, r_{33}, m_{33}, z_{29}
  404. Polygon(O_{10}, T, S, R, N, U) → poly112, o_{26}, t_{36}, s_{36}, r_{34}, n_{38}, u_{27}
  405. Polygon(I, C_1, A_1, B_1, F_1, P_{10}) → poly113, i_{34}, c_{32}, a_{31}, b_{40}, f_{35}, p_{32}
  406. Intersect(i, j) → C_{11}
  407. Polygon(C_{11}, P_2, J_2, R_{10}, I_2, T_{10}) → poly114, c_{33}, p_{33}, j_{38}, r_{35}, i_{35}, t_{37}
  408. Polygon(R_2, S_2, K, V_2, U_2, U_{10}) → poly115, r_{36}, s_{37}, k_{33}, v_{29}, u_{28}, u_{29}
  409. Polygon(S_1, B_{11}, I_{10}, M_1, M_{10}, R_1) → poly116, s_{38}, b_{41}, i_{36}, m_{34}, m_{35}, r_{37}
  410. Polygon(S, Q, K_{10}, W, N, R) → poly117, s_{39}, q_{38}, k_{34}, w_{29}, n_{39}, r_{38}
  411. Polygon(C_1, T, O_{10}, V, B_1, A_1) → poly118, c_{34}, t_{38}, o_{27}, v_{30}, b_{42}, a_{32}
  412. Polygon(I, P_{10}, G_1, R_{10}, J_2, P_2) → poly119, i_{37}, p_{34}, g_{36}, r_{39}, j_{39}, p_{35}
  413. Polygon(C_{11}, T_{10}, Q_2, U_{10}, U_2, V_2) → poly120, c_{35}, t_{39}, q_{39}, u_{30}, u_{31}, v_{31}

AI Drawing Prompt Reference

Draw a geometric tiling showing the Pythagorean theorem and circle intersection. The figure includes a rhombus, circles, intersection points, and line segments connecting them. The construction order is: first draw basic line segments and points, then construct the rhombus using orthogonal lines, then draw a semicircle, and finally connect points to form the overall structure.
The prompt above was compiled from the original drawing commands and is for reference only.