毕达哥拉斯镶嵌

GeoGebra 命令及参数

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