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勾股定理的镶嵌演示

勾股定理的镶嵌演示
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2015-02-08 00:12
测试改名0函数几何作图
①本范例通过镶嵌图案直观演示勾股定理，即直角三角形两直角边的平方和等于斜边的平方；②涉及的核心数学概念包括勾股定理、正方形、面积计算；③作图要点——从下方『构造摘要』提炼用到了 Line（线）、OrthogonalLine（垂线）、Point（点）、Segment（线段）、Intersect（交点）等 GeoGebra 命令/对象；④适合初中及以上学生学习和理解勾股定理的几何意义，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. OrthogonalLine(A, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Point(b) → D
  7. OrthogonalLine(D, b) → 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(g) → J
  19. OrthogonalLine(J, g) → k
  20. Point(g) → K
  21. OrthogonalLine(K, g) → l
  22. Point(g) → L
  23. OrthogonalLine(L, g) → m
  24. Point(g) → M
  25. OrthogonalLine(M, g) → n
  26. Point(c) → N
  27. Point(b) → O
  28. Segment(N, O) → p
  29. Point(j) → P
  30. Segment(P, N) → q
  31. Point(a) → Q
  32. Point(d) → R
  33. Segment(Q, R) → r
  34. Point(b) → S
  35. Point(c) → T
  36. Segment(S, T) → s
  37. Point(c) → U
  38. Point(k) → V
  39. Segment(U, V) → t
  40. Point(a) → W
  41. Point(e) → Z
  42. Segment(W, Z) → a_1
  43. Point(a) → A_1
  44. Point(d) → B_1
  45. Segment(A_1, B_1) → b_1
  46. Point(a) → C_1
  47. Point(e) → D_1
  48. Segment(C_1, D_1) → c_1
  49. Point(d) → E_1
  50. Point(f) → F_1
  51. Segment(E_1, F_1) → d_1
  52. Point(j) → G_1
  53. Point(b) → H_1
  54. Segment(G_1, H_1) → e_1
  55. Point(b) → I_1
  56. Point(c) → J_1
  57. Segment(I_1, J_1) → f_1
  58. Point(c) → K_1
  59. Point(k) → L_1
  60. Segment(K_1, L_1) → g_1
  61. Point(j) → M_1
  62. Point(k) → N_1
  63. Segment(M_1, N_1) → h_1
  64. Point(d) → O_1
  65. Point(f) → P_1
  66. Segment(O_1, P_1) → i_1
  67. Point(e) → Q_1
  68. Point(g) → R_1
  69. Segment(Q_1, R_1) → j_1
  70. Point(f) → S_1
  71. Point(h) → T_1
  72. Segment(S_1, T_1) → k_1
  73. Point(g) → U_1
  74. Point(i) → V_1
  75. Segment(U_1, V_1) → l_1
  76. Point(h) → W_1
  77. Point(i) → Z_1
  78. Segment(W_1, Z_1) → m_1
  79. Point(b) → A_2
  80. Point(j) → B_2
  81. Segment(A_2, B_2) → n_1
  82. Point(c) → C_2
  83. Point(b) → D_2
  84. Segment(C_2, D_2) → p_1
  85. Point(b) → E_2
  86. Point(j) → F_2
  87. Segment(E_2, F_2) → q_1
  88. Point(c) → G_2
  89. Point(b) → H_2
  90. Segment(G_2, H_2) → r_1
  91. Point(b) → I_2
  92. Point(j) → J_2
  93. Segment(I_2, J_2) → s_1
  94. Point(c) → K_2
  95. Point(b) → L_2
  96. Segment(K_2, L_2) → t_1
  97. Point(b) → M_2
  98. Point(j) → N_2
  99. Segment(M_2, N_2) → a_2
  100. Point(c) → O_2
  101. Point(b) → P_2
  102. Segment(O_2, P_2) → b_2
  103. Point(k) → Q_2
  104. Point(c) → R_2
  105. Segment(Q_2, R_2) → c_2
  106. Point(e) → S_2
  107. Point(g) → T_2
  108. Segment(S_2, T_2) → d_2
  109. Point(f) → U_2
  110. Point(h) → V_2
  111. Segment(U_2, V_2) → e_2
  112. Point(g) → W_2
  113. Point(i) → Z_2
  114. Segment(W_2, Z_2) → f_2
  115. Point(c) → A_3
  116. Point(k) → B_3
  117. Segment(A_3, B_3) → g_2
  118. Point(h) → C_3
  119. Point(i) → D_3
  120. Segment(C_3, D_3) → h_2
  121. Point(k) → E_3
  122. Point(c) → F_3
  123. Segment(E_3, F_3) → i_2
  124. Point(g) → G_3
  125. Point(i) → H_3
  126. Segment(G_3, H_3) → j_2
  127. Point(h) → I_3
  128. Point(i) → J_3
  129. Segment(I_3, J_3) → k_2
  130. Point(k) → K_3
  131. Point(j) → L_3
  132. Segment(K_3, L_3) → l_2
  133. Point(k) → M_3
  134. Point(j) → N_3
  135. Segment(M_3, N_3) → m_2
  136. Point(f) → O_3
  137. Point(h) → P_3
  138. Segment(O_3, P_3) → n_2
  139. Point(k) → Q_3
  140. Point(c) → R_3
  141. Segment(Q_3, R_3) → p_2
  142. Point(e) → S_3
  143. Point(g) → T_3
  144. Segment(S_3, T_3) → q_2
  145. Point(j) → U_3
  146. Point(k) → V_3
  147. Segment(U_3, V_3) → r_2
  148. Point(f) → W_3
  149. Point(e) → Z_3
  150. Segment(W_3, Z_3) → s_2
  151. Point(d) → A_4
  152. Segment(A_4, Z_3) → t_2
  153. Point(a) → B_4
  154. Point(d) → C_4
  155. Segment(B_4, C_4) → a_3
  156. Point(a) → D_4
  157. Point(e) → E_4
  158. Segment(D_4, E_4) → b_3
  159. Point(l) → F_4
  160. Point(j) → G_4
  161. Segment(F_4, G_4) → c_3
  162. Point(a) → H_4
  163. Point(d) → I_4
  164. Segment(H_4, I_4) → d_3
  165. Point(a) → J_4
  166. Point(e) → K_4
  167. Segment(J_4, K_4) → e_3
  168. Point(k) → L_4
  169. Point(m) → M_4
  170. Segment(L_4, M_4) → f_3
  171. Point(d) → N_4
  172. Point(f) → O_4
  173. Segment(N_4, O_4) → g_3
  174. Point(l) → P_4
  175. Segment(P_4, N_1) → h_3
  176. Point(m) → Q_4
  177. Point(k) → R_4
  178. Segment(Q_4, R_4) → i_3
  179. Point(m) → S_4
  180. Point(k) → T_4
  181. Segment(S_4, T_4) → j_3
  182. Point(l) → U_4
  183. Segment(U_4, V_3) → k_3
  184. Point(m) → V_4
  185. Point(l) → W_4
  186. Segment(V_4, W_4) → l_3
  187. Point(e) → Z_4
  188. Point(g) → A_5
  189. Segment(Z_4, A_5) → m_3
  190. Point(k) → B_5
  191. Point(m) → C_5
  192. Segment(B_5, C_5) → n_3
  193. Point(f) → D_5
  194. Point(h) → E_5
  195. Segment(D_5, E_5) → p_3
  196. Point(l) → F_5
  197. Point(k) → G_5
  198. Segment(F_5, G_5) → q_3
  199. Point(g) → H_5
  200. Point(i) → I_5
  201. Segment(H_5, I_5) → r_3
  202. Point(l) → J_5
  203. Segment(J_5, K_3) → s_3
  204. Point(l) → K_5
  205. Point(k) → L_5
  206. Segment(K_5, L_5) → t_3
  207. Point(d_1) → M_5
  208. Point(d_1) → N_5
  209. Point(d_1) → O_5
  210. Point(k) → P_5
  211. Point(m) → Q_5
  212. Segment(P_5, Q_5) → a_4
  213. Point(f) → R_5
  214. Point(h) → S_5
  215. Segment(R_5, S_5) → b_4
  216. Point(g) → T_5
  217. Point(i) → U_5
  218. Segment(T_5, U_5) → c_4
  219. Point(m) → V_5
  220. Point(l) → W_5
  221. Segment(V_5, W_5) → d_4
  222. Point(l) → Z_5
  223. Segment(M_3, Z_5) → e_4
  224. Point(m) → A_6
  225. Segment(A_6, K_5) → f_4
  226. Point(h) → B_6
  227. Point(i) → C_6
  228. Segment(B_6, C_6) → g_4
  229. Point(h) → D_6
  230. Point(i) → E_6
  231. Segment(D_6, E_6) → h_4
  232. Point(m) → F_6
  233. Point(l) → G_6
  234. Segment(F_6, G_6) → i_4
  235. Point(m) → H_6
  236. Point(l) → I_6
  237. Segment(H_6, I_6) → j_4
  238. Point(e) → J_6
  239. Point(g) → K_6
  240. Segment(J_6, K_6) → k_4
  241. Point(d) → L_6
  242. Point(f) → M_6
  243. Segment(L_6, M_6) → l_4
  244. Point(a) → N_6
  245. Point(d) → O_6
  246. Segment(N_6, O_6) → m_4
  247. Point(a) → P_6
  248. Point(e) → Q_6
  249. Segment(P_6, Q_6) → n_4
  250. Point(d) → R_6
  251. Point(f) → S_6
  252. Segment(R_6, S_6) → p_4
  253. Point(l) → T_6
  254. Point(n) → U_6
  255. Segment(T_6, U_6) → q_4
  256. Point(n) → V_6
  257. Point(m) → W_6
  258. Segment(V_6, W_6) → r_4
  259. Point(n) → Z_6
  260. Point(m) → A_7
  261. Segment(Z_6, A_7) → s_4
  262. Point(m) → B_7
  263. Point(n) → C_7
  264. Segment(B_7, C_7) → t_4
  265. Point(l) → D_7
  266. Segment(D_7, A_7) → a_5
  267. Point(a) → E_7
  268. Point(d) → F_7
  269. Segment(E_7, F_7) → b_5
  270. Point(a) → G_7
  271. Point(e) → H_7
  272. Segment(G_7, H_7) → c_5
  273. Point(e) → I_7
  274. Point(g) → J_7
  275. Segment(I_7, J_7) → d_5
  276. Point(f) → K_7
  277. Point(h) → L_7
  278. Segment(K_7, L_7) → e_5
  279. Point(g) → M_7
  280. Point(i) → N_7
  281. Segment(M_7, N_7) → f_5
  282. Point(h) → O_7
  283. Point(i) → P_7
  284. Segment(O_7, P_7) → g_5
  285. Point(n) → Q_7
  286. Segment(Q_7, V_5) → h_5
  287. Point(n) → R_7
  288. Segment(R_7, F_6) → i_5
  289. Point(n) → S_7
  290. Segment(S_7, H_6) → j_5
  291. Point(n) → T_7
  292. Segment(T_7, V_4) → k_5
  293. Point(m) → U_7
  294. Point(n) → V_7
  295. Segment(U_7, V_7) → l_5
  296. Point(m) → W_7
  297. Point(n) → Z_7
  298. Segment(W_7, Z_7) → m_5
  299. Point(m) → A_8
  300. Point(n) → B_8
  301. Segment(A_8, B_8) → n_5
  302. Point(m) → C_8
  303. Point(n) → D_8
  304. Segment(C_8, D_8) → p_5
  305. Point(j) → E_8
  306. Segment(E_8, G_5) → q_5
  307. Segment(G_7, F_8) → r_5
  308. Segment(G_7, B) → s_5
  309. Segment(B, H) → t_5
  310. Point(n) → G_8
  311. Segment(H, G_8) → a_6
  312. Segment(F_8, G_8) → b_6
  313. Segment(R_6, C) → c_6
  314. Segment(J_6, D) → d_6
  315. Segment(S_6, E) → e_6
  316. Segment(K_6, F) → f_6
  317. Segment(D_6, G) → g_6
  318. Point(c) → H_8
  319. Segment(H_8, A) → h_6
  320. Point(j) → I_8
  321. Segment(I_8, I) → i_6
  322. Intersect(i, k) → J_8
  323. Intersect(a, k) → K_8
  324. Segment(J_8, K_8) → j_6
  325. Intersect(a, l) → L_8
  326. Intersect(i, l) → M_8
  327. Segment(L_8, M_8) → k_6
  328. Intersect(h, n) → N_8
  329. Segment(N_8, D_6) → l_6
  330. Segment(M, K_6) → m_6
  331. Intersect(f, n) → O_8
  332. Segment(O_8, S_6) → n_6
  333. Intersect(i, m) → P_8
  334. Intersect(a, m) → Q_8
  335. Segment(P_8, Q_8) → p_6
  336. Intersect(d, n) → R_8
  337. Segment(R_8, R_6) → q_6
  338. Intersect(e, n) → S_8
  339. Segment(S_8, J_6) → r_6

AI 绘图提示语参考

绘制一个直角三角形，并围绕其斜边进行无限次正交线的平铺，形成一个几何图案。首先画出直角三角形的两条直角边，然后从每个顶点出发，画出与直角边垂直的线，接着在这些线上依次画出新的点和线，形成一个由正交线组成的网格状图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。