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三角数演示

三角数演示
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2018-11-16 23:24
数列解析几何几何作图
①本范例演示了三角数的生成与几何表示，通过点与线段构建三角形状；②涉及核心数学概念包括数列、几何作图、解析几何；③构造要点使用了Segment（线段）、Midpoint（中点）等GeoGebra命令与对象；④适合高中数学教学，用于理解数列与几何的关联，以及动态几何演示。

GeoGebra 命令及参数

  1. Segment(A, K) → a
  2. Segment(K, U) → b
  3. Segment(U, G_1) → c
  4. Segment(G_1, Q_1) → d
  5. Segment(Q_1, C_2) → e
  6. Segment(C_2, M_2) → f
  7. Segment(M_2, W_2) → g
  8. Segment(W_2, I_3) → h
  9. Segment(I_3, S_3) → i
  10. Segment(S_3, A_5) → j
  11. Segment(B, A) → k
  12. Segment(L, K) → l
  13. Segment(V, U) → m
  14. Segment(H_1, G_1) → p
  15. Segment(R_1, Q_1) → q
  16. Segment(D_2, C_2) → r
  17. Segment(N_2, M_2) → s
  18. Segment(Z_2, W_2) → t
  19. Segment(J_3, I_3) → a_1
  20. Segment(T_3, S_3) → b_1
  21. Segment(Z_4, A_5) → c_1
  22. Segment(B, L) → d_1
  23. Segment(L, V) → e_1
  24. Segment(V, H_1) → f_1
  25. Segment(H_1, R_1) → g_1
  26. Segment(R_1, D_2) → h_1
  27. Segment(D_2, N_2) → i_1
  28. Segment(N_2, Z_2) → j_1
  29. Segment(Z_2, J_3) → k_1
  30. Segment(J_3, T_3) → l_1
  31. Segment(T_3, Z_4) → m_1
  32. Segment(C, B) → n_1
  33. Segment(M, L) → p_1
  34. Segment(W, V) → q_1
  35. Segment(I_1, H_1) → r_1
  36. Segment(S_1, R_1) → s_1
  37. Segment(E_2, D_2) → t_1
  38. Segment(O_2, N_2) → a_2
  39. Segment(A_3, Z_2) → b_2
  40. Segment(K_3, J_3) → c_2
  41. Segment(U_3, T_3) → d_2
  42. Segment(W_4, Z_4) → e_2
  43. Segment(C, M) → f_2
  44. Segment(M, W) → g_2
  45. Segment(W, I_1) → h_2
  46. Segment(I_1, S_1) → i_2
  47. Segment(S_1, E_2) → j_2
  48. Segment(E_2, O_2) → k_2
  49. Segment(O_2, A_3) → l_2
  50. Segment(A_3, K_3) → m_2
  51. Segment(K_3, U_3) → n_2
  52. Segment(U_3, W_4) → p_2
  53. Segment(D, C) → q_2
  54. Segment(N, M) → r_2
  55. Segment(Z, W) → s_2
  56. Segment(J_1, I_1) → t_2
  57. Segment(T_1, S_1) → a_3
  58. Segment(F_2, E_2) → b_3
  59. Segment(P_2, O_2) → c_3
  60. Segment(B_3, A_3) → d_3
  61. Segment(L_3, K_3) → e_3
  62. Segment(V_3, U_3) → f_3
  63. Segment(V_4, W_4) → g_3
  64. Segment(D, N) → h_3
  65. Segment(N, Z) → i_3
  66. Segment(Z, J_1) → j_3
  67. Segment(J_1, T_1) → k_3
  68. Segment(T_1, F_2) → l_3
  69. Segment(F_2, P_2) → m_3
  70. Segment(P_2, B_3) → n_3
  71. Segment(B_3, L_3) → p_3
  72. Segment(L_3, V_3) → q_3
  73. Segment(V_3, V_4) → r_3
  74. Segment(V_4, U_4) → s_3
  75. Segment(U_4, W_3) → t_3
  76. Segment(W_3, V_3) → a_4
  77. Segment(L_3, M_3) → b_4
  78. Segment(M_3, W_3) → c_4
  79. Segment(M_3, C_3) → d_4
  80. Segment(C_3, B_3) → e_4
  81. Segment(C_3, Q_2) → f_4
  82. Segment(Q_2, P_2) → g_4
  83. Segment(Q_2, G_2) → h_4
  84. Segment(G_2, F_2) → i_4
  85. Segment(G_2, U_1) → j_4
  86. Segment(U_1, T_1) → k_4
  87. Segment(U_1, K_1) → l_4
  88. Segment(K_1, J_1) → m_4
  89. Segment(K_1, A_1) → n_4
  90. Segment(A_1, Z) → p_4
  91. Segment(A_1, O) → q_4
  92. Segment(O, N) → r_4
  93. Segment(O, E) → s_4
  94. Segment(E, D) → t_4
  95. Segment(F, E) → a_5
  96. Segment(F, P) → b_5
  97. Segment(P, O) → c_5
  98. Segment(P, B_1) → d_5
  99. Segment(B_1, A_1) → e_5
  100. Segment(B_1, L_1) → f_5
  101. Segment(L_1, K_1) → g_5
  102. Segment(L_1, V_1) → h_5
  103. Segment(V_1, U_1) → i_5
  104. Segment(V_1, H_2) → j_5
  105. Segment(H_2, G_2) → k_5
  106. Segment(H_2, R_2) → l_5
  107. Segment(R_2, Q_2) → m_5
  108. Segment(R_2, D_3) → n_5
  109. Segment(D_3, C_3) → p_5
  110. Segment(D_3, N_3) → q_5
  111. Segment(N_3, M_3) → r_5
  112. Segment(N_3, Z_3) → s_5
  113. Segment(Z_3, W_3) → t_5
  114. Segment(Z_3, T_4) → a_6
  115. Segment(T_4, U_4) → b_6
  116. Segment(S_4, T_4) → c_6
  117. Segment(S_4, A_4) → d_6
  118. Segment(A_4, Z_3) → e_6
  119. Segment(A_4, O_3) → f_6
  120. Segment(O_3, N_3) → g_6
  121. Segment(O_3, E_3) → h_6
  122. Segment(E_3, D_3) → i_6
  123. Segment(E_3, S_2) → j_6
  124. Segment(S_2, R_2) → k_6
  125. Segment(S_2, I_2) → l_6
  126. Segment(I_2, H_2) → m_6
  127. Segment(I_2, W_1) → n_6
  128. Segment(W_1, V_1) → p_6
  129. Segment(W_1, M_1) → q_6
  130. Segment(M_1, L_1) → r_6
  131. Segment(M_1, C_1) → s_6
  132. Segment(C_1, B_1) → t_6
  133. Segment(C_1, Q) → a_7
  134. Segment(Q, P) → b_7
  135. Segment(Q, G) → c_7
  136. Segment(G, F) → d_7
  137. Segment(H, G) → e_7
  138. Segment(H, R) → f_7
  139. Segment(R, Q) → g_7
  140. Segment(R, D_1) → h_7
  141. Segment(D_1, C_1) → i_7
  142. Segment(D_1, N_1) → j_7
  143. Segment(N_1, M_1) → k_7
  144. Segment(N_1, Z_1) → l_7
  145. Segment(Z_1, W_1) → m_7
  146. Segment(Z_1, J_2) → n_7
  147. Segment(J_2, I_2) → p_7
  148. Segment(J_2, T_2) → q_7
  149. Segment(T_2, S_2) → r_7
  150. Segment(T_2, F_3) → s_7
  151. Segment(F_3, E_3) → t_7
  152. Segment(F_3, P_3) → a_8
  153. Segment(P_3, O_3) → b_8
  154. Segment(P_3, B_4) → c_8
  155. Segment(B_4, A_4) → d_8
  156. Segment(B_4, R_4) → e_8
  157. Segment(R_4, S_4) → f_8
  158. Segment(Q_4, R_4) → g_8
  159. Segment(Q_4, C_4) → h_8
  160. Segment(C_4, B_4) → i_8
  161. Segment(C_4, Q_3) → j_8
  162. Segment(Q_3, P_3) → k_8
  163. Segment(Q_3, G_3) → l_8
  164. Segment(G_3, F_3) → m_8
  165. Segment(G_3, U_2) → n_8
  166. Segment(U_2, T_2) → p_8
  167. Segment(U_2, K_2) → q_8
  168. Segment(K_2, J_2) → r_8
  169. Segment(K_2, A_2) → s_8
  170. Segment(A_2, Z_1) → t_8
  171. Segment(A_2, O_1) → a_9
  172. Segment(O_1, N_1) → b_9
  173. Segment(O_1, E_1) → c_9
  174. Segment(E_1, D_1) → d_9
  175. Segment(E_1, S) → e_9
  176. Segment(S, R) → f_9
  177. Segment(S, I) → g_9
  178. Segment(I, H) → h_9
  179. Segment(J, I) → i_9
  180. Segment(J, T) → j_9
  181. Segment(T, S) → k_9
  182. Segment(T, F_1) → l_9
  183. Segment(F_1, E_1) → m_9
  184. Segment(F_1, P_1) → n_9
  185. Segment(P_1, O_1) → p_9
  186. Segment(P_1, B_2) → q_9
  187. Segment(B_2, A_2) → r_9
  188. Segment(B_2, L_2) → s_9
  189. Segment(L_2, K_2) → t_9
  190. Segment(L_2, V_2) → a_{10}
  191. Segment(V_2, U_2) → b_{10}
  192. Segment(V_2, H_3) → c_{10}
  193. Segment(H_3, G_3) → d_{10}
  194. Segment(H_3, R_3) → e_{10}
  195. Segment(Q_3, R_3) → f_{10}
  196. Segment(R_3, D_4) → g_{10}
  197. Segment(D_4, C_4) → h_{10}
  198. Segment(D_4, P_4) → i_{10}
  199. Segment(P_4, Q_4) → j_{10}
  200. Segment(O_4, P_4) → k_{10}
  201. Segment(O_4, N_4) → l_{10}
  202. Segment(N_4, D_4) → m_{10}
  203. Segment(M_4, R_3) → n_{10}
  204. Segment(M_4, N_4) → p_{10}
  205. Segment(L_4, M_4) → q_{10}
  206. Segment(L_4, H_3) → r_{10}
  207. Segment(L_4, K_4) → s_{10}
  208. Segment(K_4, V_2) → t_{10}
  209. Segment(K_4, J_4) → a_{11}
  210. Segment(J_4, L_2) → b_{11}
  211. Segment(J_4, I_4) → c_{11}
  212. Segment(I_4, B_2) → d_{11}
  213. Segment(I_4, H_4) → e_{11}
  214. Segment(H_4, P_1) → f_{11}
  215. Segment(H_4, G_4) → g_{11}
  216. Segment(G_4, F_1) → h_{11}
  217. Segment(G_4, F_4) → i_{11}
  218. Segment(F_4, T) → j_{11}
  219. Segment(F_4, E_4) → k_{11}
  220. Segment(E_4, J) → l_{11}
  221. Midpoint(A, L) → B_5
  222. Midpoint(B, M) → C_5
  223. Midpoint(K, V) → D_5
  224. Midpoint(C, N) → E_5
  225. Midpoint(L, W) → F_5
  226. Midpoint(U, H_1) → G_5
  227. Midpoint(D, O) → H_5
  228. Midpoint(M, Z) → I_5
  229. Midpoint(V, I_1) → J_5
  230. Midpoint(G_1, R_1) → K_5
  231. Midpoint(E, P) → L_5
  232. Midpoint(N, A_1) → M_5
  233. Midpoint(W, J_1) → N_5
  234. Midpoint(H_1, S_1) → O_5
  235. Midpoint(Q_1, D_2) → P_5
  236. Midpoint(C_2, N_2) → Q_5
  237. Midpoint(R_1, E_2) → R_5
  238. Midpoint(I_1, T_1) → S_5
  239. Midpoint(Z, K_1) → T_5
  240. Midpoint(O, B_1) → U_5
  241. Midpoint(F, Q) → V_5
  242. Midpoint(G, R) → W_5
  243. Midpoint(P, C_1) → Z_5
  244. Midpoint(A_1, L_1) → A_6
  245. Midpoint(J_1, U_1) → B_6
  246. Midpoint(S_1, F_2) → C_6
  247. Midpoint(D_2, O_2) → D_6
  248. Midpoint(M_2, Z_2) → E_6
  249. Midpoint(H, S) → F_6
  250. Midpoint(Q, D_1) → G_6
  251. Midpoint(B_1, M_1) → H_6
  252. Midpoint(K_1, V_1) → I_6
  253. Midpoint(T_1, G_2) → J_6
  254. Midpoint(E_2, P_2) → K_6
  255. Midpoint(N_2, A_3) → L_6
  256. Midpoint(W_2, J_3) → M_6
  257. Midpoint(I, T) → N_6
  258. Midpoint(R, E_1) → O_6
  259. Midpoint(C_1, N_1) → P_6
  260. Midpoint(L_1, W_1) → Q_6
  261. Midpoint(U_1, H_2) → R_6
  262. Midpoint(F_2, Q_2) → S_6
  263. Midpoint(O_2, B_3) → T_6
  264. Midpoint(Z_2, K_3) → U_6
  265. Midpoint(I_3, T_3) → V_6
  266. Midpoint(J, F_4) → W_6
  267. Midpoint(S, F_1) → Z_6
  268. Midpoint(D_1, O_1) → A_7
  269. Midpoint(M_1, Z_1) → B_7
  270. Midpoint(V_1, I_2) → C_7
  271. Midpoint(G_2, R_2) → D_7
  272. Midpoint(P_2, C_3) → E_7
  273. Midpoint(A_3, L_3) → F_7
  274. Midpoint(J_3, U_3) → G_7
  275. Midpoint(S_3, Z_4) → H_7