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Triangular Numbers Demo

Triangular Numbers Demo
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2018-11-16 23:24
SequenceCoordinate GeometryGeometric Construction
This example demonstrates the generation and geometric representation of triangular numbers, constructing triangular shapes through points and segments. It involves core mathematical concepts like sequences, geometric constructions, and coordinate geometry. The construction uses commands like Segment and Midpoint in GeoGebra. Suitable for high school mathematics teaching, helping students understand the connection between sequences and geometry, and for dynamic geometry demonstrations.

GeoGebra Commands & Parameters

  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