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Multiplication Table Triangle

Multiplication Table Triangle
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2017-04-08 04:09
TriangleVectorGeometric ConstructionGraphing
This example demonstrates how to construct a multiplication table triangle using GeoGebra, visually integrating multiplication with geometric shapes. Core math concepts include multiplication, triangles, vectors, rotation, etc. Construction involves commands/objects like Point, Intersect, Ray, Circle, Rotate, Angle, Segment, Line, Polygon, Vector as per the summary. Suitable for middle school and above to explore geometric constructions and mathematical visualization, particularly the geometric properties of multiplication tables.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → A
  3. Ray(A, B) → f
  4. Point(f) → D
  5. Circle(A, D) → d
  6. Rotate(B, 60°, A) → B'
  7. Ray(A, B') → g
  8. Intersect(d, g, 1) → O
  9. Circle(A, C) → c
  10. Intersect(c, g, 1) → R
  11. Circle(A, E) → e
  12. Intersect(e, g, 1) → I
  13. Circle(A, F) → h
  14. Intersect(h, g, 1) → J
  15. Circle(A, G) → k
  16. Intersect(k, g, 1) → N
  17. Circle(A, W) → c_1
  18. Intersect(c_1, g, 1) → D_1
  19. Circle(A, Z) → d_1
  20. Intersect(d_1, g, 1) → E_1
  21. Circle(A, A_1) → e_1
  22. Intersect(e_1, g, 1) → F_1
  23. Circle(A, B_1) → k_1
  24. Intersect(k_1, g, 1) → G_1
  25. Circle(A, C_1) → p_1
  26. Intersect(p_1, g, 1) → H_1
  27. Rotate(A, (-(60°)), B') → A'_3
  28. Ray(A, A'_3) → i
  29. Intersect(c_1, i, 1) → M_1
  30. Intersect(p_1, i, 1) → L_1
  31. Intersect(k_1, i, 1) → K_1
  32. Intersect(e_1, i, 1) → J_1
  33. Intersect(d_1, i) → I_1,
  34. Intersect(c, i, 1) → Q
  35. Intersect(k, i, 1) → M
  36. Intersect(e, i, 1) → L
  37. Intersect(h, i, 1) → K
  38. Intersect(d, i, 1) → P
  39. Angle(B, A, B') → β
  40. Rotate(A, 60°, B') → A'_2
  41. Angle(A, B', A'_2) → ζ
  42. Angle(A'_3, B', A) → η
  43. Circle(A, H) → p
  44. Segment(M, N) → j
  45. Segment(K, J) → l
  46. Segment(L, I) → m
  47. Segment(P, O) → n
  48. Segment(Q, R) → q
  49. Line(R, i) → r
  50. Intersect(r, j) → S
  51. Ray(R, S) → s
  52. Line(O, s) → t
  53. Line(I, t) → a_9
  54. Intersect(n, s) → T
  55. Ray(Q, T) → b_7
  56. Intersect(a_9, j) → U
  57. Ray(P, U) → f_1
  58. Intersect(t, j) → V
  59. Ray(L, V) → g_1
  60. Ray(I, U) → h_1
  61. Ray(O, V) → i_1
  62. Segment(I_1, E_1) → j_1
  63. Segment(F_1, J_1) → l_1
  64. Segment(K_1, G_1) → m_1
  65. Segment(L_1, H_1) → n_1
  66. Segment(M_1, D_1) → q_1
  67. Intersect(s, q_1) → N_1
  68. Intersect(s, j_1) → O_1
  69. Intersect(s, l_1) → P_1
  70. Intersect(s, m_1) → Q_1
  71. Intersect(s, n_1) → R_1
  72. Intersect(j, b_7) → S_1
  73. Intersect(b_7, q_1) → T_1
  74. Intersect(b_7, j_1) → U_1
  75. Intersect(b_7, l_1) → V_1
  76. Intersect(b_7, m_1) → W_1
  77. Intersect(b_7, n_1) → Z_1
  78. Ray(J, S_1) → r_1
  79. Ray(N, T_1) → s_1
  80. Ray(D_1, U_1) → t_1
  81. Ray(E_1, V_1) → a_1
  82. Ray(F_1, W_1) → b_1
  83. Ray(G_1, Z_1) → f_2
  84. Ray(K, S) → g_2
  85. Ray(M, N_1) → h_2
  86. Ray(M_1, O_1) → i_2
  87. Ray(I_1, P_1) → j_2
  88. Ray(J_1, Q_1) → k_2
  89. Ray(K_1, R_1) → l_2
  90. Intersect(l, s) → A_2
  91. Intersect(l, f_1) → B_2
  92. Intersect(l, b_7) → C_2
  93. Intersect(m, b_7) → D_2
  94. Intersect(m, s) → E_2
  95. Intersect(n, s) → F_2
  96. Intersect(g_1, h_1) → G_2
  97. Intersect(f_1, s_1) → H_2
  98. Intersect(g_1, j_1) → I_2
  99. Intersect(h_1, j_1) → J_2
  100. Intersect(i_1, j_1) → K_2
  101. Intersect(i_1, i_2) → L_2
  102. Intersect(r_1, g_2) → M_2
  103. Intersect(g_1, l_1) → N_2
  104. Intersect(f_1, t_1) → O_2
  105. Intersect(f_1, r_1) → P_2
  106. Intersect(i_1, q_1) → Q_2
  107. Intersect(i_1, n_1) → R_2
  108. Intersect(h_1, n_1) → S_2
  109. Intersect(n_1, s_1) → T_2
  110. Intersect(f_1, n_1) → U_2
  111. Intersect(g_1, n_1) → V_2
  112. Intersect(n_1, t_1) → W_2
  113. Intersect(n_1, r_1) → Z_2
  114. Intersect(i_1, m_1) → A_3
  115. Intersect(m_1, r_1) → B_3
  116. Intersect(f_1, m_1) → C_3
  117. Intersect(g_1, m_1) → D_3
  118. Intersect(m_1, s_1) → E_3
  119. Intersect(h_1, l_1) → F_3
  120. Circle(A, G_3) → c_2
  121. Circle(A, H_3) → d_2
  122. Circle(A, I_3) → e_2
  123. Circle(A, J_3) → p_2
  124. Circle(A, K_3) → q_2
  125. Circle(A, L_3) → r_2
  126. Circle(A, M_3) → s_2
  127. Circle(A, N_3) → t_2
  128. Circle(A, O_3) → c_3
  129. Circle(A, P_3) → d_3
  130. Segment(R, P) → m_2
  131. Segment(R, L) → n_2
  132. Segment(R, K) → a_2
  133. Segment(R, M) → b_2
  134. Segment(R, M_1) → f_3
  135. Segment(R, I_1) → g_3
  136. Segment(R, K_1) → h_3
  137. Segment(R, J_1) → i_3
  138. Segment(R, L_1) → j_3
  139. Segment(Q, D_1) → k_3
  140. Segment(Q, E_1) → l_3
  141. Segment(Q, O) → m_3
  142. Segment(Q, I) → n_3
  143. Segment(Q, J) → p_3
  144. Segment(Q, N) → q_3
  145. Segment(Q, H_1) → r_3
  146. Segment(Q, F_1) → s_3
  147. Segment(Q, G_1) → t_3
  148. Segment(P, I) → a_3
  149. Segment(P, J) → b_3
  150. Segment(P, D_1) → e_3
  151. Segment(P, N) → f_4
  152. Segment(P, F_1) → g_4
  153. Segment(P, E_1) → h_4
  154. Segment(P, G_1) → i_4
  155. Segment(P, H_1) → j_4
  156. Segment(L, J) → k_4
  157. Segment(L, N) → l_4
  158. Segment(L, D_1) → m_4
  159. Segment(L, E_1) → n_4
  160. Segment(L, F_1) → p_4
  161. Segment(L, G_1) → q_4
  162. Segment(L, H_1) → r_4
  163. Segment(O, L) → s_4
  164. Segment(K, O) → t_4
  165. Segment(M, O) → a_4
  166. Segment(M_1, O) → b_4
  167. Segment(I_1, O) → c_4
  168. Segment(O, J_1) → d_4
  169. Segment(O, K_1) → e_4
  170. Segment(O, L_1) → f_5
  171. Segment(I, K) → g_5
  172. Segment(I, M) → h_5
  173. Segment(M_1, I) → i_5
  174. Segment(I_1, I) → j_5
  175. Segment(J_1, I) → k_5
  176. Segment(K_1, I) → l_5
  177. Segment(L_1, I) → m_5
  178. Segment(J, M) → n_5
  179. Segment(M_1, J) → p_5
  180. Segment(J, I_1) → q_5
  181. Segment(J, J_1) → r_5
  182. Segment(J, K_1) → s_5
  183. Segment(L_1, J) → t_5
  184. Segment(K, H_1) → a_5
  185. Segment(G_1, K) → b_5
  186. Segment(F_1, K) → c_5
  187. Segment(E_1, K) → d_5
  188. Segment(D_1, K) → e_5
  189. Segment(N, K) → f_6
  190. Segment(M, H_1) → g_6
  191. Segment(M, D_1) → h_6
  192. Segment(M, E_1) → i_6
  193. Segment(M, F_1) → j_6
  194. Segment(M, G_1) → k_6
  195. Segment(N, M_1) → l_6
  196. Segment(N, I_1) → m_6
  197. Segment(N, J_1) → n_6
  198. Segment(N, K_1) → p_6
  199. Segment(N, L_1) → q_6
  200. Segment(M_1, E_1) → r_6
  201. Segment(M_1, F_1) → s_6
  202. Segment(M_1, G_1) → t_6
  203. Segment(M_1, H_1) → a_6
  204. Segment(D_1, L_1) → b_6
  205. Segment(D_1, K_1) → c_6
  206. Segment(D_1, J_1) → d_6
  207. Segment(D_1, I_1) → e_6
  208. Segment(I_1, F_1) → f_7
  209. Segment(I_1, G_1) → g_7
  210. Segment(I_1, H_1) → h_7
  211. Segment(E_1, J_1) → i_7
  212. Segment(E_1, K_1) → j_7
  213. Segment(E_1, L_1) → k_7
  214. Segment(J_1, G_1) → l_7
  215. Segment(J_1, H_1) → m_7
  216. Segment(F_1, K_1) → n_7
  217. Segment(L_1, F_1) → p_7
  218. Segment(G_1, L_1) → q_7
  219. Segment(K_1, H_1) → r_7
  220. Intersect(h_1, m_1) → Q_3
  221. Point(L_a) → a
  222. Segment(a, A) → s_7
  223. Point(L_b) → b
  224. Segment(A, b) → t_7
  225. Segment(a, b) → a_7
  226. Polygon(A, a, b) → poly1, s_8, a_8, r_8
  227. Vector(A, a) → u
  228. Vector(A, b) → v
  229. Point(i) → R_3
  230. Point(g) → S_3
  231. Point(i) → T_3
  232. Point(g) → U_3
  233. Polygon(T_3, U_3, H_1, L_1) → poly2, t_8, u_3, h_8, l_8