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乘法表三角形

乘法表三角形
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2017-04-08 04:09
测试改名0向量几何作图函数图像
①本范例演示了如何利用 GeoGebra 构建一个乘法表三角形，直观展示乘法与几何图形的结合；②涉及的核心数学概念包括乘法、三角形、向量、旋转等；③作图要点提炼自构造摘要，使用了 Point, Intersect, Ray, Circle, Rotate, Angle, Segment, Line, Polygon, Vector 等命令和对象；④适合初中及以上学生学习几何作图与数学可视化，可用于探索乘法表的几何性质。

GeoGebra 命令及参数

  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