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分数乘法可视化：通过几何图形展示乘法原理

分数乘法可视化：通过几何图形展示乘法原理
几何画板及绘图内容加载中，请稍等……
2023-02-21 16:51
函数解析几何几何作图
所属专题 Primary School Mathematics Collection
这个范例通过几何图形直观展示分数乘法的计算过程。核心数学概念包括分数运算、几何变换和比例关系。作图要点涉及使用GeoGebra命令如OrthogonalLine、Circle、Intersect等来构造图形。适合初中生学习分数乘法，或用于数学教学演示。

GeoGebra 命令及参数

  1. OrthogonalLine(A, yAxis) → e
  2. OrthogonalLine(A, e) → f
  3. Circle(A, Taille) → h
  4. Intersect(h, e, 1) → B
  5. Intersect(h, f, 2) → C
  6. Intersect(h, e, 1) → D
  7. OrthogonalLine(B, e) → i
  8. Intersect(h, f, 2) → E
  9. OrthogonalLine(C, f) → j
  10. Intersect(i, j) → F
  11. Polygon(A, B, F, C) → P, a_1, b_1, f_1, c_1
  12. Circle(A, VarRayon) → k
  13. Intersect(k, a_1) → G,
  14. Circle(G, A) → p
  15. Intersect(p, a_1, 2) → H
  16. Circle(H, G) → q
  17. Intersect(q, a_1) → I, J
  18. Circle(J, H) → r
  19. Intersect(r, a_1) → K, L
  20. Circle(L, J) → s
  21. Intersect(s, a_1) → M, N
  22. Circle(N, L) → t
  23. Intersect(t, a_1) → O, Q
  24. Circle(Q, N) → d_1
  25. Intersect(d_1, a_1) → R, S
  26. Circle(S, Q) → e_1
  27. Intersect(e_1, a_1) → T, U
  28. Circle(U, S) → g_1
  29. Intersect(g_1, a_1) → V, W
  30. Circle(W, U) → h_1
  31. OrthogonalLine(G, a_1) → l
  32. OrthogonalLine(H, a_1) → m
  33. OrthogonalLine(J, a_1) → n
  34. OrthogonalLine(L, a_1) → i_1
  35. OrthogonalLine(N, a_1) → j_1
  36. OrthogonalLine(Q, a_1) → k_1
  37. OrthogonalLine(S, a_1) → l_1
  38. OrthogonalLine(U, a_1) → m_1
  39. OrthogonalLine(W, a_1) → n_1
  40. Intersect(f_1, l) → Y
  41. Intersect(f_1, m) → Z
  42. Intersect(f_1, n) → A_1
  43. Intersect(f_1, i_1) → B_1
  44. Intersect(f_1, j_1) → C_1
  45. Intersect(f_1, k_1) → D_1
  46. Intersect(l_1, f_1) → E_1
  47. Intersect(f_1, m_1) → F_1
  48. Intersect(f_1, n_1) → G_1
  49. Ray(A, B) → p_1
  50. Point(p_1) → H_1
  51. Vector(A, H_1) → u
  52. Translate(A, u) → A'
  53. Translate(B, u) → B'
  54. Translate(F, u) → F'
  55. Translate(C, u) → C'
  56. Polygon(A', B', F', C') → P', a', b', f', c'
  57. OrthogonalLine(V, a_1) → q_1
  58. Circle(V, U) → r_1
  59. Segment(G, Y) → s_1
  60. Segment(H, Z) → t_1
  61. Segment(J, A_1) → a_2
  62. Segment(L, B_1) → b_2
  63. Segment(N, C_1) → c_2
  64. Segment(Q, D_1) → d_2
  65. Segment(S, E_1) → e_2
  66. Segment(U, F_1) → f_2
  67. Segment(W, G_1) → g_2
  68. Circle(H_1, VarRayon_2) → h_2
  69. Intersect(h_2, c', 1) → J_1
  70. Circle(J_1, H_1) → k_2
  71. Intersect(k_2, c', 2) → K_1
  72. Circle(K_1, J_1) → p_2
  73. Intersect(p_2, c', 2) → L_1
  74. Circle(L_1, K_1) → q_2
  75. Intersect(q_2, c', 2) → M_1
  76. Circle(M_1, L_1) → r_2
  77. Intersect(r_2, c', 2) → N_1
  78. Circle(N_1, M_1) → s_2
  79. Intersect(s_2, c') → O_1, P_1
  80. Circle(P_1, N_1) → t_2
  81. Intersect(t_2, c', 2) → Q_1
  82. Circle(Q_1, P_1) → c_3
  83. Intersect(c_3, c', 2) → R_1
  84. Circle(R_1, Q_1) → d_3
  85. Intersect(d_3, c', 2) → S_1
  86. Circle(S_1, R_1) → e_3
  87. OrthogonalLine(J_1, c') → i_2
  88. OrthogonalLine(K_1, c') → j_2
  89. OrthogonalLine(L_1, c') → l_2
  90. OrthogonalLine(M_1, c') → m_2
  91. OrthogonalLine(N_1, c') → n_2
  92. OrthogonalLine(P_1, c') → a_3
  93. OrthogonalLine(Q_1, c') → b_3
  94. OrthogonalLine(R_1, c') → f_3
  95. OrthogonalLine(S_1, c') → g_3
  96. Intersect(b', i_2) → T_1
  97. Intersect(b', j_2) → U_1
  98. Intersect(b', l_2) → V_1
  99. Intersect(b', m_2) → W_1
  100. Intersect(b', n_2) → Y_1
  101. Intersect(b', a_3) → Z_1
  102. Intersect(b', b_3) → A_2
  103. Intersect(b', f_3) → B_2
  104. Intersect(b', g_3) → C_2
  105. Segment(J_1, T_1) → h_3
  106. Segment(U_1, K_1) → i_3
  107. Segment(L_1, V_1) → j_3
  108. Segment(W_1, M_1) → k_3
  109. Segment(N_1, Y_1) → l_3
  110. Segment(Z_1, P_1) → m_3
  111. Segment(Q_1, A_2) → n_3
  112. Segment(B_2, R_1) → p_3
  113. Segment(S_1, C_2) → q_3
  114. Circle(A, largeur_1) → r_3
  115. Intersect(r_3, a_1) → D_2, S_2
  116. OrthogonalLine(D_2, f_1) → s_3
  117. Intersect(s_3, f_1) → E_2
  118. OrthogonalLine(E_2, s_3) → t_3
  119. Intersect(t_3, c_1) → F_2
  120. Polygon(A, D_2, E_2, F_2) → P_2, a_4, d_4, e_4, f_4
  121. OrthogonalLine(O, a_1) → b_4
  122. Intersect(b_4, f_1) → G_2
  123. Circle(O, N) → g_4
  124. Circle(O_1, N_1) → q_4
  125. OrthogonalLine(O_1, c') → t_4
  126. Circle(H_1, Largeur_2) → h_5
  127. Intersect(h_5, c') → F_3, B1
  128. OrthogonalLine(F_3, c') → i_5
  129. Intersect(i_5, b') → G_3
  130. Polygon(H_1, F_3, G_3, B') → P_3, h_6, f_6, g_6, b'_1
  131. Line(A, H_1) → a
  132. Point(a) → A1
  133. Line(A1, yAxis) → b
  134. Mirror(A', b) → A''
  135. Mirror(B', b) → B''
  136. Mirror(F', b) → F''
  137. Mirror(C', b) → C''
  138. Polygon(A'', B'', F'', C'') → P'', a'', b'', f'', c''
  139. Mirror(H_1, b) → H_1'
  140. Mirror(F_3, b) → F_3'
  141. Mirror(G_3, b) → G_3'
  142. Mirror(B', b) → B''_1
  143. Polygon(H_1', F_3', G_3', B''_1) → P_3', h_1', f_3', g_3', b''_1
  144. Mirror(J_1, b) → J_1'
  145. Mirror(T_1, b) → T_1'
  146. Segment(J_1', T_1') → c
  147. Mirror(U_1, b) → U_1'
  148. Mirror(K_1, b) → K_1'
  149. Segment(U_1', K_1') → d
  150. Mirror(L_1, b) → L_1'
  151. Mirror(V_1, b) → V_1'
  152. Segment(L_1', V_1') → g
  153. Mirror(W_1, b) → W_1'
  154. Mirror(M_1, b) → M_1'
  155. Segment(W_1', M_1') → a1
  156. Mirror(N_1, b) → N_1'
  157. Mirror(Y_1, b) → Y_1'
  158. Segment(N_1', Y_1') → b1
  159. Mirror(Z_1, b) → Z_1'
  160. Mirror(P_1, b) → P_1'
  161. Segment(Z_1', P_1') → c1
  162. Mirror(Q_1, b) → Q_1'
  163. Mirror(A_2, b) → A_2'
  164. Segment(Q_1', A_2') → d1
  165. Mirror(B_2, b) → B_2'
  166. Mirror(R_1, b) → R_1'
  167. Segment(B_2', R_1') → e1
  168. Mirror(S_1, b) → S_1'
  169. Mirror(C_2, b) → C_2'
  170. Segment(S_1', C_2') → f1
  171. Vector(A, B'') → v
  172. Translate(A, v) → A'_1
  173. Translate(D_2, v) → D_2'
  174. Translate(E_2, v) → E_2'
  175. Translate(F_2, v) → F_2'
  176. Polygon(A'_1, D_2', E_2', F_2') → P_2', a'_1, d_2', e_2', f_2'
  177. Translate(G, v) → G'
  178. Translate(Y, v) → Y'
  179. Segment(G', Y') → g1
  180. Translate(H, v) → H'
  181. Translate(Z, v) → Z'
  182. Segment(H', Z') → h1
  183. Translate(J, v) → J'
  184. Translate(A_1, v) → A_1'
  185. Segment(J', A_1') → i1
  186. Translate(L, v) → L'
  187. Translate(B_1, v) → B_1'
  188. Segment(L', B_1') → j1
  189. Translate(N, v) → N'
  190. Translate(C_1, v) → C_1'
  191. Segment(N', C_1') → k1
  192. Translate(Q, v) → Q'
  193. Translate(D_1, v) → D_1'
  194. Segment(Q', D_1') → l1
  195. Translate(S, v) → S'
  196. Translate(E_1, v) → E_1'
  197. Segment(S', E_1') → m1
  198. Translate(U, v) → U'
  199. Translate(F_1, v) → F_1'
  200. Segment(U', F_1') → n1
  201. Translate(W, v) → W'
  202. Translate(G_1, v) → G_1'
  203. Segment(W', G_1') → p1
  204. Midpoint(f_1) → C1
  205. Midpoint(g_6) → E1
  206. Midpoint(c') → D1
  207. Midpoint(f'') → F1
  208. Midpoint(c'') → G1
  209. Midpoint(a_4) → H1
  210. Midpoint(a'_1) → I1
  211. Midpoint(g_3') → J1
  212. Circle(D1, 1.5) → q1
  213. Circle(C1, 2) → r1
  214. Circle(F1, 2) → s1
  215. Circle(G1, 1.5) → t1
  216. Line(C1, b) → a2
  217. Intersect(r1, a2) → K1, L1
  218. Line(L1, f_1) → b2
  219. Intersect(s1, b2) → M1, N1
  220. Line(F_2', b) → c2
  221. Line(C'', b) → d2
  222. Line(F, b) → e2
  223. Line(C, b) → f2
  224. Intersect(e2, b2) → O1
  225. Intersect(e2, f2) → P1
  226. Intersect(b2, f2) → Q1
  227. Vector(L1, O1) → w
  228. Vector(L1, Q1) → z
  229. Line(D_2, b) → g2
  230. Circle(H1, 1.5) → h2
  231. Line(H1, b) → i2
  232. Intersect(h2, i2) → R1, S1
  233. Line(R1, v) → j2
  234. Intersect(g2, j2) → U1
  235. Intersect(f2, j2) → V1
  236. Circle(I1, 1.5) → k2
  237. Intersect(k2, j2) → W1, Z1
  238. Line(D_2', b) → l2
  239. Intersect(l2, j2) → A2
  240. Intersect(c2, j2) → B2
  241. Intersect(b2, c2) → C2
  242. Intersect(b2, d2) → D2
  243. Vector(R1, U1) → u1
  244. Vector(R1, V1) → v1
  245. Vector(W1, A2) → w1
  246. Vector(W1, B2) → z1
  247. Vector(M1, C2) → u2
  248. Vector(M1, D2) → v2
  249. Line(F, C') → m2
  250. Line(D1, j2) → n2
  251. Intersect(q1, n2) → E2, F2
  252. Line(E2, b) → p2
  253. Intersect(p2, m2) → G2
  254. Line(H_1, B) → q2
  255. Intersect(q2, p2) → H2
  256. Vector(E2, H2) → w2
  257. Vector(E2, G2) → z2
  258. Line(G_3, j2) → r2
  259. Circle(E1, 1.5) → s2
  260. Circle(J1, 1.5) → t2
  261. Intersect(t1, n2) → I2, J2
  262. Line(J2, b) → a3
  263. Intersect(q2, a3) → K2
  264. Intersect(m2, a3) → L2
  265. Vector(J2, K2) → u3
  266. Vector(J2, L2) → v3
  267. Line(J1, j2) → b3
  268. Intersect(t2, b3) → M2, N2
  269. Line(M2, b) → c3
  270. Intersect(c3, q2) → O2
  271. Intersect(r2, c3) → P2
  272. Vector(M2, O2) → w3
  273. Vector(M2, P2) → z3
  274. Intersect(s2, b3) → Q2, R2
  275. Line(R2, b) → d3
  276. Intersect(d3, q2) → S2
  277. Intersect(r2, d3) → U2
  278. Vector(R2, S2) → e3
  279. Vector(R2, U2) → f3
  280. Line(V2, xAxis) → g3
  281. Point(g3) → Z2
  282. Point(g3) → A3
  283. Point(g3) → B3
  284. Point(g3) → C3
  285. Point(g3) → D3
  286. Point(g3) → E3
  287. Segment(Z2, A3) → h3
  288. Segment(B3, C3) → i3
  289. Line(W2, h_6) → k3
  290. Line(F3, k3) → l3
  291. Point(g3) → G3
  292. Point(g3) → H3
  293. Point(g3) → I3
  294. Point(g3) → J3
  295. Segment(G3, H3) → j3
  296. Segment(I3, J3) → m3
  297. Intersect(c2, e) → M3
  298. Intersect(e, l2) → L3
  299. Line(P2, j2) → n3
  300. Intersect(c2, n3) → K3
  301. Midpoint(K3, L3) → N3
  302. Circle(N3, L3) → p3
  303. Intersect(p3, l2) → O3, P3
  304. Polygon(M3, L3, P3, K3) → poly1, m3_1, l3_1, p3_1, k3_1
  305. GCD((Num1 * Num2), (Den1 * Den2)) → o

AI 绘图提示语参考

画一个几何图形来演示分数乘法，包含一个圆和两条垂直线。首先，从圆心向x轴作垂线，再从交点向圆心作垂线，形成两个交点。接着，以圆心为圆心画一个圆，与垂线相交得到四个点。用这四个点和一个交点构成一个四边形。然后，在四边形的一边上画一个圆，与该边相交得到两个点。再以这两个点为圆心分别画圆，与四边形边相交得到更多点。最后，将这些点连接起来，形成多个嵌套的四边形和圆，展示分数乘法的几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。