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Rick的分数活动与视频

Rick的分数活动与视频
几何画板及绘图内容加载中，请稍等……
2020-05-14 23:27
圆三角函数几何作图滑块动画
①本范例通过操作矩形和圆形面积模型来演示分数的探究与比较；②涉及的核心数学概念包括分数、面积模型、几何分布、三角函数等；③作图要点提炼自构造摘要，使用了Point、Circle、OrthogonalLine、Intersect、Rotate、CircleSector、Segment、Vector、Translate、Polygon、Line等GeoGebra命令和对象；④适合初中及以上数学教学，用于分数理解和几何直观。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, 3) → e
  3. Point(xAxis) → B
  4. OrthogonalLine(A, xAxis) → f
  5. Intersect(e, f, 2) → C
  6. Rotate(C, (360 * ° / b), A) → C'
  7. Rotate(C', (360 * ° / b), A) → C''
  8. Rotate(C'', (360 * ° / b), A) → C'''
  9. Rotate(C''', (360 * ° / b), A) → D
  10. Rotate(D, (360 * ° / b), A) → D'
  11. Rotate(D', (360 * ° / b), A) → D''
  12. Rotate(D'', (360 * ° / b), A) → D'''
  13. Rotate(D''', (360 * ° / b), A) → E
  14. Rotate(E, (360 * ° / b), A) → E'
  15. Rotate(E', (360 * ° / b), A) → E''
  16. Rotate(E'', (360 * ° / b), A) → E'''
  17. Rotate(E''', (360 * ° / b), A) → F
  18. Rotate(F, (360 * ° / b), A) → F'
  19. Rotate(F', (360 * ° / b), A) → F''
  20. Rotate(F'', (360 * ° / b), A) → F'''
  21. Rotate(F''', (360 * ° / b), A) → G
  22. Rotate(G, (360 * ° / b), A) → G'
  23. Rotate(G', (360 * ° / b), A) → G''
  24. Rotate(G'', (360 * ° / b), A) → G'''
  25. CircleSector(A, C, C') → g
  26. CircleSector(A, C', C'') → h
  27. CircleSector(A, C'', C''') → k
  28. CircleSector(A, C''', D) → p
  29. CircleSector(A, D, D') → q
  30. CircleSector(A, D', D'') → r
  31. CircleSector(A, D'', D''') → s
  32. CircleSector(A, D''', E) → t
  33. CircleSector(A, E, E') → c_1
  34. CircleSector(A, E', E'') → d_1
  35. CircleSector(A, E'', E''') → e_1
  36. CircleSector(A, E''', F) → f_1
  37. CircleSector(A, F, F') → g_1
  38. CircleSector(A, F', F'') → h_1
  39. CircleSector(A, F'', F''') → k_1
  40. CircleSector(A, F''', G) → p_1
  41. CircleSector(A, G, G') → q_1
  42. CircleSector(A, G', G'') → r_1
  43. CircleSector(A, G'', G''') → s_1
  44. CircleSector(A, G''', C) → t_1
  45. Segment(A, C) → i
  46. Segment(A, C') → j
  47. Segment(A, C'') → l
  48. Segment(A, C''') → m
  49. Segment(A, D) → n
  50. Segment(A, D') → a_1
  51. Segment(A, D'') → b_1
  52. Segment(A, D''') → i_1
  53. Segment(A, E) → j_1
  54. Segment(A, E') → l_1
  55. Segment(A, E'') → m_1
  56. Segment(A, E''') → n_1
  57. Segment(A, F) → a_2
  58. Segment(A, F') → b_2
  59. Segment(A, F'') → c_2
  60. Segment(A, F''') → d_2
  61. Segment(A, G) → e_2
  62. Segment(A, G') → f_2
  63. Segment(A, G'') → g_2
  64. Segment(A, G''') → h_2
  65. Intersect(e, xAxis, 1) → H
  66. Intersect(e, xAxis, 2) → I
  67. OrthogonalLine(H, xAxis) → i_2
  68. OrthogonalLine(I, xAxis) → j_2
  69. OrthogonalLine(J, i_2) → k_2
  70. OrthogonalLine(K, i_2) → l_2
  71. Intersect(j_2, k_2) → L
  72. Intersect(j_2, l_2) → M
  73. Segment(J, L) → m_2
  74. Segment(K, M) → n_2
  75. Segment(K, J) → p_2
  76. Segment(M, L) → q_2
  77. Vector(J, L) → u
  78. Translate(i_2, Vector[u / b]) → r_2
  79. Translate(i_2, Vector[(u * 2 / b)]) → s_2
  80. Translate(i_2, Vector[(u * 18 / b)]) → t_2
  81. Translate(i_2, Vector[(u * 19 / b)]) → a_3
  82. Translate(i_2, Vector[(u * 17 / b)]) → b_3
  83. Translate(i_2, Vector[(u * 16 / b)]) → c_3
  84. Translate(i_2, Vector[(u * 15 / b)]) → d_3
  85. Translate(i_2, Vector[(u * 14 / b)]) → e_3
  86. Translate(i_2, Vector[(u * 13 / b)]) → f_3
  87. Translate(i_2, Vector[(u * 12 / b)]) → h_3
  88. Translate(i_2, Vector[(u * 11 / b)]) → i_3
  89. Translate(i_2, Vector[(u * 10 / b)]) → j_3
  90. Translate(i_2, Vector[(u * 9 / b)]) → k_3
  91. Translate(i_2, Vector[(u * 8 / b)]) → l_3
  92. Translate(i_2, Vector[(u * 7 / b)]) → m_3
  93. Translate(i_2, Vector[(u * 6 / b)]) → n_3
  94. Translate(i_2, Vector[(u * 5 / b)]) → p_3
  95. Translate(i_2, Vector[(u * 4 / b)]) → q_3
  96. Translate(i_2, Vector[(u * 3 / b)]) → r_3
  97. Intersect(r_2, n_2) → N
  98. Intersect(r_2, m_2) → O
  99. Intersect(s_2, m_2) → P
  100. Intersect(r_3, m_2) → Q
  101. Intersect(q_3, m_2) → R
  102. Intersect(p_3, m_2) → S
  103. Intersect(n_3, m_2) → T
  104. Intersect(m_3, m_2) → U
  105. Intersect(l_3, m_2) → V
  106. Intersect(k_3, m_2) → W
  107. Intersect(j_3, m_2) → Z
  108. Intersect(i_3, m_2) → A_1
  109. Intersect(h_3, m_2) → B_1
  110. Intersect(m_2, f_3) → D_1
  111. Intersect(e_3, m_2) → E_1
  112. Intersect(d_3, m_2) → F_1
  113. Intersect(c_3, m_2) → G_1
  114. Intersect(b_3, m_2) → H_1
  115. Intersect(t_2, m_2) → I_1
  116. Intersect(a_3, m_2) → J_1
  117. Intersect(a_3, n_2) → K_1
  118. Intersect(t_2, n_2) → L_1
  119. Intersect(b_3, n_2) → M_1
  120. Intersect(c_3, n_2) → N_1
  121. Intersect(d_3, n_2) → O_1
  122. Intersect(e_3, n_2) → P_1
  123. Intersect(n_2, h_3) → R_1
  124. Intersect(i_3, n_2) → S_1
  125. Intersect(j_3, n_2) → T_1
  126. Intersect(k_3, n_2) → U_1
  127. Intersect(l_3, n_2) → V_1
  128. Intersect(m_3, n_2) → W_1
  129. Intersect(n_3, n_2) → Z_1
  130. Intersect(p_3, n_2) → A_2
  131. Intersect(q_3, n_2) → B_2
  132. Intersect(r_3, n_2) → C_2
  133. Intersect(s_2, n_2) → D_2
  134. Intersect(f_3, n_2) → C_1
  135. Polygon(J, O, N, K) → poly1, j_4, o, n_4, k_4
  136. Polygon(N, D_2, P, O) → poly2, n_5, d_4, p_4, o_1
  137. Polygon(D_2, C_2, Q, P) → poly3, d_5, c_4, q_4, p_5
  138. Polygon(C_2, B_2, R, Q) → poly4, c_5, b_4, r_4, q_5
  139. Polygon(A_2, B_2, R, S) → poly5, a_4, b_5, r_5, s_3
  140. Polygon(A_2, Z_1, T, S) → poly6, a_5, z_1, t_3, s_4
  141. Polygon(Z_1, W_1, U, T) → poly7, z_2, w_1, u_1, t_4
  142. Polygon(W_1, V_1, V, U) → poly8, w_2, v_1, v, u_2
  143. Polygon(V_1, U_1, W, V) → poly9, v_2, u_3, w, v_3
  144. Polygon(U_1, T_1, Z, W) → poly10, u_4, t_5, z, w_3
  145. Polygon(T_1, S_1, A_1, Z) → poly11, t_6, s_5, a_6, z_3
  146. Polygon(S_1, R_1, B_1, A_1) → poly12, s_6, r_6, b_6, a_7
  147. Polygon(R_1, C_1, D_1, B_1) → poly13, r_7, c_6, d_6, b_7
  148. Polygon(C_1, P_1, E_1, D_1) → poly14, c_7, p_6, e_4, d_7
  149. Polygon(P_1, O_1, F_1, E_1) → poly15, p_7, o_2, f_4, e_5
  150. Polygon(O_1, N_1, G_1, F_1) → poly16, o_3, n_6, g_3, f_5
  151. Polygon(M_1, N_1, G_1, H_1) → poly17, m_4, n_7, g_4, h_4
  152. Polygon(M_1, L_1, I_1, H_1) → poly18, m_5, l_4, i_4, h_5
  153. Polygon(L_1, K_1, J_1, I_1) → poly19, l_5, k_5, j_5, i_5
  154. Polygon(K_1, M, L, J_1) → poly20, k_6, m_6, l_6, j_6
  155. Circle(B, 3) → g_5
  156. Intersect(g_5, xAxis) → Q_1, E_2
  157. OrthogonalLine(Q_1, xAxis) → e_6
  158. OrthogonalLine(B, xAxis) → f_6
  159. Line(E_2, f_6) → g_6
  160. Intersect(k_2, g_6) → H_2
  161. Intersect(l_2, g_6) → I_2
  162. Intersect(g_5, f_6, 1) → J_2
  163. Rotate(J_2, (360 * ° / d), B) → K_2
  164. Rotate(K_2, (360 * ° / d), B) → L_2
  165. Rotate(L_2, (360 * ° / d), B) → M_2
  166. Rotate(M_2, (360 * ° / d), B) → N_2
  167. Rotate(N_2, (360 * ° / d), B) → O_2
  168. Rotate(O_2, (360 * ° / d), B) → P_2
  169. Rotate(P_2, (360 * ° / d), B) → Q_2
  170. Rotate(Q_2, (360 * ° / d), B) → R_2
  171. Rotate(R_2, (360 * ° / d), B) → S_2
  172. Rotate(S_2, (360 * ° / d), B) → T_2
  173. Rotate(T_2, (360 * ° / d), B) → U_2
  174. Rotate(U_2, (360 * ° / d), B) → V_2
  175. Rotate(V_2, (360 * ° / d), B) → W_2
  176. Rotate(W_2, (360 * ° / d), B) → Z_2
  177. Rotate(Z_2, (360 * ° / d), B) → A_3
  178. Rotate(A_3, (360 * ° / d), B) → B_3
  179. Rotate(B_3, (360 * ° / d), B) → C_3
  180. Rotate(C_3, (360 * ° / d), B) → D_3
  181. Rotate(D_3, (360 * ° / d), B) → E_3
  182. CircleSector(B, J_2, K_2) → h_6
  183. CircleSector(B, K_2, L_2) → q_6
  184. CircleSector(B, L_2, M_2) → e_7
  185. CircleSector(B, M_2, N_2) → f_7
  186. CircleSector(B, N_2, O_2) → g_7
  187. CircleSector(B, O_2, P_2) → h_7
  188. CircleSector(B, P_2, Q_2) → k_7
  189. CircleSector(B, Q_2, R_2) → q_7
  190. CircleSector(B, R_2, S_2) → s_7
  191. CircleSector(B, S_2, T_2) → t_7
  192. CircleSector(B, T_2, U_2) → c_8
  193. CircleSector(B, U_2, V_2) → d_8
  194. CircleSector(B, V_2, W_2) → e_8
  195. CircleSector(B, W_2, Z_2) → f_8
  196. CircleSector(B, Z_2, A_3) → g_8
  197. CircleSector(B, A_3, B_3) → h_8
  198. CircleSector(B, B_3, C_3) → k_8
  199. CircleSector(B, C_3, D_3) → p_8
  200. CircleSector(B, D_3, E_3) → q_8
  201. CircleSector(B, E_3, J_2) → r_8
  202. Segment(J_2, B) → i_6
  203. Segment(K_2, B) → i_7
  204. Segment(L_2, B) → j_7
  205. Segment(M_2, B) → l_7
  206. Segment(N_2, B) → m_7
  207. Segment(O_2, B) → a_8
  208. Segment(P_2, B) → b_8
  209. Segment(Q_2, B) → i_8
  210. Segment(R_2, B) → j_8
  211. Segment(S_2, B) → l_8
  212. Segment(T_2, B) → m_8
  213. Segment(U_2, B) → n_8
  214. Segment(V_2, B) → s_8
  215. Segment(W_2, B) → t_8
  216. Segment(Z_2, B) → a_9
  217. Segment(A_3, B) → b_9
  218. Segment(B_3, B) → c_9
  219. Segment(C_3, B) → d_9
  220. Segment(D_3, B) → e_9
  221. Segment(E_3, B) → f_9
  222. Segment(F_2, H_2) → g_9
  223. Segment(G_2, I_2) → h_9
  224. Segment(I_2, H_2) → i_9
  225. Segment(G_2, F_2) → j_9
  226. Vector(F_2, H_2) → v_4
  227. Translate(e_6, Vector[(v_4 * 1 / d)]) → k_9
  228. Translate(e_6, Vector[(v_4 * 2 / d)]) → l_9
  229. Translate(e_6, Vector[(v_4 * 3 / d)]) → m_9
  230. Translate(e_6, Vector[(v_4 * 4 / d)]) → n_9
  231. Translate(e_6, Vector[(v_4 * 5 / d)]) → p_9
  232. Translate(e_6, Vector[(v_4 * 6 / d)]) → q_9
  233. Translate(e_6, Vector[(v_4 * 7 / d)]) → r_9
  234. Translate(e_6, Vector[(v_4 * 8 / d)]) → s_9
  235. Translate(e_6, Vector[(v_4 * 9 / d)]) → t_9
  236. Translate(e_6, Vector[(v_4 * 10 / d)]) → a_{10}
  237. Translate(e_6, Vector[(v_4 * 11 / d)]) → b_{10}
  238. Translate(e_6, Vector[(v_4 * 12 / d)]) → c_{10}
  239. Translate(e_6, Vector[(v_4 * 13 / d)]) → d_{10}
  240. Translate(e_6, Vector[(v_4 * 14 / d)]) → e_{10}
  241. Translate(e_6, Vector[(v_4 * 15 / d)]) → f_{10}
  242. Translate(e_6, Vector[(v_4 * 16 / d)]) → g_{10}
  243. Translate(e_6, Vector[(v_4 * 17 / d)]) → h_{10}
  244. Translate(e_6, Vector[(v_4 * 18 / d)]) → i_{10}
  245. Translate(e_6, Vector[(v_4 * 19 / d)]) → j_{10}
  246. Intersect(g_9, k_9) → F_3
  247. Intersect(k_9, h_9) → G_3
  248. Intersect(l_9, h_9) → H_3
  249. Intersect(m_9, h_9) → I_3
  250. Intersect(n_9, h_9) → J_3
  251. Intersect(p_9, h_9) → K_3
  252. Intersect(q_9, h_9) → L_3
  253. Intersect(r_9, h_9) → M_3
  254. Intersect(s_9, h_9) → N_3
  255. Intersect(t_9, h_9) → O_3
  256. Intersect(a_{10}, h_9) → P_3
  257. Intersect(b_{10}, h_9) → Q_3
  258. Intersect(c_{10}, h_9) → R_3
  259. Intersect(d_{10}, h_9) → S_3
  260. Intersect(e_{10}, h_9) → T_3
  261. Intersect(f_{10}, h_9) → U_3
  262. Intersect(g_{10}, h_9) → V_3
  263. Intersect(h_{10}, h_9) → W_3
  264. Intersect(i_{10}, h_9) → Z_3
  265. Intersect(j_{10}, h_9) → A_4
  266. Intersect(j_{10}, g_9) → B_4
  267. Intersect(i_{10}, g_9) → C_4
  268. Intersect(h_{10}, g_9) → D_4
  269. Intersect(g_{10}, g_9) → E_4
  270. Intersect(f_{10}, g_9) → F_4
  271. Intersect(e_{10}, g_9) → G_4
  272. Intersect(d_{10}, g_9) → H_4
  273. Intersect(c_{10}, g_9) → I_4
  274. Intersect(b_{10}, g_9) → J_4
  275. Intersect(a_{10}, g_9) → K_4
  276. Intersect(t_9, g_9) → L_4
  277. Intersect(s_9, g_9) → M_4
  278. Intersect(r_9, g_9) → N_4
  279. Intersect(q_9, g_9) → O_4
  280. Intersect(p_9, g_9) → P_4
  281. Intersect(n_9, g_9) → Q_4
  282. Intersect(m_9, g_9) → R_4
  283. Intersect(l_9, g_9) → S_4
  284. Polygon(G_2, G_3, F_3, F_2) → poly21, g_{11}, g_{12}, f_{11}, f_{12}
  285. Polygon(G_3, H_3, S_4, F_3) → poly22, g_{13}, h_{11}, s_{10}, f_{13}
  286. Polygon(H_3, I_3, R_4, S_4) → poly23, h_{12}, i_{11}, r_{10}, s_{11}
  287. Polygon(I_3, J_3, Q_4, R_4) → poly24, i_{12}, j_{11}, q_{10}, r_{11}
  288. Polygon(J_3, K_3, P_4, Q_4) → poly25, j_{12}, k_{10}, p_{10}, q_{11}
  289. Polygon(K_3, L_3, O_4, P_4) → poly26, k_{11}, l_{10}, o_4, p_{11}
  290. Polygon(L_3, M_3, N_4, O_4) → poly27, l_{11}, m_{10}, n_{10}, o_5
  291. Polygon(M_3, N_3, M_4, N_4) → poly28, m_{11}, n_{11}, m_{12}, n_{12}
  292. Polygon(N_3, O_3, L_4, M_4) → poly29, n_{13}, o_6, l_{12}, m_{13}
  293. Polygon(O_3, P_3, K_4, L_4) → poly30, o_7, p_{12}, k_{12}, l_{13}
  294. Polygon(P_3, Q_3, J_4, K_4) → poly31, p_{13}, q_{12}, j_{13}, k_{13}
  295. Polygon(Q_3, R_3, I_4, J_4) → poly32, q_{13}, r_{12}, i_{13}, j_{14}
  296. Polygon(R_3, S_3, H_4, I_4) → poly33, r_{13}, s_{12}, h_{13}, i_{14}
  297. Polygon(S_3, T_3, G_4, H_4) → poly34, s_{13}, t_{10}, g_{14}, h_{14}
  298. Polygon(T_3, U_3, F_4, G_4) → poly35, t_{11}, u_5, f_{14}, g_{15}
  299. Polygon(U_3, V_3, E_4, F_4) → poly36, u_6, v_5, e_{11}, f_{15}
  300. Polygon(V_3, W_3, D_4, E_4) → poly37, v_6, w_4, d_{11}, e_{12}
  301. Polygon(W_3, Z_3, C_4, D_4) → poly38, w_5, z_4, c_{11}, d_{12}
  302. Polygon(Z_3, A_4, B_4, C_4) → poly39, z_5, a_{11}, b_{11}, c_{12}
  303. Polygon(A_4, I_2, H_2, B_4) → poly40, a_{12}, i_{15}, h_{15}, b_{12}