积极 AI Logo 积极 AI

等价分数圆面积模型演示

等价分数圆面积模型演示
几何画板及绘图内容加载中，请稍等……
2015-03-03 02:59
圆几何作图滑块动画
本范例通过圆面积模型展示等价分数的概念。核心数学概念包括分数相等、面积比例与圆周率的关系。作图要点涉及使用GeoGebra命令如Circle、CircleSector、Segment等构建圆面积模型，并利用Intersect命令验证等价性。适合小学高年级或初中数学课堂，用于直观理解分数与几何的关联。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 3) → c_6
  3. Point(xAxis) → C
  4. Circle(C, 1.5) → d
  5. OrthogonalLine(C, xAxis) → a_1
  6. Intersect(d, a_1, 2) → D
  7. Intersect(d, a_1, 1) → E
  8. OrthogonalLine(D, a_1) → e
  9. OrthogonalLine(E, a_1) → f
  10. Point(xAxis) → F
  11. OrthogonalLine(F, e) → g_2
  12. Intersect(e, g_2) → G
  13. Point(g_2) → H
  14. Intersect(c_6, yAxis, 1) → B
  15. Rotate(B, (360 * ° / b), A) → B'
  16. CircleSector(A, B, B') → k
  17. Rotate(B', (360 * ° / b), A) → B''
  18. Rotate(B'', (360 * ° / b), A) → B'''
  19. Rotate(B''', (360 * ° / b), A) → I
  20. Rotate(I, (360 * ° / b), A) → I'
  21. Rotate(I', (360 * ° / b), A) → I''
  22. Rotate(I'', (360 * ° / b), A) → I'''
  23. Rotate(I''', (360 * ° / b), A) → J
  24. Rotate(J, (360 * ° / b), A) → J'
  25. CircleSector(A, B', B'') → p
  26. CircleSector(A, B'', B''') → q
  27. CircleSector(A, B''', I) → r
  28. CircleSector(A, I, I') → s_6
  29. CircleSector(A, I', I'') → t
  30. CircleSector(A, I'', I''') → c_1
  31. CircleSector(A, I''', J) → f_1
  32. CircleSector(A, J, J') → k_1
  33. CircleSector(A, J', B) → p_1
  34. Segment(B, A) → i
  35. Segment(B', A) → j
  36. Segment(B'', A) → l
  37. Segment(B''', A) → m
  38. Segment(I, A) → n
  39. Segment(I', A) → b_1
  40. Segment(I'', A) → i_1
  41. Segment(I''', A) → j_1
  42. Segment(J, A) → l_1
  43. Segment(J', A) → m_1
  44. Circle(A, B) → q_1
  45. Rotate(B, (360 * ° / ((b * s))), A) → B'_1
  46. Rotate(B'_1, (360 * ° / ((b * s))), A) → K
  47. Rotate(K, (360 * ° / ((b * s))), A) → K'
  48. Rotate(K', (360 * ° / ((b * s))), A) → K''
  49. Rotate(B', (360 * ° / ((b * s))), A) → B''_1
  50. Rotate(B''_1, (360 * ° / ((b * s))), A) → L
  51. Rotate(L, (360 * ° / ((b * s))), A) → L'
  52. Rotate(L', (360 * ° / ((b * s))), A) → L''
  53. Rotate(B'', (360 * ° / ((b * s))), A) → B'''_1
  54. Rotate(B'''_1, (360 * ° / ((b * s))), A) → M
  55. Rotate(M, (360 * ° / ((b * s))), A) → M'
  56. Rotate(M', (360 * ° / ((b * s))), A) → M''
  57. Rotate(B''', (360 * ° / ((b * s))), A) → N
  58. Rotate(N, (360 * ° / ((b * s))), A) → N'
  59. Rotate(N', (360 * ° / ((b * s))), A) → N''
  60. Rotate(N'', (360 * ° / ((b * s))), A) → N'''
  61. Rotate(I, (360 * ° / ((b * s))), A) → I'_1
  62. Rotate(I'_1, (360 * ° / ((b * s))), A) → O
  63. Rotate(O, (360 * ° / ((b * s))), A) → O'
  64. Rotate(O', (360 * ° / ((b * s))), A) → O''
  65. Rotate(I', (360 * ° / ((b * s))), A) → I''_1
  66. Rotate(I''_1, (360 * ° / ((b * s))), A) → P
  67. Rotate(P, (360 * ° / ((b * s))), A) → P'
  68. Rotate(P', (360 * ° / ((b * s))), A) → P''
  69. Rotate(I'', (360 * ° / ((b * s))), A) → I'''_1
  70. Rotate(I'''_1, (360 * ° / ((b * s))), A) → Q
  71. Rotate(Q, (360 * ° / ((b * s))), A) → Q'
  72. Rotate(Q', (360 * ° / ((b * s))), A) → Q''
  73. Rotate(I''', (360 * ° / ((b * s))), A) → R
  74. Rotate(R, (360 * ° / ((b * s))), A) → R'
  75. Rotate(R', (360 * ° / ((b * s))), A) → R''
  76. Rotate(R'', (360 * ° / ((b * s))), A) → R'''
  77. Rotate(J, (360 * ° / ((b * s))), A) → J'_1
  78. Rotate(J'_1, (360 * ° / ((b * s))), A) → S
  79. Rotate(S, (360 * ° / ((b * s))), A) → S'
  80. Rotate(S', (360 * ° / ((b * s))), A) → S''
  81. Rotate(J', (360 * ° / ((b * s))), A) → J''
  82. Rotate(J'', (360 * ° / ((b * s))), A) → J'''
  83. Rotate(J''', (360 * ° / ((b * s))), A) → T
  84. Rotate(T, (360 * ° / ((b * s))), A) → T'
  85. Vector(B'_1, A) → u
  86. Translate(B'_1, Vector[(u * c)]) → U
  87. Circle(A, U) → r_1
  88. Segment(K, A) → n_1
  89. Segment(K', A) → s_1
  90. Segment(K'', A) → t_1
  91. Segment(B''_1, A) → a_2
  92. Segment(L, A) → b_2
  93. Segment(L', A) → c_2
  94. Segment(L'', A) → d_2
  95. Segment(B'''_1, A) → e_2
  96. Segment(M, A) → f_2
  97. Segment(M', A) → h_2
  98. Segment(M'', A) → i_2
  99. Segment(N, A) → j_2
  100. Segment(N', A) → k_2
  101. Segment(N'', A) → l_2
  102. Segment(N''', A) → m_2
  103. Segment(I'_1, A) → n_2
  104. Segment(O, A) → p_2
  105. Segment(O', A) → q_2
  106. Segment(O'', A) → r_2
  107. Segment(I''_1, A) → s_2
  108. Segment(P, A) → t_2
  109. Segment(P', A) → a_3
  110. Segment(P'', A) → b_3
  111. Segment(I'''_1, A) → c_3
  112. Segment(Q, A) → d_3
  113. Segment(Q', A) → e_3
  114. Segment(Q'', A) → f_3
  115. Segment(R, A) → g_3
  116. Segment(R', A) → h_3
  117. Segment(R'', A) → i_3
  118. Segment(R''', A) → j_3
  119. Segment(J'_1, A) → k_3
  120. Segment(S, A) → l_3
  121. Segment(S', A) → m_3
  122. Segment(S'', A) → n_3
  123. Segment(J'', A) → p_3
  124. Segment(J''', A) → q_3
  125. Segment(T, A) → r_3
  126. Segment(T', A) → s_3
  127. Intersect(r_1, n_1) → V,
  128. Intersect(r_1, s_1) → W,
  129. Intersect(r_1, t_1) → Z,
  130. Intersect(r_1, a_2) → A_1,
  131. Intersect(b_2, c_2) → B_1
  132. Intersect(r_1, b_2) → C_1,
  133. Intersect(r_1, c_2) → D_1,
  134. Intersect(r_1, d_2) → E_1,
  135. Intersect(r_1, e_2, 1) → F_1
  136. Intersect(r_1, f_2, 1) → G_1
  137. Intersect(r_1, h_2, 1) → H_1
  138. Intersect(r_1, i_2, 1) → I_1
  139. Intersect(r_1, j_2, 1) → J_1
  140. Intersect(r_1, k_2, 1) → K_1
  141. Intersect(r_1, l_2, 1) → L_1
  142. Intersect(r_1, m_2, 1) → M_1
  143. Intersect(r_1, n_2, 1) → N_1
  144. Intersect(r_1, p_2, 1) → O_1
  145. Intersect(r_1, q_2, 1) → P_1
  146. Intersect(r_1, r_2, 1) → Q_1
  147. Intersect(r_1, s_2, 1) → R_1
  148. Intersect(r_1, t_2, 1) → S_1
  149. Intersect(r_1, a_3, 1) → T_1
  150. Intersect(r_1, b_3, 1) → U_1
  151. Intersect(r_1, c_3, 1) → V_1
  152. Intersect(r_1, d_3, 1) → W_1
  153. Intersect(r_1, e_3, 1) → Z_1
  154. Intersect(r_1, f_3, 1) → A_2
  155. Intersect(r_1, g_3, 1) → B_2
  156. Intersect(r_1, h_3, 1) → C_2
  157. Intersect(r_1, i_3, 1) → D_2
  158. Intersect(r_1, j_3, 1) → E_2
  159. Intersect(r_1, k_3, 1) → F_2
  160. Intersect(r_1, l_3, 1) → G_2
  161. Intersect(r_1, m_3, 1) → H_2
  162. Intersect(r_1, n_3, 1) → I_2
  163. Intersect(r_1, p_3, 1) → J_2
  164. Intersect(r_1, q_3, 1) → K_2
  165. Intersect(r_1, r_3, 1) → L_2
  166. Intersect(r_1, s_3, 1) → M_2
  167. Segment(B'_1, U) → t_3
  168. Segment(K, V) → a_4
  169. Segment(K', W) → b_4
  170. Segment(K'', Z) → c_4
  171. Segment(B''_1, A_1) → d_4
  172. Segment(L, C_1) → e_4
  173. Segment(L', D_1) → f_4
  174. Segment(L'', E_1) → g_4
  175. Segment(B'''_1, F_1) → h_4
  176. Segment(M, G_1) → i_4
  177. Segment(M', H_1) → j_4
  178. Segment(M'', I_1) → k_4
  179. Segment(N, J_1) → l_4
  180. Segment(N', K_1) → m_4
  181. Segment(N'', L_1) → n_4
  182. Segment(N''', M_1) → p_4
  183. Segment(I'_1, N_1) → q_4
  184. Segment(O, O_1) → r_4
  185. Segment(O', P_1) → s_4
  186. Segment(O'', Q_1) → t_4
  187. Segment(I''_1, R_1) → a_5
  188. Segment(P, S_1) → b_5
  189. Segment(P', T_1) → c_5
  190. Segment(P'', U_1) → d_5
  191. Segment(I'''_1, V_1) → e_5
  192. Segment(Q, W_1) → f_5
  193. Segment(Q', Z_1) → g_5
  194. Segment(Q'', A_2) → h_5
  195. Segment(R, B_2) → i_5
  196. Segment(R', C_2) → j_5
  197. Segment(R'', D_2) → k_5
  198. Segment(R''', E_2) → l_5
  199. Segment(J'_1, F_2) → m_5
  200. Segment(S, G_2) → n_5
  201. Segment(S', H_2) → p_5
  202. Segment(S'', I_2) → q_5
  203. Segment(J'', J_2) → r_5
  204. Segment(J''', K_2) → s_5
  205. Segment(T, L_2) → t_5
  206. Segment(T', M_2) → a_6
  207. Circle(A, B) → h
  208. Segment(B, A) → d_1
  209. Intersect(r_1, d_1, 1) → N_2
  210. Segment(B, N_2) → e_1

AI 绘图提示语参考

画一个圆，然后在这个圆上画出多个扇形，表示等价分数。首先画一个半径为3的圆，接着画一个半径为1.5的圆，然后通过旋转和交点操作，生成多个扇形，每个扇形的角度是360度除以b的倍数，b是一个滑块控制的值。
以上提示语为根据原始绘图命令整理而来，仅供参考。