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等值分数 by Melissa

等值分数 by Melissa
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2020-01-29 02:21
函数几何作图
①本范例通过动态演示分数的等值关系，直观展示不同分数形式间的转换；②涉及核心数学概念包括分数的基本性质、等值分数的判定、几何图形的分割与组合；③构造过程中运用了线段、点、多边形等基本元素，通过拖动滑块观察分数变化，并利用文本标注解释原理；④适合初中数学教学，用于帮助学生理解抽象的分数概念，提升几何直观和数形结合能力。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Point(f) → C
  3. Point(f) → G
  4. Segment(B, K) → g
  5. Point(Circle[D_5, 2]) → E_5
  6. Polygon(D_5, E_5, F_5, G_5) → q1, d_5, e_5, f_5, g_5
  7. Point(Circle[P_5, 2]) → Q_5
  8. Polygon(P_5, Q_5, R_5, S_5) → q2, p_5, q_5, r_5, s_5
  9. Point(Circle[Z_5, 2]) → A_6
  10. Polygon(Z_5, A_6, B_6, C_6) → q3, z_5, a_6, b_6, c_6
  11. Point(Circle[D_6, 2]) → E_6
  12. Polygon(D_6, E_6, F_6, G_6) → q4, d_6, e_6, f_6, g_6
  13. Point(Circle[P_6, 3.7076237040084377]) → Q_6
  14. Point(Circle[Z_6, 6.692047753852707]) → A_7
  15. Polygon(Z_6, A_7, B_7, C_7) → q5, z_6, a_7, b_7, c_7
  16. Point(Circle[Z_7, 6.692047753852707]) → A_8
  17. Polygon(Z_7, A_8, B_8, C_8) → q5_1, z_1, a_1, b_1, c_1
  18. Point(Circle[Z_8, 6.692047753852707]) → A_9
  19. Polygon(Z_8, A_9, B_9, C_9) → q5_2, z_2, a_2, b_2, c_2
  20. Point(Circle[P_7, 2]) → Q_7
  21. Polygon(P_7, Q_7, R_7, S_7) → q2_1, p_1, q_1, r_1, s_1
  22. Point(Circle[P_8, 2]) → Q_8
  23. Polygon(P_8, Q_8, R_8, S_8) → q2_2, p_2, q_2, r_2, s_2
  24. Point(Circle[P_9, 2]) → Q_9
  25. Polygon(P_9, Q_9, R_9, S_9) → q2_3, p_3, q_3, r_3, s_3
  26. Point(Circle[D_7, 2]) → E_7
  27. Polygon(D_7, E_7, F_7, G_7) → q1_1, d_1, e_1, f_1, g_1
  28. Point(Circle[Z_9, 2]) → A_{10}
  29. Polygon(Z_9, A_{10}, B_{10}, C_{10}) → q3_1, z_3, a_3, b_3, c_3
  30. Point(Circle[Z_{10}, 2]) → A_{11}
  31. Polygon(Z_{10}, A_{11}, B_{11}, C_{11}) → q3_2, z_4, a_4, b_4, c_4
  32. Point(Circle[Z_{11}, 2]) → A_{12}
  33. Polygon(Z_{11}, A_{12}, B_{12}, C_{12}) → q3_3, z_7, a_5, b_5, c_5
  34. Point(Circle[Z_{12}, 2]) → A_{13}
  35. Polygon(Z_{12}, A_{13}, B_{13}, C_{13}) → q3_4, z_8, a_8, b_8, c_8
  36. Point(Circle[Z_{13}, 2]) → A_{14}
  37. Polygon(Z_{13}, A_{14}, B_{14}, C_{14}) → q3_5, z_9, a_9, b_9, c_9
  38. Point(Circle[Z_{14}, 2]) → A_{15}
  39. Polygon(Z_{14}, A_{15}, B_{15}, C_{15}) → q3_6, z_{10}, a_{10}, b_{10}, c_{10}
  40. Point(Circle[Z_{15}, 2]) → A_{16}
  41. Polygon(Z_{15}, A_{16}, B_{16}, C_{16}) → q3_7, z_{11}, a_{11}, b_{11}, c_{11}
  42. Point(Circle[D_8, 2]) → E_8
  43. Polygon(D_8, E_8, F_8, G_8) → q4_1, d_2, e_2, f_2, g_2
  44. Point(Circle[D_9, 2]) → E_9
  45. Polygon(D_9, E_9, F_9, G_9) → q4_2, d_3, e_3, f_3, g_3
  46. Point(Circle[D_{10}, 2]) → E_{10}
  47. Polygon(D_{10}, E_{10}, F_{10}, G_{10}) → q4_3, d_4, e_4, f_4, g_4
  48. Point(Circle[D_{11}, 2]) → E_{11}
  49. Polygon(D_{11}, E_{11}, F_{11}, G_{11}) → q4_4, d_7, e_7, f_7, g_7
  50. Point(Circle[D_{12}, 2]) → E_{12}
  51. Polygon(D_{12}, E_{12}, F_{12}, G_{12}) → q4_5, d_8, e_8, f_8, g_8
  52. Point(Circle[D_{13}, 2]) → E_{13}
  53. Polygon(D_{13}, E_{13}, F_{13}, G_{13}) → q4_6, d_9, e_9, f_9, g_9
  54. Point(Circle[D_{14}, 2]) → E_{14}
  55. Polygon(D_{14}, E_{14}, F_{14}, G_{14}) → q4_7, d_{10}, e_{10}, f_{10}, g_{10}
  56. Point(Circle[D_{15}, 2]) → E_{15}
  57. Polygon(D_{15}, E_{15}, F_{15}, G_{15}) → q4_8, d_{11}, e_{11}, f_{11}, g_{11}
  58. Point(Circle[D_{16}, 2]) → E_{16}
  59. Polygon(D_{16}, E_{16}, F_{16}, G_{16}) → q4_9, d_{12}, e_{12}, f_{12}, g_{12}
  60. Point(Circle[I_7, 3.318493038763244]) → J_7
  61. Polygon(I_7, J_7, K_7, I_8) → q6, i_7, j_7, k_7, i_8
  62. Point(Circle[I_9, 3.318493038763244]) → J_8
  63. Polygon(I_9, J_8, K_8, I_{10}) → q6_1, i_1, j_1, k_1, i_2
  64. Point(Circle[I_{11}, 3.318493038763244]) → J_9
  65. Polygon(I_{11}, J_9, K_9, I_{12}) → q6_2, i_3, j_2, k_2, i_4
  66. Point(Circle[I_{13}, 3.318493038763244]) → J_{10}
  67. Polygon(I_{13}, J_{10}, K_{10}, I_{14}) → q6_3, i_5, j_3, k_3, i_6
  68. Point(Circle[I_{15}, 3.318493038763244]) → J_{11}
  69. Polygon(I_{15}, J_{11}, K_{11}, I_{16}) → q6_4, i_9, j_4, k_4, i_{10}
  70. Point(Circle[I_{17}, 3.318493038763244]) → J_{12}
  71. Polygon(I_{17}, J_{12}, K_{12}, I_{18}) → q6_5, i_{11}, j_5, k_5, i_{12}
  72. Point(Circle[P_{10}, 4]) → Q_{10}
  73. Polygon(P_{10}, Q_{10}, R_{10}, S_{10}) → q7, p_{10}, q_{10}, r_{10}, s_{10}
  74. Point(Circle[P_{11}, 4]) → Q_{11}
  75. Polygon(P_{11}, Q_{11}, R_{11}, S_{11}) → q7_1, p_4, q_4, r_4, s_4
  76. Point(Circle[P_{12}, 4]) → Q_{12}
  77. Polygon(P_{12}, Q_{12}, R_{12}, S_{12}) → q7_2, p_6, q_6, r_6, s_6
  78. Point(Circle[P_{13}, 4]) → Q_{13}
  79. Polygon(P_{13}, Q_{13}, R_{13}, S_{13}) → q7_3, p_7, q_7, r_7, s_7
  80. Point(Circle[P_{14}, 4]) → Q_{14}
  81. Polygon(P_{14}, Q_{14}, R_{14}, S_{14}) → q7_4, p_8, q_8, r_8, s_8
  82. Point(Circle[J_{14}, 2.8477655083416864]) → K_{14}
  83. Polygon(J_{14}, K_{14}, H_{15}, J_{15}) → q8, j_{14}, k_{14}, h_{15}, j_{15}
  84. Point(Circle[J_{13}, 2.8477655083416864]) → K_{13}
  85. Polygon(J_{13}, K_{13}, H_{13}, J_{16}) → q8_1, j_6, k_6, h_1, j_8
  86. Point(Circle[J_{17}, 2.8477655083416864]) → K_{15}
  87. Polygon(J_{17}, K_{15}, H_{14}, J_{18}) → q8_2, j_9, k_8, h_2, j_{10}
  88. Point(Circle[J_{19}, 2.8477655083416864]) → K_{16}
  89. Polygon(J_{19}, K_{16}, H_{16}, J_{20}) → q8_3, j_{11}, k_9, h_3, j_{12}
  90. Point(Circle[J_{21}, 2.8477655083416864]) → K_{17}
  91. Polygon(J_{21}, K_{17}, H_{17}, J_{22}) → q8_4, j_{16}, k_{10}, h_4, j_{13}
  92. Point(Circle[J_{23}, 2.8477655083416864]) → K_{18}
  93. Polygon(J_{23}, K_{18}, H_{18}, J_{24}) → q8_5, j_{17}, k_{11}, h_5, j_{18}
  94. Point(Circle[J_{25}, 2.8477655083416864]) → K_{19}
  95. Polygon(J_{25}, K_{19}, H_{19}, J_{26}) → q8_6, j_{19}, k_{12}, h_6, j_{20}
  96. Point(Circle[P_{15}, 2.2024410791962357]) → Q_{15}
  97. Polygon(P_{15}, Q_{15}, R_{15}, S_{15}) → q9, p_{15}, q_{15}, r_{15}, s_{15}
  98. Point(Circle[P_{16}, 2.2024410791962357]) → Q_{16}
  99. Polygon(P_{16}, Q_{16}, R_{16}, S_{16}) → q9_1, p_9, q_9, r_9, s_9
  100. Point(Circle[P_{17}, 2.2024410791962357]) → Q_{17}
  101. Polygon(P_{17}, Q_{17}, R_{17}, S_{17}) → q9_2, p_{11}, q_{11}, r_{11}, s_{11}
  102. Point(Circle[P_{18}, 2.2024410791962357]) → Q_{18}
  103. Polygon(P_{18}, Q_{18}, R_{18}, S_{18}) → q9_3, p_{12}, q_{12}, r_{12}, s_{12}
  104. Point(Circle[P_{19}, 2.2024410791962357]) → Q_{19}
  105. Polygon(P_{19}, Q_{19}, R_{19}, S_{19}) → q9_4, p_{13}, q_{13}, r_{13}, s_{13}
  106. Point(Circle[P_{20}, 2.2024410791962357]) → Q_{20}
  107. Polygon(P_{20}, Q_{20}, R_{20}, S_{20}) → q9_5, p_{14}, q_{14}, r_{14}, s_{14}
  108. Point(Circle[P_{21}, 2.2024410791962357]) → Q_{21}
  109. Polygon(P_{21}, Q_{21}, R_{21}, S_{21}) → q9_6, p_{16}, q_{16}, r_{16}, s_{16}
  110. Point(Circle[P_{22}, 2.2024410791962357]) → Q_{22}
  111. Polygon(P_{22}, Q_{22}, R_{22}, S_{22}) → q9_7, p_{17}, q_{17}, r_{17}, s_{17}
  112. Point(Circle[P_{23}, 2.2024410791962357]) → Q_{23}
  113. Polygon(P_{23}, Q_{23}, R_{23}, S_{23}) → q9_8, p_{18}, q_{18}, r_{18}, s_{18}
  114. Point(Circle[Z_{16}, 20]) → A_{17}
  115. Polygon(Z_{16}, A_{17}, B_{17}, C_{17}) → q10, z_{16}, a_{17}, b_{17}, c_{17}