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十进制与分数可视化器

十进制与分数可视化器
几何画板及绘图内容加载中，请稍等……
2020-04-01 03:11
函数解析几何最值优化几何作图滑块动画
①本范例演示了十进制与分数之间的转换关系及几何表示；②涉及核心数学概念包括十进制、分数、函数图像、散点图、线性规划；③作图要点：使用了点、多边形、圆等GeoGebra命令，构建了基本几何图形和函数图像；④适合初中及以上数学教学，用于理解数值表示与几何模型的关联。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. Polygon(A, B, C, D) → q1, a, b, c, d
  5. Point(xAxis) → E
  6. Point(xAxis) → H
  7. Polygon(F, I, J, G) → tenths2, f_1, i, j, g_1
  8. Polygon(I, K, L, J) → tenths3, i_1, k, l, j_1
  9. Polygon((7, 1.5), (7, 2), (12, 2), (12, 1.5)) → tenths4, s, tenths4_1, h_1, k_1
  10. Polygon((7, 2.5), (7, 3), (12, 3), (12, 2.5)) → tenths6, m, p, q, r
  11. Polygon((7, 2), (7, 2.5), (12, 2.5), (12, 2)) → tenths5, l_1, m_1, n_1, p_1
  12. Polygon((7, 4), (7, 4.5), (12, 4.5), (12, 4)) → tenths9, q_1, r_1, s_1, t_1
  13. Polygon((7, 4.5), (7, 5), (12, 5), (12, 4.5)) → tenths10, a_1, b_1, c_1, d_1
  14. Polygon((7, 3.5), (7, 4), (12, 4), (12, 3.5)) → tenths8, e_1, f_2, g_2, h_2
  15. Polygon((7, 3), (7, 3.5), (12, 3.5), (12, 3)) → tenths7, i_2, j_2, k_2, l_2
  16. Polygon((14.5, 0.5), (14.5, 1), 4) → poly11
  17. Polygon((15, 0.5), (15, 1), 4) → poly12
  18. Polygon((15.5, 0.5), (15.5, 1), 4) → poly13
  19. Polygon((16, 0.5), (16, 1), 4) → poly14
  20. Polygon((16.5, 0.5), (16.5, 1), 4) → poly15
  21. Polygon((17, 0.5), (17, 1), 4) → poly16
  22. Polygon((17.5, 0.5), (17.5, 1), 4) → poly17
  23. Polygon((18, 0.5), (18, 1), 4) → poly18
  24. Polygon((18.5, 0.5), (18.5, 1), 4) → poly19
  25. Polygon((14.5, 1), (14.5, 1.5), 4) → poly20
  26. Polygon((19, 0.5), (19, 1), 4) → poly21
  27. Polygon((15, 1), (15, 1.5), 4) → poly22
  28. Polygon((15.5, 1), (15.5, 1.5), 4) → poly23
  29. Polygon((116, 1), (116, 1.5), 4) → poly24
  30. Polygon((16, 1), (16, 1.5), 4) → poly25
  31. Polygon((16.5, 1), (16.5, 1.5), 4) → poly26
  32. Polygon((17, 1), (17, 1.5), 4) → poly27
  33. Polygon((17.5, 1), (17.5, 1.5), 4) → poly28
  34. Polygon((18, 1), (18, 1.5), 4) → poly29
  35. Polygon((18.5, 1), (18.5, 1.5), 4) → poly30
  36. Polygon((19, 1), (19, 1.5), 4) → poly31
  37. Polygon((14.5, 1.5), (14.5, 2), 4) → poly32
  38. Polygon((15, 1.5), (15, 2), 4) → poly32_1
  39. Polygon((15.5, 1.5), (15.5, 2), 4) → poly32_2
  40. Polygon((16, 1.5), (16, 2), 4) → poly32_3
  41. Polygon((16.5, 1.5), (16.5, 2), 4) → poly32_4
  42. Polygon((17, 1.5), (17, 2), 4) → poly32_5
  43. Polygon((17.5, 1.5), (17.5, 2), 4) → poly32_6
  44. Polygon((18, 1.5), (18, 2), 4) → poly32_7
  45. Polygon((18.5, 1.5), (18.5, 2), 4) → poly32_8
  46. Polygon((19, 1.5), (19, 2), 4) → poly32_9
  47. Polygon((14.5, 2), (14.5, 2.5), 4) → poly32_{10}
  48. Polygon((15, 2), (15, 2.5), 4) → poly32_{11}
  49. Polygon((15.5, 2), (15.5, 2.5), 4) → poly32_{12}
  50. Polygon((16, 2), (16, 2.5), 4) → poly32_{13}
  51. Polygon((16.5, 2), (16.5, 2.5), 4) → poly32_{14}
  52. Polygon((17, 2), (17, 2.5), 4) → poly32_{15}
  53. Polygon((17.5, 2), (17.5, 2.5), 4) → poly32_{16}
  54. Polygon((18, 2), (18, 2.5), 4) → poly32_{17}
  55. Polygon((18.5, 2), (18.5, 2.5), 4) → poly32_{18}
  56. Polygon((19, 2.0000000000000004), (19, 2.5000000000000004), 4) → poly32_{19}
  57. Polygon((14.5, 2.5), (14.5, 3), 4) → poly32_{20}
  58. Polygon((15, 2.5), (15, 3), 4) → poly32_{21}
  59. Polygon((15.5, 2.5), (15.5, 3), 4) → poly32_{22}
  60. Polygon((16, 2.5), (16, 3), 4) → poly32_{23}
  61. Polygon((16.5, 2.5), (16.5, 3), 4) → poly32_{24}
  62. Polygon((17, 2.5), (17, 3), 4) → poly32_{25}
  63. Polygon((17.5, 2.5), (17.5, 3), 4) → poly32_{26}
  64. Polygon((18, 2.5), (18, 3), 4) → poly32_{27}
  65. Polygon((18.5, 2.5), (18.5, 3), 4) → poly32_{28}
  66. Polygon((19, 2.5), (19, 3), 4) → poly32_{29}
  67. Polygon((14.5, 3), (14.5, 3.5), 4) → poly32_{30}
  68. Polygon((15, 3), (15, 3.5), 4) → poly32_{31}
  69. Polygon((15.5, 3), (15.5, 3.5), 4) → poly32_{32}
  70. Polygon((16, 3), (16, 3.5), 4) → poly32_{33}
  71. Polygon((16.5, 3), (16.5, 3.5), 4) → poly32_{34}
  72. Polygon((17, 3), (17, 3.5), 4) → poly32_{35}
  73. Polygon((17.5, 3), (17.5, 3.5), 4) → poly32_{36}
  74. Polygon((18, 3.0000000000000004), (18, 3.5000000000000004), 4) → poly32_{37}
  75. Polygon((18.5, 3), (18.5, 3.5), 4) → poly32_{38}
  76. Polygon((19, 3), (19, 3.5), 4) → poly32_{39}
  77. Polygon((14.5, 3.5), (14.5, 4), 4) → poly32_{40}
  78. Polygon((15, 3.5), (15, 4), 4) → poly32_{41}
  79. Polygon((15.5, 3.5), (15.5, 4), 4) → poly32_{42}
  80. Polygon((16, 3.5), (16, 4), 4) → poly32_{43}
  81. Polygon((16.5, 3.5), (16.5, 4), 4) → poly32_{44}
  82. Polygon((17, 3.5), (17, 4), 4) → poly32_{45}
  83. Polygon((17.5, 3.5), (17.5, 4), 4) → poly32_{46}
  84. Polygon((18, 3.5), (18, 4), 4) → poly32_{47}
  85. Polygon((18.5, 3.5), (18.5, 4), 4) → poly32_{48}
  86. Polygon((19, 3.5), (19, 4), 4) → poly32_{49}
  87. Polygon((14.5, 4), (14.5, 4.5), 4) → poly32_{50}
  88. Polygon((15, 4), (15, 4.5), 4) → poly32_{51}
  89. Polygon((15.5, 4), (15.5, 4.5), 4) → poly32_{52}
  90. Polygon((16, 4), (16, 4.5), 4) → poly32_{53}
  91. Polygon((16.5, 4), (16.5, 4.5), 4) → poly32_{54}
  92. Polygon((17, 4), (17, 4.5), 4) → poly32_{55}
  93. Polygon((17.5, 4.000000000000001), (17.5, 4.500000000000001), 4) → poly32_{56}
  94. Polygon((18, 4), (18, 4.5), 4) → poly32_{57}
  95. Polygon((18.5, 4.000000000000001), (18.5, 4.500000000000001), 4) → poly32_{58}
  96. Polygon((19, 4.000000000000001), (19, 4.500000000000001), 4) → poly32_{59}
  97. Polygon((14.5, 4.5), (14.5, 5), 4) → poly32_{60}
  98. Polygon((15, 4.5), (15, 5), 4) → poly32_{61}
  99. Polygon((15.5, 4.5), (15.5, 5), 4) → poly32_{62}
  100. Polygon((16, 4.5), (16, 5), 4) → poly32_{63}
  101. Polygon((16.5, 4.5), (16.5, 5), 4) → poly32_{64}
  102. Polygon((17, 4.5), (17, 5), 4) → poly32_{65}
  103. Polygon((17.5, 4.5), (17.5, 5), 4) → poly32_{66}
  104. Polygon((18, 4.5), (18, 5), 4) → poly32_{67}
  105. Polygon((18.5, 4.5), (18.5, 5), 4) → poly32_{68}
  106. Polygon((19, 4.5), (19, 5), 4) → poly32_{69}
  107. Polygon((15, 0), (15, 0.5), (14.5, 0.5), (14.5, 0)) → H2, q_2, r_2, s_2, t_2
  108. Polygon((15, 0), (15, 0.5), (15.5, 0.5), (15.5, 0)) → H3, a_2, b_2, c_2, d_2
  109. Polygon((16, 0), (16, 0.5), (15.5, 0.5), (15.5, 0)) → H4, e_2, f_3, g_3, h_3
  110. Polygon((16, 0), (16, 0.5), (16.5, 0.5), (16.5, 0)) → H5, i_3, j_3, k_3, l_3
  111. Polygon((17, 0), (17, 0.5), (16.5, 0.5), (16.5, 0)) → H6, m_3, n_3, p_3, q_3
  112. Polygon((17, 0), (17, 0.5), (17.5, 0.5), (17.5, 0)) → H7, r_3, s_3, t_3, a_3
  113. Polygon((18, 0), (18, 0.5), (17.5, 0.5), (17.5, 0)) → H8, b_3, c_3, d_3, e_3
  114. Polygon((18, 0), (18, 0.5), (18.5, 0.5), (18.5, 0)) → H9, f_4, g_4, h_4, i_4
  115. Polygon((19, 0), (19, 0.5), (18.5, 0.5), (18.5, 0)) → H10, j_4, k_4, l_4, m_4
  116. Polygon(G, F, E, H) → tenths1, g_5, f_5, e, h_5
  117. Circle(M, 0.1) → c_4
  118. Point(Circle[O, 0.5]) → P
  119. Polygon(O, P, Q, R) → H1, o, p_2, q_4, r_4

AI 绘图提示语参考

画一个几何图形来展示小数和分数的转换关系，包含多个正方形和三角形，这些形状沿着x轴和y轴排列，形成小数位数的视觉表示，例如用四个小正方形表示十分之一，五个表示二十分之一，以此类推，更高的小数用更多正方形表示，同时包含一些连接这些形状的线条，以展示函数关系和几何模型之间的联系。
以上提示语为根据原始绘图命令整理而来，仅供参考。