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Decimal and Fraction Visualiser

Decimal and Fraction Visualiser
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2020-04-01 03:11
FunctionCoordinate GeometryOptimizationGeometric ConstructionSlider Animation
This example demonstrates the conversion relationship and geometric representation between decimals and fractions. It involves core math concepts like decimals, fractions, function graphs, scatter plots, and linear programming. Construction highlights include using GeoGebra commands such as Point, Polygon, and Circle to build basic geometric shapes and function images. Suitable for middle school and above mathematics education to understand the connection between numerical representation and geometric models.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a geometric visualization showing the conversion relationship between decimals and fractions, featuring multiple squares and triangles arranged along the x and y axes, representing decimal places like using four small squares for tenths, five for twentieths, etc., with higher decimals shown by more squares, and include connecting lines to illustrate the function relationships and the connection between geometric models and numerical representations.
The prompt above was compiled from the original drawing commands and is for reference only.