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分数域演示

分数域演示
几何画板及绘图内容加载中，请稍等……
2019-01-21 05:31
函数解析几何复数几何作图滑块动画
①本范例演示分数域的构建过程与性质；②涉及核心数学概念包括分数、集合论、统计、金字塔、阶跃函数和连续性；③作图要点：运用了Element, Polygon, Textfield, Sequence, Sum, If, FractionText等GeoGebra命令与对象，如CheckPolyPt2, step3Verify等；④适合高中及以上数学学习者，用于理解抽象代数与数论中的分数域概念。

GeoGebra 命令及参数

  1. Element({3, 3, 4, 3, 6, 6, 3, 3, 5, 6, 4, 4}, prob) → plantDenom
  2. Element({1, 2, 3, 1, 5, 1, 2, 2, 3, 5, 3, 3}, prob) → plantNum
  3. Element({4, 6, 2, 5, 3, 4, 4, 5, 4, 3, 4, 6}, prob) → plowDenom
  4. Element({1, 1, 1, 4, 1, 3, 3, 4, 3, 2, 3, 5}, prob) → plowNum
  5. Polygon(Step2ArrowsPt + (0, 0.2), Step2ArrowsPt + (0.3, 0.2), Step2ArrowsPt + (0.15, 0.6)) → step2arrowUp, step2arrowSeg_5, step2arrowSeg, step2arrowSeg_2
  6. Polygon(Step2ArrowsPt + (0, -0.2), Step2ArrowsPt + (0.3, -0.2), Step2ArrowsPt + (0.15, -0.6)) → step2arrowDown, step2arrowSeg_1, step2arrowSeg_3, step2arrowSeg_4
  7. Element({"Ted", "Anna", "Jasmine", "Miguel", "Alessia", "Mohammad", "Meredith", "Jasper", "Elinor", "Doug", "Raul", "Maria"}, prob) → names
  8. Textfield(inputNum) → inputBoxNum
  9. Textfield(inputDenom) → inputBoxDenom
  10. Element({"blueberries", "pumpkins", "blackberries", "tomatoes", "strawberries", "corn"}, crop) → cropName
  11. Polygon(BoxPt, BoxPt + (fieldWidth, 0), BoxPt + (fieldWidth, fieldHeight), BoxPt + (0, fieldHeight)) → field, fieldSeg_1, fieldSeg_2, fieldSeg_3, fieldSeg
  12. Polygon(Step1ArrowsPt + (-0.1, 0), Step1ArrowsPt + (-0.1, 0.5), Step1ArrowsPt + (-0.3, 0.25)) → step1arrowLeft, step1arrowSeg_1, step1arrowSeg_2, step1arrowSeg_3
  13. Polygon(Step1ArrowsPt + (0.1, 0), Step1ArrowsPt + (0.1, 0.5), Step1ArrowsPt + (0.3, 0.25)) → step1arrowsRt, step1arrowSeg_4, step1arrowSeg_5, step1arrowSeg
  14. Sequence(Segment[BoxPt + ((i * fieldWidth / columns), 0), BoxPt + ((i * fieldWidth / columns), fieldHeight)], i, x(BoxPt), columns - 1) → plowDivisions
  15. Polygon(BoxPt, BoxPt + (fieldWidth / columns, 0), BoxPt + (fieldWidth / columns, fieldHeight), BoxPt + (0, fieldHeight)) → plow1, plowPartSeg_{24}, plowPartSeg_{21}, plowPartSeg_{25}, plowPartSeg_{27}
  16. Polygon(BoxPt + (fieldWidth / columns, 0), BoxPt + ((2 * fieldWidth / columns), 0), BoxPt + ((2 * fieldWidth / columns), fieldHeight), BoxPt + (fieldWidth / columns, fieldHeight)) → plow2, plowPartSeg_{29}, plowPartSeg_{31}, plowPartSeg_3, plowPartSeg_5
  17. Polygon(BoxPt + ((2 * fieldWidth / columns), 0), BoxPt + ((3 * fieldWidth / columns), 0), BoxPt + ((3 * fieldWidth / columns), fieldHeight), BoxPt + ((2 * fieldWidth / columns), fieldHeight)) → plow3, plowPartSeg_7, plowPartSeg_9, plowPartSeg_{11}, plowPartSeg_{13}
  18. Polygon(BoxPt + ((3 * fieldWidth / columns), 0), BoxPt + ((4 * fieldWidth / columns), 0), BoxPt + ((4 * fieldWidth / columns), fieldHeight), BoxPt + ((3 * fieldWidth / columns), fieldHeight)) → plow4, plowPartSeg_{15}, plowPartSeg_{17}, plowPartSeg_{19}, plowPartSeg_{33}
  19. Polygon(BoxPt + ((4 * fieldWidth / columns), 0), BoxPt + ((5 * fieldWidth / columns), 0), BoxPt + ((5 * fieldWidth / columns), fieldHeight), BoxPt + ((4 * fieldWidth / columns), fieldHeight)) → plow5, plowPartSeg_{35}, plowPartSeg_{37}, plowPartSeg_{39}, plowPartSeg_1
  20. Polygon(BoxPt + ((5 * fieldWidth / columns), 0), BoxPt + ((6 * fieldWidth / columns), 0), BoxPt + ((6 * fieldWidth / columns), fieldHeight), BoxPt + ((5 * fieldWidth / columns), fieldHeight)) → plow6, plowPartSeg_{22}, plowPartSeg_{26}, plowPartSeg_{28}, plowPartSeg_{30}
  21. Polygon(BoxPt + ((6 * fieldWidth / columns), 0), BoxPt + ((7 * fieldWidth / columns), 0), BoxPt + ((7 * fieldWidth / columns), fieldHeight), BoxPt + ((6 * fieldWidth / columns), fieldHeight)) → plow7, plowPartSeg_{32}, plowPartSeg_4, plowPartSeg_6, plowPartSeg_8
  22. Polygon(BoxPt + ((7 * fieldWidth / columns), 0), BoxPt + ((8 * fieldWidth / columns), 0), BoxPt + ((8 * fieldWidth / columns), fieldHeight), BoxPt + ((7 * fieldWidth / columns), fieldHeight)) → plow8, plowPartSeg_{10}, plowPartSeg_{12}, plowPartSeg_{14}, plowPartSeg_{16}
  23. Polygon(BoxPt + ((8 * fieldWidth / columns), 0), BoxPt + ((9 * fieldWidth / columns), 0), BoxPt + ((9 * fieldWidth / columns), fieldHeight), BoxPt + ((8 * fieldWidth / columns), fieldHeight)) → plow9, plowPartSeg_{18}, plowPartSeg_{20}, plowPartSeg_{34}, plowPartSeg_{36}
  24. Polygon(BoxPt + ((9 * fieldWidth / columns), 0), BoxPt + ((10 * fieldWidth / columns), 0), BoxPt + ((10 * fieldWidth / columns), fieldHeight), BoxPt + ((9 * fieldWidth / columns), fieldHeight)) → plow10, plowPartSeg_{38}, plowPartSeg, plowPartSeg_2, plowPartSeg_{23}
  25. Sum({If[plow1select, 1, 0], If[plow2select, 1, 0], If[plow3select, 1, 0], If[plow4select, 1, 0], If[plow5select, 1, 0], If[plow6select, 1, 0], If[plow7select, 1, 0], If[plow8select, 1, 0], If[plow9select, 1, 0], If[plow10select, 1, 0]}) → plowCount
  26. If(plowCount / columns ≟ plowNum / plowDenom, true, false) → step1Verify
  27. Sequence(Segment[BoxPt + (0, (i * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows1
  28. Sequence(Segment[BoxPt + (fieldWidth / columns, (i * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows2
  29. Sequence(Segment[BoxPt + ((2 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows3
  30. Sequence(Segment[BoxPt + ((3 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows4
  31. Sequence(Segment[BoxPt + ((4 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows5
  32. Sequence(Segment[BoxPt + ((5 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows6
  33. Sequence(Segment[BoxPt + ((6 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows7
  34. Sequence(Segment[BoxPt + ((7 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows8
  35. Sequence(Segment[BoxPt + ((8 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows9
  36. Sequence(Segment[BoxPt + ((9 * fieldWidth / columns), (i * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantRows10
  37. Polygon(BoxPt, BoxPt + (fieldWidth / columns, 0), BoxPt + (fieldWidth / columns, fieldHeight / rows), BoxPt + (0, fieldHeight / rows)) → plantC1R1, boxpt, b, c, d
  38. Polygon(BoxPt + (0, fieldHeight / rows), BoxPt + (fieldWidth / columns, fieldHeight / rows), BoxPt + (fieldWidth / columns, (2 * fieldHeight / rows)), BoxPt + (0, (2 * fieldHeight / rows))) → plantC1R2, e, f, g, h
  39. Polygon(BoxPt + (0, (2 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (2 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (3 * fieldHeight / rows)), BoxPt + (0, (3 * fieldHeight / rows))) → plantC1R3, i, j, k, l
  40. Polygon(BoxPt + (0, (3 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (3 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (4 * fieldHeight / rows)), BoxPt + (0, (4 * fieldHeight / rows))) → plantC1R4, m, n, p, q
  41. Polygon(BoxPt + (0, (4 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (4 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (5 * fieldHeight / rows)), BoxPt + (0, (5 * fieldHeight / rows))) → plantC1R5, r, s, t, a_1
  42. Sum({If[plantSelectC1R1, 1, 0], If[plantSelectC1R2, 1, 0], If[plantSelectC1R3, 1, 0], If[plantSelectC1R4, 1, 0], If[plantSelectC1R5, 1, 0], If[plantSelectC1R6, 1, 0], If[plantSelectC1R7, 1, 0], If[plantSelectC1R8, 1, 0], If[plantSelectC2R1, 1, 0], If[plantSelectC2R2, 1, 0], If[plantSelectC2R3, 1, 0], If[plantSelectC2R4, 1, 0], If[plantSelectC2R5, 1, 0], If[plantSelectC2R6, 1, 0], If[plantSelectC2R7, 1, 0], If[plantSelectC2R8, 1, 0], If[plantSelectC3R1, 1, 0], If[plantSelectC3R2, 1, 0], If[plantSelectC3R3, 1, 0], If[plantSelectC3R4, 1, 0], If[plantSelectC3R5, 1, 0], If[plantSelectC3R6, 1, 0], If[plantSelectC3R7, 1, 0], If[plantSelectC3R8, 1, 0], If[plantSelectC4R1, 1, 0], If[plantSelectC4R2, 1, 0], If[plantSelectC4R3, 1, 0], If[plantSelectC4R4, 1, 0], If[plantSelectC4R5, 1, 0], If[plantSelectC4R6, 1, 0], If[plantSelectC4R7, 1, 0], If[plantSelectC4R8, 1, 0], If[plantSelectC5R1, 1, 0], If[plantSelectC5R2, 1, 0], If[plantSelectC5R3, 1, 0], If[plantSelectC5R4, 1, 0], If[plantSelectC5R5, 1, 0], If[plantSelectC5R6, 1, 0], If[plantSelectC5R7, 1, 0], If[plantSelectC5R8, 1, 0], If[plantSelectC6R1, 1, 0], If[plantSelectC6R2, 1, 0], If[plantSelectC6R3, 1, 0], If[plantSelectC6R4, 1, 0], If[plantSelectC6R5, 1, 0], If[plantSelectC6R6, 1, 0], If[plantSelectC6R7, 1, 0], If[plantSelectC6R8, 1, 0], If[plantSelectC7R1, 1, 0], If[plantSelectC7R2, 1, 0], If[plantSelectC7R3, 1, 0], If[plantSelectC7R4, 1, 0], If[plantSelectC7R5, 1, 0], If[plantSelectC7R6, 1, 0], If[plantSelectC7R7, 1, 0], If[plantSelectC7R8, 1, 0], If[plantSelectC8R1, 1, 0], If[plantSelectC8R2, 1, 0], If[plantSelectC8R3, 1, 0], If[plantSelectC8R4, 1, 0], If[plantSelectC8R5, 1, 0], If[plantSelectC8R6, 1, 0], If[plantSelectC8R7, 1, 0], If[plantSelectC8R8, 1, 0], If[plantSelectC9R1, 1, 0], If[plantSelectC9R2, 1, 0], If[plantSelectC9R3, 1, 0], If[plantSelectC9R4, 1, 0], If[plantSelectC9R5, 1, 0], If[plantSelectC9R6, 1, 0], If[plantSelectC9R7, 1, 0], If[plantSelectC9R8, 1, 0], If[plantSelectC10R1, 1, 0], If[plantSelectC10R2, 1, 0], If[plantSelectC10R3, 1, 0], If[plantSelectC10R4, 1, 0], If[plantSelectC10R5, 1, 0], If[plantSelectC10R6, 1, 0], If[plantSelectC10R7, 1, 0], If[plantSelectC10R8, 1, 0]}) → plantCount
  43. Polygon(BoxPt + (0, (5 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (5 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (6 * fieldHeight / rows)), BoxPt + (0, (6 * fieldHeight / rows))) → plantC1R6, b_1, c_1, d_1, e_1
  44. Polygon(BoxPt + (0, (6 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (6 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (7 * fieldHeight / rows)), BoxPt + (0, (7 * fieldHeight / rows))) → plantC1R7, f_1, g_1, h_1, i_1
  45. Polygon(BoxPt + (0, (7 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (7 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (8 * fieldHeight / rows)), BoxPt + (0, (8 * fieldHeight / rows))) → plantC1R8, j_1, k_1, l_1, m_1
  46. Polygon(BoxPt + (fieldWidth / columns, 0), BoxPt + ((2 * fieldWidth / columns), 0), BoxPt + ((2 * fieldWidth / columns), fieldHeight / rows), BoxPt + (fieldWidth / columns, fieldHeight / rows)) → plantC2R1, n_1, p_1, q_1, r_1
  47. Polygon(BoxPt + (fieldWidth / columns, fieldHeight / rows), BoxPt + ((2 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((2 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (2 * fieldHeight / rows))) → plantC2R2, s_1, t_1, a_2, b_2
  48. Polygon(BoxPt + (fieldWidth / columns, (2 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (3 * fieldHeight / rows))) → plantC2R3, c_2, d_2, e_2, f_2
  49. Polygon(BoxPt + (fieldWidth / columns, (3 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (4 * fieldHeight / rows))) → plantC2R4, g_2, h_2, i_2, j_2
  50. Polygon(BoxPt + (fieldWidth / columns, (4 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (5 * fieldHeight / rows))) → plantC2R5, k_2, l_2, m_2, n_2
  51. Polygon(BoxPt + (fieldWidth / columns, (5 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (6 * fieldHeight / rows))) → plantC2R6, p_2, q_2, r_2, s_2
  52. Polygon(BoxPt + (fieldWidth / columns, (6 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (7 * fieldHeight / rows))) → plantC2R7, t_2, a_3, b_3, c_3
  53. Polygon(BoxPt + (fieldWidth / columns, (7 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + (fieldWidth / columns, (8 * fieldHeight / rows))) → plantC2R8, d_3, e_3, f_3, g_3
  54. Polygon(BoxPt + ((2 * fieldWidth / columns), 0), BoxPt + ((3 * fieldWidth / columns), 0), BoxPt + ((3 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((2 * fieldWidth / columns), fieldHeight / rows)) → plantC3R1, h_3, i_3, j_3, k_3
  55. Polygon(BoxPt + ((2 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((3 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((3 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC3R2, l_3, m_3, n_3, p_3
  56. Polygon(BoxPt + ((2 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC3R3, q_3, r_3, s_3, t_3
  57. Polygon(BoxPt + ((2 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC3R4, a_4, b_4, c_4, d_4
  58. Polygon(BoxPt + ((2 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC3R5, e_4, f_4, g_4, h_4
  59. Polygon(BoxPt + ((2 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC3R6, i_4, j_4, k_4, l_4
  60. Polygon(BoxPt + ((2 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC3R7, m_4, n_4, p_4, q_4
  61. Polygon(BoxPt + ((2 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((2 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC3R8, r_4, s_4, t_4, a_5
  62. Polygon(BoxPt + ((3 * fieldWidth / columns), 0), BoxPt + ((4 * fieldWidth / columns), 0), BoxPt + ((4 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((3 * fieldWidth / columns), fieldHeight / rows)) → plantC4R1, b_5, c_5, d_5, e_5
  63. Polygon(BoxPt + ((3 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((4 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((4 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC4R2, f_5, g_5, h_5, i_5
  64. Polygon(BoxPt + ((3 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC4R3, j_5, k_5, l_5, m_5
  65. Polygon(BoxPt + ((3 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC4R4, n_5, p_5, q_5, r_5
  66. Polygon(BoxPt + ((3 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC4R5, s_5, t_5, a_6, b_6
  67. Polygon(BoxPt + ((3 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC4R6, c_6, d_6, e_6, f_6
  68. Polygon(BoxPt + ((3 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC4R7, g_6, h_6, i_6, j_6
  69. Polygon(BoxPt + ((3 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((3 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC4R8, k_6, l_6, m_6, n_6
  70. Polygon(BoxPt + ((4 * fieldWidth / columns), 0), BoxPt + ((5 * fieldWidth / columns), 0), BoxPt + ((5 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((4 * fieldWidth / columns), fieldHeight / rows)) → plantC5R1, p_6, q_6, r_6, s_6
  71. Polygon(BoxPt + ((4 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((5 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((5 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC5R2, t_6, a_7, b_7, c_7
  72. Polygon(BoxPt + ((4 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC5R3, d_7, e_7, f_7, g_7
  73. Polygon(BoxPt + ((4 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC5R4, h_7, i_7, j_7, k_7
  74. Polygon(BoxPt + ((4 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC5R5, l_7, m_7, n_7, p_7
  75. Polygon(BoxPt + ((4 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC5R6, q_7, r_7, s_7, t_7
  76. Polygon(BoxPt + ((4 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC5R7, a_8, b_8, c_8, d_8
  77. Polygon(BoxPt + ((4 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((4 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC5R8, e_8, f_8, g_8, h_8
  78. Polygon(BoxPt + ((5 * fieldWidth / columns), 0), BoxPt + ((6 * fieldWidth / columns), 0), BoxPt + ((6 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((5 * fieldWidth / columns), fieldHeight / rows)) → plantC6R1, i_8, j_8, k_8, l_8
  79. Polygon(BoxPt + ((5 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((6 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((6 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC6R2, m_8, n_8, p_8, q_8
  80. Polygon(BoxPt + ((5 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC6R3, r_8, s_8, t_8, a_9
  81. Polygon(BoxPt + ((5 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC6R4, b_9, c_9, d_9, e_9
  82. Polygon(BoxPt + ((5 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC6R5, f_9, g_9, h_9, i_9
  83. Polygon(BoxPt + ((5 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC6R6, j_9, k_9, l_9, m_9
  84. Polygon(BoxPt + ((5 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC6R7, n_9, p_9, q_9, r_9
  85. Polygon(BoxPt + ((5 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((5 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC6R8, s_9, t_9, a_{10}, b_{10}
  86. Polygon(BoxPt + ((6 * fieldWidth / columns), 0), BoxPt + ((7 * fieldWidth / columns), 0), BoxPt + ((7 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((6 * fieldWidth / columns), fieldHeight / rows)) → plantC7R1, c_{10}, d_{10}, e_{10}, f_{10}
  87. Polygon(BoxPt + ((6 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((7 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((7 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC7R2, g_{10}, h_{10}, i_{10}, j_{10}
  88. Polygon(BoxPt + ((6 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC7R3, k_{10}, l_{10}, m_{10}, n_{10}
  89. Polygon(BoxPt + ((6 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC7R4, p_{10}, q_{10}, r_{10}, s_{10}
  90. Polygon(BoxPt + ((6 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC7R5, t_{10}, a_{11}, b_{11}, c_{11}
  91. Polygon(BoxPt + ((6 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC7R6, d_{11}, e_{11}, f_{11}, g_{11}
  92. Polygon(BoxPt + ((6 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC7R7, h_{11}, i_{11}, j_{11}, k_{11}
  93. Polygon(BoxPt + ((6 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((6 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC7R8, l_{11}, m_{11}, n_{11}, p_{11}
  94. Polygon(BoxPt + ((7 * fieldWidth / columns), 0), BoxPt + ((8 * fieldWidth / columns), 0), BoxPt + ((8 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((7 * fieldWidth / columns), fieldHeight / rows)) → plantC8R1, q_{11}, r_{11}, s_{11}, t_{11}
  95. Polygon(BoxPt + ((7 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((8 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((8 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC8R2, a_{12}, b_{12}, c_{12}, d_{12}
  96. Polygon(BoxPt + ((7 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC8R3, e_{12}, f_{12}, g_{12}, h_{12}
  97. Polygon(BoxPt + ((7 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC8R4, i_{12}, j_{12}, k_{12}, l_{12}
  98. Polygon(BoxPt + ((7 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC8R5, m_{12}, n_{12}, p_{12}, q_{12}
  99. Polygon(BoxPt + ((7 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC8R6, r_{12}, s_{12}, t_{12}, a_{13}
  100. Polygon(BoxPt + ((7 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC8R7, b_{13}, c_{13}, d_{13}, e_{13}
  101. Polygon(BoxPt + ((7 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((7 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC8R8, f_{13}, g_{13}, h_{13}, i_{13}
  102. Polygon(BoxPt + ((8 * fieldWidth / columns), 0), BoxPt + ((9 * fieldWidth / columns), 0), BoxPt + ((9 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((8 * fieldWidth / columns), fieldHeight / rows)) → plantC9R1, j_{13}, k_{13}, l_{13}, m_{13}
  103. Polygon(BoxPt + ((8 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((9 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((9 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC9R2, n_{13}, p_{13}, q_{13}, r_{13}
  104. Polygon(BoxPt + ((8 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC9R3, s_{13}, t_{13}, a_{14}, b_{14}
  105. Polygon(BoxPt + ((8 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC9R4, c_{14}, d_{14}, e_{14}, f_{14}
  106. Polygon(BoxPt + ((8 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC9R5, g_{14}, h_{14}, i_{14}, j_{14}
  107. Polygon(BoxPt + ((8 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC9R6, k_{14}, l_{14}, m_{14}, n_{14}
  108. Polygon(BoxPt + ((8 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC9R7, p_{14}, q_{14}, r_{14}, s_{14}
  109. Polygon(BoxPt + ((8 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((8 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC9R8, t_{14}, a_{15}, b_{15}, c_{15}
  110. Polygon(BoxPt + ((9 * fieldWidth / columns), 0), BoxPt + ((10 * fieldWidth / columns), 0), BoxPt + ((10 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((9 * fieldWidth / columns), fieldHeight / rows)) → plantC10R1, d_{15}, e_{15}, f_{15}, g_{15}
  111. Polygon(BoxPt + ((9 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((10 * fieldWidth / columns), fieldHeight / rows), BoxPt + ((10 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (2 * fieldHeight / rows))) → plantC10R2, h_{15}, i_{15}, j_{15}, k_{15}
  112. Polygon(BoxPt + ((9 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (2 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (3 * fieldHeight / rows))) → plantC10R3, l_{15}, m_{15}, n_{15}, p_{15}
  113. Polygon(BoxPt + ((9 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (3 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (4 * fieldHeight / rows))) → plantC10R4, q_{15}, r_{15}, s_{15}, t_{15}
  114. Polygon(BoxPt + ((9 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (4 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (5 * fieldHeight / rows))) → plantC10R5, a_{16}, b_{16}, c_{16}, d_{16}
  115. Polygon(BoxPt + ((9 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (5 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (6 * fieldHeight / rows))) → plantC10R6, e_{16}, f_{16}, g_{16}, h_{16}
  116. Polygon(BoxPt + ((9 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (6 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (7 * fieldHeight / rows))) → plantC10R7, i_{16}, j_{16}, k_{16}, l_{16}
  117. Polygon(BoxPt + ((9 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (7 * fieldHeight / rows)), BoxPt + ((10 * fieldWidth / columns), (8 * fieldHeight / rows)), BoxPt + ((9 * fieldWidth / columns), (8 * fieldHeight / rows))) → plantC10R8, m_{16}, n_{16}, p_{16}, q_{16}
  118. If(plantAmtOfField ≟ plantedOfField, true, false) → step2Verify
  119. Sequence(Segment[BoxPt + (0, (i * fieldHeight / rows)), BoxPt + (fieldWidth, (i * fieldHeight / rows))], i, y(BoxPt), rows - 1) → plantExtendLines
  120. FractionText((plowNum * plantNum / ((plowDenom * plantDenom)))) → step3exprAnsFracHidden
  121. Element({1, 1, 3, 4, 5, 1, 1, 8, 9, 5, 9, 5}, prob) → simplifiedNum
  122. Polygon(CheckPolyPt2, CheckPolyPt2 + (0.85, 0), CheckPolyPt2 + (0.9, 0.1), CheckPolyPt2 + (0.9, 0.4), CheckPolyPt2 + (0.85, 0.5), CheckPolyPt2 + (0, 0.5), CheckPolyPt2 + (-0.05, 0.4), CheckPolyPt2 + (-0.05, 0.1)) → step2ButtonCheck, step2ButtonCheckB, step2ButtonCheckRB, step2ButtonCheckR, step2ButtonCheckRT, step2ButtonCheckT, step2ButtonCheckLT, step2ButtonCheckL, step2ButtonCheckLB
  123. Polygon(CheckPolyPt + (-0.25, 0), CheckPolyPt + (1.1, 0), CheckPolyPt + (1.15, 0.1), CheckPolyPt + (1.15, 0.4), CheckPolyPt + (1.1, 0.5), CheckPolyPt + (-0.25, 0.5), CheckPolyPt + (-0.3, 0.4), CheckPolyPt + (-0.3, 0.1)) → step1ButtonCheck, step1ButtonCheckB, step1ButtonCheckRB, step1ButtonCheckR, step1ButtonCheckRT, step1ButtonCheckT, step1ButtonCheckLT, step1ButtonCheckL, step1ButtonCheckLB
  124. Polygon(CheckPolyPt, CheckPolyPt + (0.85, 0), CheckPolyPt + (0.9, 0.1), CheckPolyPt + (0.9, 0.4), CheckPolyPt + (0.85, 0.5), CheckPolyPt + (0, 0.5), CheckPolyPt + (-0.05, 0.4), CheckPolyPt + (-0.05, 0.1)) → step3ButtonCheck, step3ButtonCheckB, step3ButtonCheckRB, step3ButtonCheckR, step3ButtonCheckRT, step3ButtonCheckT, step3ButtonCheckLT, step3ButtonCheckL, step3ButtonCheckLB