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在数轴上定位分数（2）

在数轴上定位分数（2）
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2018-09-20 22:32
向量函数解析几何几何作图滑块动画
①本范例演示如何在数轴上准确放置分数，并实时获得反馈；②涉及的核心数学概念包括分数、数轴、有理数和实数；③作图要点——使用了Polygon（多边形）、PointIn（点在内部判断）、If（条件判断）、Vector（向量）、Sequence（数列）等GeoGebra命令与对象，如onLineHeight（数轴高度）、set（设置）、restrictPts（限制点）、f, g, h, i（变量）、Frac1PtSet1至Frac1PtSet6（分数点集）、frac1MasterPt（主分数点）等；④适合初中及以上数学学习者，用于分数概念理解和数轴应用练习。

GeoGebra 命令及参数

  1. Polygon((-0.05, 0.4), (2.05, 0.4), (2.05, 3.3), (-0.05, 3.3)) → restrictPts, f, g, h, i
  2. PointIn(restrictPts) → Frac1PtSet1
  3. PointIn(restrictPts) → Frac1PtSet2
  4. PointIn(restrictPts) → Frac1PtSet3
  5. PointIn(restrictPts) → Frac1PtSet4
  6. PointIn(restrictPts) → Frac1PtSet5
  7. PointIn(restrictPts) → Frac1PtSet6
  8. If(set ≟ 1, Frac1PtSet1, If[set ≟ 2, Frac1PtSet2, If[set ≟ 3, Frac1PtSet3, If[set ≟ 4, Frac1PtSet4, If[set ≟ 5, Frac1PtSet5, Frac1PtSet6]]]]) → frac1MasterPt
  9. PointIn(restrictPts) → Frac2PtSet6
  10. PointIn(restrictPts) → Frac2PtSet5
  11. PointIn(restrictPts) → Frac2PtSet4
  12. PointIn(restrictPts) → Frac2PtSet3
  13. PointIn(restrictPts) → Frac2PtSet2
  14. PointIn(restrictPts) → Frac2PtSet1
  15. If(set ≟ 1, Frac2PtSet1, If[set ≟ 2, Frac2PtSet2, If[set ≟ 3, Frac2PtSet3, If[set ≟ 4, Frac2PtSet4, If[set ≟ 5, Frac2PtSet5, Frac2PtSet6]]]]) → frac2MasterPt
  16. PointIn(restrictPts) → Frac3PtSet6
  17. PointIn(restrictPts) → Frac3PtSet5
  18. PointIn(restrictPts) → Frac3PtSet4
  19. PointIn(restrictPts) → Frac3PtSet3
  20. PointIn(restrictPts) → Frac3PtSet2
  21. PointIn(restrictPts) → Frac3PtSet1
  22. If(set ≟ 1, Frac3PtSet1, If[set ≟ 2, Frac3PtSet2, If[set ≟ 3, Frac3PtSet3, If[set ≟ 4, Frac3PtSet4, If[set ≟ 5, Frac3PtSet5, Frac3PtSet6]]]]) → frac3MasterPt
  23. PointIn(restrictPts) → Frac4PtSet6
  24. PointIn(restrictPts) → Frac4PtSet5
  25. PointIn(restrictPts) → Frac4PtSet4
  26. PointIn(restrictPts) → Frac4PtSet3
  27. PointIn(restrictPts) → Frac4PtSet2
  28. PointIn(restrictPts) → Frac4PtSet1
  29. If(set ≟ 1, Frac4PtSet1, If[set ≟ 2, Frac4PtSet2, If[set ≟ 3, Frac4PtSet3, If[set ≟ 4, Frac4PtSet4, If[set ≟ 5, Frac4PtSet5, Frac4PtSet6]]]]) → frac4MasterPt
  30. If(set ≟ 1 ∧ ckPlaceSet1, true, If[set ≟ 2 ∧ ckPlaceSet2, true, If[set ≟ 3 ∧ ckPlaceSet3, true, If[set ≟ 4 ∧ ckPlaceSet4, true, If[set ≟ 5 ∧ ckPlaceSet5, true, If[set ≟ 6 ∧ ckPlaceSet6, true, false]]]]]) → placeMasterYN
  31. If(x(frac4MasterPt) < x(dotA) + snapHorAmt ∧ x(frac4MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac4MasterPt) < x(dotB) + snapHorAmt ∧ x(frac4MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac4MasterPt) < x(dotC) + snapHorAmt ∧ x(frac4MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac4MasterPt) < x(dotD) + snapHorAmt ∧ x(frac4MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac4MasterPt) < x(dotE) + snapHorAmt ∧ x(frac4MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac4MasterPt) < x(dotF) + snapHorAmt ∧ x(frac4MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac4MasterPt) < x(dotG) + snapHorAmt ∧ x(frac4MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac4MasterPt)]]]]]]) → frac4X
  32. If(x(frac3MasterPt) < x(dotA) + snapHorAmt ∧ x(frac3MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac3MasterPt) < x(dotB) + snapHorAmt ∧ x(frac3MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac3MasterPt) < x(dotC) + snapHorAmt ∧ x(frac3MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac3MasterPt) < x(dotD) + snapHorAmt ∧ x(frac3MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac3MasterPt) < x(dotE) + snapHorAmt ∧ x(frac3MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac3MasterPt) < x(dotF) + snapHorAmt ∧ x(frac3MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac3MasterPt) < x(dotG) + snapHorAmt ∧ x(frac3MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac3MasterPt)]]]]]]) → frac3X
  33. If(x(frac2MasterPt) < x(dotA) + snapHorAmt ∧ x(frac2MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac2MasterPt) < x(dotB) + snapHorAmt ∧ x(frac2MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac2MasterPt) < x(dotC) + snapHorAmt ∧ x(frac2MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac2MasterPt) < x(dotD) + snapHorAmt ∧ x(frac2MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac2MasterPt) < x(dotE) + snapHorAmt ∧ x(frac2MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac2MasterPt) < x(dotF) + snapHorAmt ∧ x(frac2MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac2MasterPt) < x(dotG) + snapHorAmt ∧ x(frac2MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac2MasterPt)]]]]]]) → frac2X
  34. If(x(frac1MasterPt) < x(dotA) + snapHorAmt ∧ x(frac1MasterPt) > x(dotA) - snapHorAmt, x(dotA), If[x(frac1MasterPt) < x(dotB) + snapHorAmt ∧ x(frac1MasterPt) > x(dotB) - snapHorAmt, x(dotB), If[x(frac1MasterPt) < x(dotC) + snapHorAmt ∧ x(frac1MasterPt) > x(dotC) - snapHorAmt, x(dotC), If[x(frac1MasterPt) < x(dotD) + snapHorAmt ∧ x(frac1MasterPt) > x(dotD) - snapHorAmt, x(dotD), If[x(frac1MasterPt) < x(dotE) + snapHorAmt ∧ x(frac1MasterPt) > x(dotE) - snapHorAmt, x(dotE), If[x(frac1MasterPt) < x(dotF) + snapHorAmt ∧ x(frac1MasterPt) > x(dotF) - snapHorAmt, x(dotF), If[x(frac1MasterPt) < x(dotG) + snapHorAmt ∧ x(frac1MasterPt) > x(dotG) - snapHorAmt, x(dotG), x(frac1MasterPt)]]]]]]) → frac1X
  35. Vector((1, 0), (-0.2, 0)) → numLnL
  36. Vector((1, 0), (2.2, 0)) → numLnR
  37. Sequence((k - 0.035, -0.4), k, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → labelPtList
  38. If(y(frac1MasterPt) ≤ onLineHeight ∧ y(frac2MasterPt) < onLineHeight ∧ y(frac3MasterPt) < onLineHeight ∧ y(frac4MasterPt) < onLineHeight, true, false) → allOnLine
  39. If(x(Frac4PtLn) ≟ x(Element[{dotD, dotD, dotE, dotA, dotD, dotC}, set]), true, false) → frac4PlaceYN
  40. If(x(Frac3PtLn) ≟ x(Element[{dotB, dotC, dotD, dotF, dotB, dotB}, set]), true, false) → frac3PlaceYN
  41. If(x(Frac2PtLn) ≟ x(Element[{dotE, dotF, dotB, dotC, dotE, dotA}, set]), true, false) → frac2PlaceYN
  42. If(x(Frac1PtLn) ≟ x(Element[{dotC, dotE, dotC, dotB, dotC, dotE}, set]), true, false) → frac1PlaceYN
  43. If(set ≟ 1 ∧ ckHintSet1, true, If[set ≟ 2 ∧ ckHintSet2, true, If[set ≟ 3 ∧ ckHintSet3, true, If[set ≟ 4 ∧ ckHintSet4, true, If[set ≟ 5 ∧ ckHintSet5, true, If[set ≟ 6 ∧ ckHintSet6, true, false]]]]]) → hintMasterYN
  44. Sequence(Segment[(i, 0.28), (i, -0.28)], i, 0, 2, (Element[numLnMax, set] * Element[numLnHash, set])) → scaleHashXaxis
  45. If(set ≟ 1 ∧ ckHintSet1b, true, If[set ≟ 2 ∧ ckHintSet2b, true, If[set ≟ 3 ∧ ckHintSet3b, true, If[set ≟ 4 ∧ ckHintSet4b, true, If[set ≟ 5 ∧ ckHintSet5b, true, If[set ≟ 6 ∧ ckHintSet6b, true, false]]]]]) → hintMasterYNb
  46. Polygon((0.01, -0.4), (0.99, -0.4), (0.99, 0.4), (0.01, 0.4)) → hideHashMarks, a, b, c, d
  47. Sequence((0.26 + j, 3), j, 0, 1.5, 0.498) → fracAlignPts