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有理数的探索 - 分析与表示

有理数的探索 - 分析与表示
几何画板及绘图内容加载中，请稍等……
2025-01-21 20:14
所属专题 Rationale Zahlen & Arbeiten mit der Zahlengerade
本范例展示了有理数的分析与表示的过程。学生可以通过重新排列词语来理解有理数的概念，并学习如何将有理数表示为分数。通过此范例，学生可以了解有理数的特性，包括它们的表示形式和相互比较的方法。 GeoGebra 命令和对象：Sequence、Element、Textfield、Join、If、PolyLine、Segment、KeepIf、Remove、RemoveUndefined、Simplify、Numerator、Denominator、Corner、Circle、Text、SelectedIndex。适合的学段或用途：初中数学教育，特别是有理数和分数的学习。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 10, 8, 10, 5, 10, 4, 2, 5, 10}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-0.39, 10.379999999999999), (0.6119083969465652, 10.379999999999999), (1.6138167938931303, 10.379999999999999), (2.6157251908396955, 10.379999999999999), (3.6176335877862607, 10.379999999999999), (4.619541984732826, 10.379999999999999), (5.6214503816793915, 10.379999999999999), (6.623358778625956, 10.379999999999999), (7.625267175572522, 10.379999999999999), (8.627175572519086, 10.379999999999999), (9.62908396946565, 10.379999999999999), (10.630992366412217, 10.379999999999999), (11.632900763358782, 10.379999999999999), (12.634809160305347, 10.379999999999999), (13.636717557251911, 10.379999999999999), (14.638625954198478, 10.379999999999999), (15.640534351145043, 10.379999999999999), (16.642442748091607, 10.379999999999999), (17.644351145038172, 10.379999999999999), (18.646259541984737, 10.379999999999999), (19.6481679389313, 10.379999999999999), (20.650076335877866, 10.379999999999999)}, {(-0.39, 9.37665551839465), (0.6119083969465652, 9.37665551839465), (1.6138167938931303, 9.37665551839465), (2.6157251908396955, 9.37665551839465), (3.6176335877862607, 9.37665551839465), (4.619541984732826, 9.37665551839465), (5.6214503816793915, 9.37665551839465), (6.623358778625956, 9.37665551839465), (7.625267175572522, 9.37665551839465), (8.627175572519086, 9.37665551839465), (9.62908396946565, 9.37665551839465), (10.630992366412217, 9.37665551839465), (11.632900763358782, 9.37665551839465), (12.634809160305347, 9.37665551839465), (13.636717557251911, 9.37665551839465), (14.638625954198478, 9.37665551839465), (15.640534351145043, 9.37665551839465), (16.642442748091607, 9.37665551839465), (17.644351145038172, 9.37665551839465), (18.646259541984737, 9.37665551839465), (19.6481679389313, 9.37665551839465), (20.650076335877866, 9.37665551839465)}, {(-0.39, 8.373311036789298), (0.6119083969465652, 8.373311036789298), (1.6138167938931303, 8.373311036789298), (2.6157251908396955, 8.373311036789298), (3.6176335877862607, 8.373311036789298), (4.619541984732826, 8.373311036789298), (5.6214503816793915, 8.373311036789298), (6.623358778625956, 8.373311036789298), (7.625267175572522, 8.373311036789298), (8.627175572519086, 8.373311036789298), (9.62908396946565, 8.373311036789298), (10.630992366412217, 8.373311036789298), (11.632900763358782, 8.373311036789298), (12.634809160305347, 8.373311036789298), (13.636717557251911, 8.373311036789298), (14.638625954198478, 8.373311036789298), (15.640534351145043, 8.373311036789298), (16.642442748091607, 8.373311036789298), (17.644351145038172, 8.373311036789298), (18.646259541984737, 8.373311036789298), (19.6481679389313, 8.373311036789298), (20.650076335877866, 8.373311036789298)}, {(-0.39, 7.3699665551839475), (0.6119083969465652, 7.3699665551839475), (1.6138167938931303, 7.3699665551839475), (2.6157251908396955, 7.3699665551839475), (3.6176335877862607, 7.3699665551839475), (4.619541984732826, 7.3699665551839475), (5.6214503816793915, 7.3699665551839475), (6.623358778625956, 7.3699665551839475), (7.625267175572522, 7.3699665551839475), (8.627175572519086, 7.3699665551839475), (9.62908396946565, 7.3699665551839475), (10.630992366412217, 7.3699665551839475), (11.632900763358782, 7.3699665551839475), (12.634809160305347, 7.3699665551839475), (13.636717557251911, 7.3699665551839475), (14.638625954198478, 7.3699665551839475), (15.640534351145043, 7.3699665551839475), (16.642442748091607, 7.3699665551839475), (17.644351145038172, 7.3699665551839475), (18.646259541984737, 7.3699665551839475), (19.6481679389313, 7.3699665551839475), (20.650076335877866, 7.3699665551839475)}, {(-0.39, 6.366622073578597), (0.6119083969465652, 6.366622073578597), (1.6138167938931303, 6.366622073578597), (2.6157251908396955, 6.366622073578597), (3.6176335877862607, 6.366622073578597), (4.619541984732826, 6.366622073578597), (5.6214503816793915, 6.366622073578597), (6.623358778625956, 6.366622073578597), (7.625267175572522, 6.366622073578597), (8.627175572519086, 6.366622073578597), (9.62908396946565, 6.366622073578597), (10.630992366412217, 6.366622073578597), (11.632900763358782, 6.366622073578597), (12.634809160305347, 6.366622073578597), (13.636717557251911, 6.366622073578597), (14.638625954198478, 6.366622073578597), (15.640534351145043, 6.366622073578597), (16.642442748091607, 6.366622073578597), (17.644351145038172, 6.366622073578597), (18.646259541984737, 6.366622073578597), (19.6481679389313, 6.366622073578597), (20.650076335877866, 6.366622073578597)}, {(-0.39, 5.3632775919732465), (0.6119083969465652, 5.3632775919732465), (1.6138167938931303, 5.3632775919732465), (2.6157251908396955, 5.3632775919732465), (3.6176335877862607, 5.3632775919732465), (4.619541984732826, 5.3632775919732465), (5.6214503816793915, 5.3632775919732465), (6.623358778625956, 5.3632775919732465), (7.625267175572522, 5.3632775919732465), (8.627175572519086, 5.3632775919732465), (9.62908396946565, 5.3632775919732465), (10.630992366412217, 5.3632775919732465), (11.632900763358782, 5.3632775919732465), (12.634809160305347, 5.3632775919732465), (13.636717557251911, 5.3632775919732465), (14.638625954198478, 5.3632775919732465), (15.640534351145043, 5.3632775919732465), (16.642442748091607, 5.3632775919732465), (17.644351145038172, 5.3632775919732465), (18.646259541984737, 5.3632775919732465), (19.6481679389313, 5.3632775919732465), (20.650076335877866, 5.3632775919732465)}, {(-0.39, 4.359933110367896), (0.6119083969465652, 4.359933110367896), (1.6138167938931303, 4.359933110367896), (2.6157251908396955, 4.359933110367896), (3.6176335877862607, 4.359933110367896), (4.619541984732826, 4.359933110367896), (5.6214503816793915, 4.359933110367896), (6.623358778625956, 4.359933110367896), (7.625267175572522, 4.359933110367896), (8.627175572519086, 4.359933110367896), (9.62908396946565, 4.359933110367896), (10.630992366412217, 4.359933110367896), (11.632900763358782, 4.359933110367896), (12.634809160305347, 4.359933110367896), (13.636717557251911, 4.359933110367896), (14.638625954198478, 4.359933110367896), (15.640534351145043, 4.359933110367896), (16.642442748091607, 4.359933110367896), (17.644351145038172, 4.359933110367896), (18.646259541984737, 4.359933110367896), (19.6481679389313, 4.359933110367896), (20.650076335877866, 4.359933110367896)}, {(-0.39, 3.3565886287625455), (0.6119083969465652, 3.3565886287625455), (1.6138167938931303, 3.3565886287625455), (2.6157251908396955, 3.3565886287625455), (3.6176335877862607, 3.3565886287625455), (4.619541984732826, 3.3565886287625455), (5.6214503816793915, 3.3565886287625455), (6.623358778625956, 3.3565886287625455), (7.625267175572522, 3.3565886287625455), (8.627175572519086, 3.3565886287625455), (9.62908396946565, 3.3565886287625455), (10.630992366412217, 3.3565886287625455), (11.632900763358782, 3.3565886287625455), (12.634809160305347, 3.3565886287625455), (13.636717557251911, 3.3565886287625455), (14.638625954198478, 3.3565886287625455), (15.640534351145043, 3.3565886287625455), (16.642442748091607, 3.3565886287625455), (17.644351145038172, 3.3565886287625455), (18.646259541984737, 3.3565886287625455), (19.6481679389313, 3.3565886287625455), (20.650076335877866, 3.3565886287625455)}, {(-0.39, 2.353244147157195), (0.6119083969465652, 2.353244147157195), (1.6138167938931303, 2.353244147157195), (2.6157251908396955, 2.353244147157195), (3.6176335877862607, 2.353244147157195), (4.619541984732826, 2.353244147157195), (5.6214503816793915, 2.353244147157195), (6.623358778625956, 2.353244147157195), (7.625267175572522, 2.353244147157195), (8.627175572519086, 2.353244147157195), (9.62908396946565, 2.353244147157195), (10.630992366412217, 2.353244147157195), (11.632900763358782, 2.353244147157195), (12.634809160305347, 2.353244147157195), (13.636717557251911, 2.353244147157195), (14.638625954198478, 2.353244147157195), (15.640534351145043, 2.353244147157195), (16.642442748091607, 2.353244147157195), (17.644351145038172, 2.353244147157195), (18.646259541984737, 2.353244147157195), (19.6481679389313, 2.353244147157195), (20.650076335877866, 2.353244147157195)}, {(-0.39, 1.3498996655518454), (0.6119083969465652, 1.3498996655518454), (1.6138167938931303, 1.3498996655518454), (2.6157251908396955, 1.3498996655518454), (3.6176335877862607, 1.3498996655518454), (4.619541984732826, 1.3498996655518454), (5.6214503816793915, 1.3498996655518454), (6.623358778625956, 1.3498996655518454), (7.625267175572522, 1.3498996655518454), (8.627175572519086, 1.3498996655518454), (9.62908396946565, 1.3498996655518454), (10.630992366412217, 1.3498996655518454), (11.632900763358782, 1.3498996655518454), (12.634809160305347, 1.3498996655518454), (13.636717557251911, 1.3498996655518454), (14.638625954198478, 1.3498996655518454), (15.640534351145043, 1.3498996655518454), (16.642442748091607, 1.3498996655518454), (17.644351145038172, 1.3498996655518454), (18.646259541984737, 1.3498996655518454), (19.6481679389313, 1.3498996655518454), (20.650076335877866, 1.3498996655518454)}, {(-0.39, 0.346555183946494), (0.6119083969465652, 0.346555183946494), (1.6138167938931303, 0.346555183946494), (2.6157251908396955, 0.346555183946494), (3.6176335877862607, 0.346555183946494), (4.619541984732826, 0.346555183946494), (5.6214503816793915, 0.346555183946494), (6.623358778625956, 0.346555183946494), (7.625267175572522, 0.346555183946494), (8.627175572519086, 0.346555183946494), (9.62908396946565, 0.346555183946494), (10.630992366412217, 0.346555183946494), (11.632900763358782, 0.346555183946494), (12.634809160305347, 0.346555183946494), (13.636717557251911, 0.346555183946494), (14.638625954198478, 0.346555183946494), (15.640534351145043, 0.346555183946494), (16.642442748091607, 0.346555183946494), (17.644351145038172, 0.346555183946494), (18.646259541984737, 0.346555183946494), (19.6481679389313, 0.346555183946494), (20.650076335877866, 0.346555183946494)}, {(-0.39, -0.6567892976588574), (0.6119083969465652, -0.6567892976588574), (1.6138167938931303, -0.6567892976588574), (2.6157251908396955, -0.6567892976588574), (3.6176335877862607, -0.6567892976588574), (4.619541984732826, -0.6567892976588574), (5.6214503816793915, -0.6567892976588574), (6.623358778625956, -0.6567892976588574), (7.625267175572522, -0.6567892976588574), (8.627175572519086, -0.6567892976588574), (9.62908396946565, -0.6567892976588574), (10.630992366412217, -0.6567892976588574), (11.632900763358782, -0.6567892976588574), (12.634809160305347, -0.6567892976588574), (13.636717557251911, -0.6567892976588574), (14.638625954198478, -0.6567892976588574), (15.640534351145043, -0.6567892976588574), (16.642442748091607, -0.6567892976588574), (17.644351145038172, -0.6567892976588574), (18.646259541984737, -0.6567892976588574), (19.6481679389313, -0.6567892976588574), (20.650076335877866, -0.6567892976588574)}, {(-0.39, -1.660133779264207), (0.6119083969465652, -1.660133779264207), (1.6138167938931303, -1.660133779264207), (2.6157251908396955, -1.660133779264207), (3.6176335877862607, -1.660133779264207), (4.619541984732826, -1.660133779264207), (5.6214503816793915, -1.660133779264207), (6.623358778625956, -1.660133779264207), (7.625267175572522, -1.660133779264207), (8.627175572519086, -1.660133779264207), (9.62908396946565, -1.660133779264207), (10.630992366412217, -1.660133779264207), (11.632900763358782, -1.660133779264207), (12.634809160305347, -1.660133779264207), (13.636717557251911, -1.660133779264207), (14.638625954198478, -1.660133779264207), (15.640534351145043, -1.660133779264207), (16.642442748091607, -1.660133779264207), (17.644351145038172, -1.660133779264207), (18.646259541984737, -1.660133779264207), (19.6481679389313, -1.660133779264207), (20.650076335877866, -1.660133779264207)}}
  7. If(step ≟ 1, (2, 3.3), (-0.2, 6.5)) → PosImgSam1
  8. PolyLine(PosSB, Corner[txt011, 1] + (1.25, -0.1), Corner[txt011, 2] + (0.1, -0.1), Corner[txt011, 3] + (0.1, 0.1), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 1] + (-0.1, -0.1), Corner[txt011, 1] + (0.5, -0.1), PosSB) → sb01
  9. PolyLine(PosSB, Corner[txt021, 1] + (1.25, -0.1), Corner[txt021, 2] + (0.1, -0.1), Corner[txt021, 3] + (0.1, 0.1), Corner[txt021, 4] + (-0.1, 0.1), Corner[txt021, 1] + (-0.1, -0.1), Corner[txt021, 1] + (0.5, -0.1), PosSB) → sb02
  10. PolyLine(PosSB, Corner[txt031, 1] + (0.5, 0), Corner[txt031, 2] + (0.1, 0), Corner[txt031, 3] + (0.1, 0.1), Corner[txt031, 4] + (-0.1, 0.1), Corner[txt031, 1] + (-0.1, 0.25), PosSB) → sb03
  11. PolyLine(PosSB, Corner[txt051, 1] + (0.5, 0), Corner[txt051, 2] + (0.1, 0), Corner[txt051, 3] + (0.1, 0.1), Corner[txt051, 4] + (-0.1, 0.1), Corner[txt051, 1] + (-0.1, 0.25), PosSB) → sb05
  12. PolyLine(PosSB, Corner[txt061, 1] + (0.5, 0), Corner[txt061, 2] + (0.1, 0), Corner[txt061, 3] + (0.1, 0.1), Corner[txt061, 4] + (-0.1, 0.1), Corner[txt061, 1] + (-0.1, 0.25), PosSB) → sb06
  13. Textfield(input031) → InputBox031
  14. Textfield(input041) → InputBox041
  15. Textfield(input081) → InputBox081
  16. Textfield(input082) → InputBox082
  17. Segment(PosStart + ((-edgeAxis), 0), PosStart + ((6 * disAxis) + edgeAxis, 0)) → Axis
  18. Sequence(MP03 + ((k + 0.5) * ((-disA03), 0)), k, 0, 1, 1) → AxisPointsLeft031
  19. Sequence(MP03 + (k * ((-disA03), 0)), k, 1, 1, 1) → AxisPointsLeft032
  20. Sequence(MP03 + ((k + 0.5) * (disA03, 0)), k, 0, 4, 1) → AxisPointsRight031
  21. Sequence(MP03 + (k * (disA03, 0)), k, 1, 4, 1) → AxisPointsRight032
  22. Join({Reverse[AxisPointsLeft031], AxisPointsRight031}) → AxisPoints031
  23. KeepIf(A ∈ Axis, A, Join[{Reverse[AxisPointsLeft032], {MP03}, AxisPointsRight032}]) → AxisPoints032
  24. Sequence(Segment[AxisPoints032(k) + (0, If[AxisPoints032(k) ∈ Axis, (-segLength2), 0]), AxisPoints032(k) + (0, If[AxisPoints032(k) ∈ Axis, segLength2, 0])], k, 1, Length[AxisPoints032]) → segAxis032
  25. Join({Sequence[Text[(("\textsf{\(-\)" * k) * "\vphantom{,}}"), AxisPointsLeft031(k - 1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, 2, Length[AxisPointsLeft031] + 1], Sequence[Text[((("\textsf{" * If[k < 0, "\(-\)", ""]) * abs(k)) * "\vphantom{,}}"), AxisPointsRight031(k + 2) + (If[k < 0, -0.166, 0], (-segLength1) - dCapY1), false, true, 0, 0], k, -1, Length[AxisPointsRight031] + 4]}) → Cap031
  26. Join({KeepIf[AxisPointsLeft031(IndexOf[a, Cap031]) ∈ Axis, a, Cap031], KeepIf[AxisPointsRight031(IndexOf[a, Remove[Cap031, First[Cap031, 9]]]) ∈ Axis, a, Cap031]}) → Cap032
  27. Join({Sequence[Text[(("\textsf{\(-\)" * k) * ",5}"), AxisPointsLeft032(k - 1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, 2, Length[AxisPointsLeft032] + 1], {Text["\textsf{\(-\)1,5}", MP03 + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0]}, Sequence[Text[((("\textsf{" * If[k ≤ 0, "\(-\)", ""]) * abs(k)) * ",5}"), AxisPointsRight032(k + 1) + (If[k ≤ 0, -0.166, 0], (-segLength1) - dCapY1), false, true, 0, 0], k, 0, Length[AxisPointsRight032] + 2]}) → Cap033
  28. Sequence(MP04 + ((k + 0.5) * (disA04, 0)), k, 0, 1, 1) → AxisPointsRight041
  29. Sequence(MP04 + ((k + 0.5) * ((-disA04), 0)), k, 0, 0, 1) → AxisPointsLeft041
  30. Sequence(PosStart + (k * (axisLength / 4, 0)), k, 0, 4) → AxisPoints051
  31. Sequence(Segment[AxisPoints051(k) + (0, If[k ∈ {1, 5}, (-segLength1), (-segLength2)]), AxisPoints051(k) + (0, If[k ∈ {1, 5}, segLength1, segLength2])], k, 1, 5) → segAxis051
  32. Join({Reverse[AxisPointsLeft041], AxisPointsRight041}) → AxisPoints041
  33. Remove(Sequence[MP04 + (k * ((0.25 * disA04), 0)), k, -3, 3], Join[{AxisPoints041, AxisPoints042}]) → AxisPoints043
  34. Join({KeepIf[AxisPointsLeft032(IndexOf[a, Cap033]) ∈ Axis, a, Cap033], {Text["\textsf{\(-\)4,5}", MP03 + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0]}, KeepIf[AxisPointsRight032(IndexOf[a, Remove[Cap033, First[Cap033, 9]]]) ∈ Axis, a, Cap033]}) → Cap034
  35. RemoveUndefined(Sequence[Text[(("\textsf{\(-\)" * abs(k)) * ",5}"), AxisPoints042(k + If[Length[AxisPoints042] > 2, 6, 5]) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, If[Length[AxisPoints042] > 2, -5, -4], -3, 1]) → Cap042
  36. RemoveUndefined(Sequence[Text[(("\textsf{\(-\)" * abs(k)) * "\vphantom{,}}"), AxisPoints041(k + If[Length[AxisPoints041] > 2, 7, 6]) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, If[Length[AxisPoints041] > 2, -6, -5], -3, 1]) → Cap041
  37. Sequence(If[Length[AxisPoints043] > 4, -6.25, Length[AxisPoints043] > 2, -5.75, -5.25] + (k * 0.5), k, 1, If[Length[AxisPoints043] > 4, 6, Length[AxisPoints043] > 2, 4, 2]) → CapTxt043, {-5.25, -4.75, -4.25, -3.75}
  38. Sequence(Text[(("\textsf{\(-\)" * ReplaceAll[("" * abs(CapTxt043(k))), ".", ","]) * "}"), AxisPoints043(k) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, 1, Length[AxisPoints043]) → Cap043
  39. Sequence(-5 + k, k, 0, 1, 0.25) → CapTxt051, {-5, -4.75, -4.5, -4.25, -4}
  40. Sequence(Text[(("\textsf{\(-\)" * ReplaceAll[("" * abs(CapTxt051(k))), ".", ","]) * "}"), AxisPoints051(k) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, 1, Length[AxisPoints051]) → Cap051
  41. Simplify(input081) → func081
  42. Numerator(func081) → funcN081
  43. Denominator(func081) → funcD081
  44. Simplify(input082) → func082
  45. Denominator(func082) → funcD082
  46. Numerator(func082) → funcN082
  47. Join({Sequence[Text[(("\textsf{\(-\)\frac{" * k) * "5}{10}"), AxisPointsLeft032(k - 4) + (-0.2, segLength1 + dCapY2), false, true, 0, 0], k, 5, Length[AxisPointsLeft032] + 5], {Text["\textsf{\(-\)\frac{45}{10}}", MP03 + (-0.2, segLength1 + dCapY2), false, true, 0, 0]}, Sequence[Text[(((("\textsf{" * If[k < 0, "\(-\)", ""]) * "\frac{") * abs(k)) * "5}{10}}"), AxisPointsRight032(k + 4) + (If[k < 0, -0.2, 0], segLength1 + dCapY2), false, true, 0, 0], k, -3, Length[AxisPointsRight032] + 4]}) → CapF033
  48. Join({KeepIf[AxisPointsLeft032(IndexOf[a, CapF033]) ∈ Axis, a, CapF033], {Text["\textsf{\(-\)\frac{45}{10}}", MP03 + (-0.2, segLength1 + dCapY2), false, true, 0, 0]}, KeepIf[AxisPointsRight032(IndexOf[a, Remove[CapF033, First[CapF033, 9]]]) ∈ Axis, a, CapF033]}) → CapF034
  49. RemoveUndefined(Sequence[Text[(("\textsf{\(-\)\frac{" * abs(k)) * "}{1}}"), AxisPoints041(k + If[Length[AxisPoints041] > 2, 7, 6]) + (-0.2, segLength1 + dCapY2), false, true, 0, 0], k, If[Length[AxisPoints041] > 2, -6, -5], -3, 1]) → CapF041
  50. RemoveUndefined(Sequence[Text[(("\textsf{\(-\)\frac{" * abs(k)) * "5}{10}}"), AxisPoints042(k + If[Length[AxisPoints042] > 2, 6, 5]) + (-0.2, segLength1 + dCapY2), false, true, 0, 0], k, If[Length[AxisPoints042] > 2, -5, -4], -3, 1]) → CapF042
  51. Sequence(If[Length[AxisPoints043] > 4, -625, Length[AxisPoints043] > 2, -575, -525] + (k * 50), k, 1, If[Length[AxisPoints043] > 4, 6, Length[AxisPoints043] > 2, 4, 2]) → CapTxtF043, {-525, -475, -425, -375}
  52. Sequence(Text[(("\textsf{\(-\)\frac{" * abs(CapTxtF043(k))) * "}{100}}"), AxisPoints043(k) + (-0.2, segLength1 + dCapY2), false, true, 0, 0], k, 1, Length[AxisPoints043]) → CapF043
  53. Sequence(Text[(("\bold{\textcolor{db6114}{" * CapTxt071(k)) * "}}"), AxisPoints071(k) + (-0.166, (-segLength1) - dCapY1 + If[k ≟ 4, (-dCapY1), 0]), false, true, 0, 0], k, 1, 4) → Cap071
  54. Sequence(Text[CapTxtF051(k), AxisPoints051(k) + (-0.2, segLength1 + dCapY2), false, true, 0, 0], k, 1, Length[AxisPoints051]) → CapF051
  55. Sequence(Text[(("\bold{\textcolor{db6114}{" * CapTxt072(k)) * "}}"), AxisPoints071(k) + (-0.2, segLength1 + dCapY2 + If[k ≟ 4, dCapY2, 0]), false, true, 0, 0], k, 1, 4) → CapF071
  56. Sequence(Segment[PosStart + ((k * disAxis), (-segLength1)), PosStart + ((k * disAxis), segLength1)], k, 0, 6) → segAxis021
  57. PolyLine(PosSB, Corner[txt042, 1] + (0.5, 0), Corner[txt042, 2] + (0.1, 0), Corner[txt042, 3] + (0.1, 0.1), Corner[txt042, 4] + (-0.1, 0.1), Corner[txt042, 1] + (-0.1, 0.25), PosSB) → sb04
  58. KeepIf(A ∈ Axis, A, Remove[Sequence[MP03 + ((k + 0.25) * (disA03, 0)), k, 0, 5, 0.25], Join[{AxisPointsRight031, AxisPointsRight032}]]) → AxisPointsRight033
  59. KeepIf(A ∈ Axis, A, Remove[Sequence[MP03 + ((k + 0.25) * ((-disA03), 0)), k, 0, 5, 0.25], Join[{AxisPointsLeft031, AxisPointsLeft032}]]) → AxisPointsLeft033
  60. If(selected04 ≟ -1.75, selected52, selected04 ≟ -1.5, selected52 ∨ selected53 ∨ selected54, selected58) → correct5
  61. Corner(imgLupe, 3) → PosImgLupe3
  62. Circle(MPLupe, radiusLupe) → circleLupe
  63. Text("\textsf{\textcolor{50c1c3}{\bold{Zieh mich!}}}", PosImgLupe2 + (0, 1.75), false, true, 0, 0) → CapZiehMichLupe
  64. Segment(Midpoint[Corner[CapZiehMichLupe, 1], Corner[CapZiehMichLupe, 2]], Midpoint[Corner[CapZiehMichLupe, 1], Corner[CapZiehMichLupe, 2]] + (-1.5, -0.5)) → segZiehMichLupe
  65. Text((If[step ≟ 3 ∧ IsInRegion[Pos022, circleLupe], "\bold{", "{"] * "\textsf{\(-\)\frac{1}{3}}}"), Pos022 + (-0.166, segLength1 + dCapY2), false, true, 0, 0) → Cap0222
  66. Sequence(Text[(((("\textsf{" * If[k < 0, "\(-\)", ""]) * "") * abs(k)) * "\vphantom{,\dot{3}}}"), PosStart + (((k + 3) * disAxis) + If[k < 0, -0.166, 0], (-segLength1) - dCapY1), false, true, 0, 0], k, -3, 3, 1) → Cap021
  67. KeepIf(a > 0, a, Sequence[Segment[AxisPoints031(k) + (0, If[AxisPoints031(k) ∈ Axis, (-segLength1), 0]), AxisPoints031(k) + (0, If[AxisPoints031(k) ∈ Axis, segLength1, 0])], k, 1, Length[AxisPoints031]]) → segAxis031
  68. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(1), circleLupe], "\bold{", "{"] * "\textsf{\(-\)\frac{3}{1}}}"), AxisPoints031(1) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0312
  69. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(1), circleLupe], "\bold{", "{"] * Cap021(1)) * "}"), AxisPoints031(1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0311
  70. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(5), circleLupe], "\bold{", "{"] * "\textsf{\frac{1}{1}}}"), AxisPoints031(5) + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0352
  71. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(6), circleLupe], "\bold{", "{"] * "\textsf{\frac{2}{1}}}"), AxisPoints031(6) + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0362
  72. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(7), circleLupe], "\bold{", "{"] * "\textsf{\frac{3}{1}}}"), AxisPoints031(7) + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0372
  73. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(4), circleLupe], "\bold{", "{"] * "\textsf{\frac{0}{1}}}"), AxisPoints031(4) + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0342
  74. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(4), circleLupe], "\bold{", "{"] * Cap021(4)) * "}"), AxisPoints031(4) + (0, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0341
  75. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(5), circleLupe], "\bold{", "{"] * Cap021(5)) * "}"), AxisPoints031(5) + (0, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0351
  76. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(6), circleLupe], "\bold{", "{"] * Cap021(6)) * "}"), AxisPoints031(6) + (0, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0361
  77. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(7), circleLupe], "\bold{", "{"] * Cap021(7)) * "}"), AxisPoints031(7) + (0, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0371
  78. Sequence(Segment[AxisPoints033(k) + (0, If[AxisPoints033(k) ∈ Axis, (-segLength2), 0]), AxisPoints033(k) + (0, If[AxisPoints033(k) ∈ Axis, segLength2, 0])], k, 1, Length[AxisPoints033]) → segAxis033
  79. Text("\textsf{\(-2,5\)\vphantom{\dot{3}}}", AxisPoints042(1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0511
  80. Text("\textsf{\(-0,5\)\vphantom{\dot{3}}}", AxisPoints042(3) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0551
  81. KeepIf(a > 0, a, Sequence[Segment[AxisPoints041(k) + (0, If[AxisPoints041(k) ∈ Axis, (-segLength1), 0]), AxisPoints041(k) + (0, If[AxisPoints041(k) ∈ Axis, segLength1, 0])], k, 1, Length[AxisPoints041]]) → segAxis041
  82. KeepIf(a > 0, a, Sequence[Segment[AxisPoints042(k) + (0, If[AxisPoints042(k) ∈ Axis, (-segLength2), 0]), AxisPoints042(k) + (0, If[AxisPoints042(k) ∈ Axis, segLength2, 0])], k, 1, Length[AxisPoints042]]) → segAxis042
  83. KeepIf(a > 0, a, {Segment[AxisPoints043(2) + (0, If[AxisPoints043(2) ∈ Axis, (-segLength2), 0]), AxisPoints043(2) + (0, If[AxisPoints043(2) ∈ Axis, segLength2, 0])], Segment[AxisPoints043(3) + (0, If[AxisPoints043(3) ∈ Axis, (-segLength2), 0]), AxisPoints043(3) + (0, If[AxisPoints043(3) ∈ Axis, segLength2, 0])]}) → segAxis043
  84. KeepIf(a > 0, a, Sequence[Segment[AxisPoints044(k) + (0, If[AxisPoints044(k) ∈ Axis, (-segLength2), 0]), AxisPoints044(k) + (0, If[AxisPoints044(k) ∈ Axis, segLength2, 0])], k, 1, Length[AxisPoints044]]) → segAxis044
  85. Text("\textsf{\(-2,125\)\vphantom{\dot{3}}}", AxisPoints044(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0611
  86. Text("\textsf{\(-0,875\)\vphantom{\dot{3}}}", AxisPoints044(7) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0661
  87. Sequence(PosStart + (k * (axisLength / 8, 0)), k, 0, 8) → AxisPoints061
  88. Sequence(Segment[AxisPoints061(k) + (0, If[k ∈ {1, 9}, (-segLength1), (-segLength2)]), AxisPoints061(k) + (0, If[k ∈ {1, 9}, segLength1, segLength2])], k, 1, 9) → segAxis061
  89. Sequence(-2.125 + (k * 0.125), k, 1, 9) → NumberList061, {-2, -1.875, -1.75, -1.625, -1.5, -1.375, -1.25, -1.125, -1}
  90. Sequence(Text[(("\textsf{\(" * ReplaceAll[("" * NumberList061(k)), ".", ","]) * "\)\vphantom{,\dot{3}}}"), AxisPoints061(k) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0], k, 1, 9) → CapList061
  91. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected41, "\bold{", "{"] * "\textsf{\(-2,5\)\vphantom{\dot{3}}}}"), AxisPoints032(1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0411
  92. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected43, "\bold{", "{"] * "\textsf{\(-1,75\)\vphantom{\dot{3}}}}"), AxisPoints033(1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0441
  93. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected47, "\bold{", "{"] * "\textsf{\(-0,5\)\vphantom{\dot{3}}}}"), AxisPoints032(3) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0431
  94. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected45, "\bold{", "{"] * "\textsf{\(-1,25\)\vphantom{\dot{3}}}}"), AxisPoints033(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0451
  95. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected44, "\bold{", "{"] * "\textsf{\(-1,5\)\vphantom{\dot{3}}}}"), AxisPoints032(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0421
  96. Text((If[step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected52, "\bold{", "{"] * "\textsf{\(-1,875\)\vphantom{\dot{3}}}}"), AxisPoints044(3) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0621
  97. Text((If[step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected54, "\bold{", "{"] * "\textsf{\(-1,625\)\vphantom{\dot{3}}}}"), AxisPoints044(4) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0631
  98. Text((If[step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected56, "\bold{", "{"] * "\textsf{\(-1,375\)\vphantom{\dot{3}}}}"), AxisPoints044(5) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0641
  99. Text((If[step ≟ 5 ∧ selected58, "\bold{", "{"] * "\textsf{\(-1,125\)\vphantom{\dot{3}}}}"), AxisPoints044(6) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0651
  100. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(2), circleLupe] ∨ step ≟ 4, "\bold{", "{"] * Cap021(2)) * "}"), AxisPoints031(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0321
  101. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(2), circleLupe] ∨ step ≟ 4, "\bold{", "{"] * "\textsf{\(-\)\frac{2}{1}}}"), AxisPoints031(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0322
  102. Text(((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(3), circleLupe] ∨ step ≟ 4, "\bold{", "{"] * Cap021(3)) * "}"), AxisPoints031(3) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0331
  103. Text((If[step ≟ 3 ∧ IsInRegion[AxisPoints031(3), circleLupe] ∨ step ≟ 4, "\bold{", "{"] * "\textsf{\(-\)\frac{1}{1}}}"), AxisPoints031(3) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0332
  104. SelectedIndex(dropdown071) → index071
  105. Text((If[step ≟ 2 ∨ step ≟ 3 ∧ IsInRegion[Pos021, circleLupe], "\bold{", "{"] * "\textsf{\(-2,7\)\vphantom{\dot{3}}}}"), Pos021 + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0211
  106. Text((If[step ≟ 2 ∨ step ≟ 3 ∧ IsInRegion[Pos022, circleLupe], "\bold{", "{"] * "\textsf{\(-0,\dot{3}\)}}"), Pos022 + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0221
  107. Text((If[step ≟ 2 ∨ step ≟ 3 ∧ IsInRegion[Pos024, circleLupe], "\bold{", "{"] * "\textsf{2\scriptsize{\frac{1}{4}}}}"), Pos024 + (0, (-segLength1) - dCapY2 + 0.26), false, true, 0, 0) → Cap0241
  108. Text((If[step ≟ 3 ∧ IsInRegion[Pos021, circleLupe], "\bold{", "{"] * "\textsf{\(-\)\frac{27}{10}}}"), Pos021 + (-0.166, segLength1 + dCapY2), false, true, 0, 0) → Cap0212
  109. Text((If[step ≟ 3 ∧ IsInRegion[Pos024, circleLupe], "\bold{", "{"] * "\textsf{\frac{9}{4}}}"), Pos024 + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0242
  110. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected44, "\bold{", "{"] * "\textsf{\(-\)\frac{15}{10}\vphantom{\dot{3}}}}"), AxisPoints032(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0422
  111. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected43, "\bold{", "{"] * "\textsf{\(-\)\frac{175}{100}\vphantom{\dot{3}}}}"), AxisPoints033(1) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0442
  112. Text((If[zoom1 ≟ 0 ∧ step ≟ 4 ∧ selected45, "\bold{", "{"] * "\textsf{\(-\)\frac{125}{100}\vphantom{\dot{3}}}}"), AxisPoints033(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0452
  113. Text("\textsf{\(-\)\frac{175}{100}\vphantom{\dot{3}}}", AxisPoints043(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0562
  114. Text("\textsf{\(-\)\frac{125}{100}\vphantom{\dot{3}}}", AxisPoints043(3) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0572
  115. Text("\textsf{\(-\)\frac{1875}{1000}\vphantom{\dot{3}}}", AxisPoints044(3) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0622
  116. Text("\textsf{\(-\)\frac{1625}{1000}\vphantom{\dot{3}}}", AxisPoints044(4) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0632
  117. Text("\textsf{\(-\)\frac{1375}{1000}\vphantom{\dot{3}}}", AxisPoints044(5) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0642
  118. Text("\textsf{\(-\)\frac{1125}{1000}\vphantom{\dot{3}}}", AxisPoints044(6) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0652
  119. Text("\textsf{\(-\)\frac{15}{10}\vphantom{\dot{3}}}", AxisPoints042(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0532
  120. Text("\textsf{\(-\)\frac{175}{100}\vphantom{\dot{3}}}", AxisPoints043(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → CapNumber053
  121. Text("\textsf{\(-\)\frac{15}{10}\vphantom{\dot{3}}}", Midpoint[AxisPoints043(2), AxisPoints043(3)] + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → CapNumber052
  122. Text("\textsf{\(-\)\frac{125}{100}\vphantom{\dot{3}}}", AxisPoints043(3) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → CapNumber051
  123. Text((If[step ≟ 5 ∧ selected04 < -1.25 ∨ step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected51, "\bold{", "{"] * "\textsf{\(-\)\frac{2}{1}\vphantom{,\dot{3}}}}"), AxisPoints041(1) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0522
  124. Text((If[step ≟ 5 ∧ selected04 < -1.25 ∨ step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected51, "\bold{", "{"] * "\textsf{\(-2\)\vphantom{,\dot{3}}}}"), AxisPoints041(1) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0521
  125. Text((If[step ≟ 5 ∧ (selected04 ≟ -1.75 ∨ selected53), "\bold{", "{"] * "\textsf{\(-1,75\)\vphantom{\dot{3}}}}"), AxisPoints043(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0561
  126. Text((If[step ≟ 5 ∧ selected04 ≟ -1.25 ∨ step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected59, "\bold{", "{"] * "\textsf{\(-\)\frac{1}{1}\vphantom{,\dot{3}}}}"), AxisPoints041(2) + (-0.18, segLength1 + dCapY2), false, true, 0, 0) → Cap0542
  127. Text((If[step ≟ 5 ∧ selected04 ≟ -1.25 ∨ step ≟ 5 ∧ zoom2 ≟ 0 ∧ selected59, "\bold{", "{"] * "\textsf{\(-1\)\vphantom{,\dot{3}}}}"), AxisPoints041(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0541
  128. Text((If[step ≟ 5 ∧ (selected04 ≟ -1.5 ∨ selected55 ∧ zoom2 ≟ 0), "\bold{", "{"] * "\textsf{\(-1,5\)\vphantom{\dot{3}}}}"), AxisPoints042(2) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0531
  129. Text((If[step ≟ 5 ∧ (selected04 ≟ -1.25 ∨ selected57 ∧ zoom2 ≟ 0), "\bold{", "{"] * "\textsf{\(-1,25\)\vphantom{\dot{3}}}}"), AxisPoints043(3) + (-0.166, (-segLength1) - dCapY1), false, true, 0, 0) → Cap0571
  130. Text((If[step ≟ 2 ∨ step ≟ 3 ∧ IsInRegion[Pos023, circleLupe], "\textcolor{db6114}{\bold{", "{{"] * "\textsf{\frac{2}{3}}}}"), Pos023 + (0, segLength1 + dCapY2), false, true, 0, 0) → Cap0232
  131. If(step ≟ 3, CountIf[a ≟ true, a, ShowStep3] ≥ 6, step ≟ 4, zoom1 ≟ 0 ∧ (selected43 ∨ selected44 ∨ selected45), step ≟ 5, zoom2 ≟ 0 ∧ correct5, true) → clickableBtnNext

AI 绘图提示语参考

生成一个用于比较与表示有理数的互动式分数练习画面：先在画布上绘制网格背景与横竖边界线，再在网格上标注行列刻度文字（含字母与若干带负号的数值样式），并在图中预留输入框位置。随后在中心区域画出一组带标题的小图形块，由若干折线轮廓构成的分段条形边框组成，条形上方与左右两侧用多组文本标出“k”“1,5”“4,5”等分段标记。最后加入两处可解析为分子分母的输入框，并在对应位置显示由5与10形成的分数格式刻度（如带负号的 5/10 表达），使得整体布局呈现有理数分数建模与比较的结构化界面。
以上提示语为根据原始绘图命令整理而来，仅供参考。