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整数的有序性

整数的有序性
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2024-06-13 18:24
所属专题 Ordnen und Vergleichen von rationalen Zahlen Ordnen und Vergleichen von ganzen Zahlen
本范例演示了整数的有序性，展示了如何比较和排序整数。核心数学概念包括整数的定义、整数的有序性以及整数的比较。作图要点包括使用 GeoGebra 的 Sequence、Textfield 和 SpeechBubbleLeft 等命令。适合的学段或用途包括初中数学教育，特别是整数和数论的教学。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {7, 5, 5, 7, 10, 9, 8, 3, 3, 4}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. If(step ≟ 4.5, 13.5, 13) → sbwidth5
  5. SpeechBubbleLeft(PosSB, sbwidth, sbheight) → poly1
  6. Sequence(Origin + (((-lengthAxis)) / 2, 0) + ((k * lengthAxis / 10), 0), k, 0, 10) → AxisPoints
  7. Segment(Origin + (((-lengthAxis)) / 2 - edge, 0), Origin + (lengthAxis / 2 + edge, 0)) → AxisZ
  8. Sequence(Segment[AxisPoints(k) + (0, ((-lengthSeg)) / 2), AxisPoints(k) + (0, lengthSeg / 2)], k, 1, Length[AxisPoints]) → AxisSeg
  9. Segment(Origin + (((-lengthAxis)) / 10, 1.5), Origin + ((-4 * lengthAxis / 10), 1.5)) → segK
  10. Segment(Origin + (lengthAxis / 10, 1.5), Origin + ((4 * lengthAxis / 10), 1.5)) → segG
  11. Sequence(Midpoint[AxisPoints(k), AxisPoints(k + 1)], k, 1, Length[AxisPoints] - 1) → MidpointList
  12. Point(PointPList) → PointP
  13. If(step ≠ 6 ∧ step ≠ 7, 5, IndexOf[PointP, PointPList] - 5.5) → pos
  14. SelectedIndex(dropdown41) → index41
  15. SelectedIndex(dropdown42) → index42
  16. SelectedIndex(dropdown51) → index51
  17. SelectedIndex(dropdown52) → index52
  18. PolyLine(PosSB, PosSB + (0.8, 0.3), PosSB + (sbwidth, 0.3), PosSB + (sbwidth, 0.8 + sbheight + 0.2), PosSB + (0.2, 0.8 + sbheight + 0.2), PosSB + (0.2, 1), PosSB) → sb06
  19. Polygon(PointP, PointP + (0.66, 0), PointP + (0.66, -0.6), PointP + (0, -0.6)) → polyS, pointp, f, g, h
  20. SelectedIndex(dropdown61) → index61
  21. Text("\textsf{links}", Origin + ((-4 * lengthAxis / 10) - 0.1, 1.62), false, true, -1, 0) → CapLinks
  22. Text("$\textsf{rechts}$", Origin + ((4 * lengthAxis / 10) + 0.1, 1.62), false, true, 1, 0) → CapRechts
  23. SelectedIndex(dropdown4b1) → index4b1
  24. SelectedIndex(dropdown4b2) → index4b2
  25. If(step ≟ 4, correctdd41 ∧ correctdd42, true, step ≟ 4.5, correctdd4b1 ∧ correctdd4b2, step ≟ 5, correctdd51 ∧ correctdd52, step ≟ 6, activateBtnNext, step ≟ 7, correctdd61) → clickableBtnNext
  26. Sequence(Text[(((((("\textsf{\textcolor{" * If[pos + 0.5 ≟ k ∨ pos - 0.5 ≟ k, ggbBlue, k ≟ 0 ∧ step ≟ 4.5, "#DB6114", "#000000"]) * "}{") * If[pos + 0.5 ≟ k ∨ pos - 0.5 ≟ k ∨ k ≟ 0 ∧ step ≟ 4.5, "\bold{", "{"]) * "\(") * k) * "\)}}}"), AxisPoints(k + 6) + (If[k < 0, -0.17, 0], ((-lengthSeg)) / 2), false, true, 0, -1], k, -5, 5, 1) → AxisCap
  27. Vector(PointP + (0.25, -1.5), PointP + (0.25, -0.55)) → vZiehMich
  28. Text("$\textsf{Zieh mich!}$", PointP + (0.5, -1.4), false, true, 0, -1) → CapZiehMich
  29. Text("\textsf{\bold{kleiner}}", Midpoint[segK], false, true, 0, 1) → CapK
  30. Text("\textsf{\bold{größer}}", Midpoint[segG], false, true, 0, 1) → CapG