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比例关系与几何作图：通过图形展示直接与间接比例关系

比例关系与几何作图：通过图形展示直接与间接比例关系
几何画板及绘图内容加载中，请稍等……
2023-07-20 14:12
所属专题 Wiederholung: Direkte und Indirekte Proportionalität Direkte Proportionalität
本范例通过几何作图演示直接与间接比例关系。核心数学概念包括比例关系、图形表示和几何作图。作图要点包括使用GeoGebra命令如If、Rotate、CircleArc等进行图形构造。适合小学5-6年级学生用于理解比例概念和几何作图技能。

GeoGebra 命令及参数

  1. If(step ≤ 5, 0.4, 0.65) → sizecoord
  2. Rotate(O2 + ((15 * sizecoord) + 0.2, 0), 45°, O2) → Ccorrect
  3. CircleArc(O2, Cstart, Ccorrect) → c
  4. Point(c) → C
  5. If(step ≤ 5, O1, O2) → O
  6. Flatten(Sequence[Sequence[O + (m * (sizecoord, 0)) + (j * (0, sizecoord)), m, 0, widthcoord], j, 0, heightcoord + 1]) → pointsCoords
  7. Point(pointsCoords) → X9
  8. Point(pointsCoords) → X7
  9. Point(pointsCoords) → X6
  10. Point(pointsCoords) → X4
  11. Point(pointsCoords) → X3
  12. Sort({X3, X4, X6, X7, X9}) → points2
  13. Flatten(Sequence[Sequence[O + (m * (sizecoord, 0)) + (j * (0, sizecoord)), m, 0, widthcoord - 1], j, 0, heightcoord]) → pointsGoal
  14. Flatten(Sequence[Sequence[PTabularLeft + (m * (0.7, 0)) + (j * (0, (-sizetabular))) + (-2, -1.65), m, 0, 2], j, 0, 4]) → pointsStart
  15. Point(Join[{pointsGoal, pointsStart}]) → X0
  16. Point(Join[{pointsGoal, pointsStart}]) → X8
  17. Point(Join[{pointsGoal, pointsStart}]) → X5
  18. Point(Join[{pointsGoal, pointsStart}]) → X2
  19. Flatten(Sequence[Sequence[Z + (m * (sizetabular, 0)) + (j * (0, (-sizetabular))), m, 0, 2], j, 0, 7]) → l3
  20. Segment(pointsCoords(1), pointsCoords(((widthcoord + 1) * (heightcoord + 1)) - widthcoord)) → yline
  21. Sequence(O + (m * (0, sizecoord)), m, 1, heightcoord - 1) → pointsy
  22. Zip(Segment[A + ((-heightlines), 0), A + (heightlines, 0)], A, pointsy) → linesy
  23. Sequence(Text["\textsf{" + (m) + "}", ((m * sizecoord) + x(O), y(O) - 0.9), true, true, -0, 1], m, 0, widthcoord - 2) → textx
  24. Join({Sequence[Segment[pointsCoords((widthcoord * m) + m + 1), pointsCoords(((m + 1) * widthcoord) + m)], m, 0, heightcoord], Sequence[Segment[pointsCoords(m), pointsCoords(((widthcoord + 1) * heightcoord) + m)], m, 1, widthcoord]}) → linescoord
  25. Segment(pointsCoords(1), pointsCoords(widthcoord)) → xline
  26. Polygon(Corner[lineal, 1], Corner[lineal, 2], Corner[lineal, 3], Corner[lineal, 4]) → v2, f, h, i, j
  27. SpeechBubbleLeft(N, 6.1, 1.7) → Vieleck1
  28. If(step ≟ 3.5, correcttab, If[step ≟ 3.75, true, listfixed(step)]) → fixed
  29. Point(Line[S, xAxis]) → T
  30. Textfield(input1) → Eingabefeld1
  31. Textfield(input2) → Eingabefeld2
  32. Textfield(input3) → Eingabefeld3
  33. Textfield(input4) → Eingabefeld4
  34. Textfield(input5) → Eingabefeld5
  35. Textfield(input6) → Eingabefeld6
  36. Textfield(input7) → Eingabefeld7
  37. Textfield(input8) → Eingabefeld8
  38. Point(Line[A_1, xAxis]) → B_1
  39. Point(Line[A_1, xAxis]) → C_1
  40. Point(Line[L, xAxis]) → M
  41. SpeechBubbleLeft(G_1, 9.2, 1.1) → Vieleck2
  42. Point(Line[I_1, xAxis]) → H_1
  43. Point(Line[C_1, xAxis]) → D_1
  44. Segment(O, O + ((1.07 * heightcoord) * (sizecoord, sizecoord))) → g
  45. Sequence(Text["\textsf\small{" + (m) + "}", ((m * sizecoord) + x(O), y(O) - 0.9), true, true, -0, 1], m, 0, widthcoord - 2) → textxsmall
  46. Sequence(Text[(("\textsf\small{" * ReplaceAll["" + ((m * 0.5)) + "", ".", ","]) * "}"), (x(O) - 0.6, (m * sizecoord) + y(O) - 0.4), true, true, -0, 1], m, 1, heightcoord - 1) → textysmall
  47. SpeechBubbleLeft(N, 7.2, 1.1) → Vieleck3
  48. Sequence(PTabularLeft + (m * (0, aby)) + (abx, 0), m, 0, 5) → listPTabular
  49. Zip(CountIf[m ≟ Ö, m, {X3, X4, X6, X7, X9}], Ö, {X3, X4, X6, X7, X9}) → pointsSame
  50. Max(pointsSame) → numPointsSame
  51. Sequence(Text[(("\textsf{" * ReplaceAll["" + ((m * 0.5)) + "", ".", ","]) * "}"), (x(O) - 0.6, (m * sizecoord) + y(O) - 0.4), true, true, -0, 1], m, 1, heightcoord - 1) → texty
  52. Sequence(O + (m * (sizecoord, 0)), m, 1, widthcoord - 2) → pointsx
  53. Zip(Segment[A + (0, (-heightlines)), A + (0, heightlines)], A, pointsx) → linesx
  54. KeepIf(Y ∈ pointsx, Y, {X3, X4, X6, X7, X9}) → pointsonXaxis
  55. If(pointsonXaxis ≟ {}, {}, Sort[Zip[(x(Y) - x(O2)) / sizecoord, Y, pointsonXaxis]]) → xonXaxis
  56. Length(pointsonXaxis) → lengthonXaxis
  57. Point(Line[GB1, xAxis]) → GB2