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平方根

平方根
几何画板及绘图内容加载中，请稍等……
2025-11-26 03:42
所属专题 Quadratzahlen und Quadratwurzeln
这个范例演示了平方根的概念。它涉及的核心数学概念包括根号和实数。通过使用GeoGebra命令如Sequence、Element、Textfield等，用户可以探索平方根的性质。适合初中及以上学生学习平方根的相关知识。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {5, 10, 4, 7, 2, 3, 6, 3, 1, 6}
  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
  7. SelectedIndex(dropdown051) → index051
  8. Sequence(InputQList(k) ≟ SolutionQList(k), k, 1, Length[InputQList]) → CorrectQList
  9. Sequence(Sequence[Polygon[PosQ01 - ((2.5 * disQ), (2.5 * disQ)) + ((k * (dimQ + disQ)), (m * (dimQ + disQ))) + (dimQ * {(0, 0), (0, 1), (1, 1), (1, 0)})], k, 0, 5], m, 0, 5) → polyQ06
  10. If(step ≟ 9, (5.1, 4.75), (8.6, 5.85)) → Pos1
  11. Angle(MP1 + (1, 0), MP1, Pos1) → angle11
  12. Angle(MP1 + (1, 0), MP1, Pos2) → angle12
  13. CircleArc(MP1, MP1 + (Distance[MP1, Pos1] * (cos(angle12 + disAngle), sin(angle12 + disAngle))), MP1 + (Distance[MP1, Pos1] * (cos(angle11 - disAngle), sin(angle11 - disAngle)))) → arc01
  14. Mirror(arc01, Spiegelgerade) → arc02
  15. Text((("\textsf{\bold{\Large{" * If[step < 7, "6", step ≟ 7, "3", step ≟ 8, "1", "x\vphantom{x²}"]) * "}}}"), Pos1 + (0, If[step > 8, 0.15, 0]), false, true, 0, 0) → txt1
  16. Text((("\textsf{\bold{\Large{" * If[step < 7, "36", step ≟ 7, "9", step ≟ 8, "1", "x²"]) * "}}}"), Pos2 + (0, If[step > 8, 0.15, 0]), false, true, 0, 0) → txt2
  17. Segment(Point[arc01, 0], Point[arc01, 0] + (0.001 * UnitVector[Tangent[Point[arc01, 0], arc01]])) → arrow01
  18. Segment(Point[arc02, 1], Point[arc02, 1] + (0.001 * UnitVector[Tangent[Point[arc02, 1], arc02]])) → arrow02
  19. Translate(arc01, Vector[Pos1, Pos3]) → arc03
  20. Translate(arc02, Vector[Pos1, Pos3]) → arc04
  21. Translate(arrow01, Vector[Pos1, Pos3]) → arrow03
  22. Translate(arrow02, Vector[Pos1, Pos3]) → arrow04
  23. Translate(MP1, Vector[Pos1, Pos3]) → MP3
  24. Translate(MP2, Vector[Pos1, Pos3]) → MP4
  25. Text((("\textsf{\bold{\Large{" * If[step < 7, "6", step ≟ 7, "3", step ≟ 8, "1", "x\vphantom{x²}"]) * "}}}"), Pos3 + (0, If[step > 8, 0.15, 0]), false, true, 0, 0) → txt3
  26. Text((("\textsf{\bold{\Large{" * If[step < 7, "36", step ≟ 7, "9", step ≟ 8, "1", "x²"]) * "}}}"), Pos4 + (0, If[step > 8, 0.15, 0]), false, true, 0, 0) → txt4
  27. Text("\bold{\textsf{Quadrieren}}", MP4 + (0, 0.15), false, true, 0, 0) → txt7
  28. Text("\bold{\textsf{Quadratwurzelziehen}}", MP3 + (0, -0.15), false, true, 0, 0) → txt8
  29. Textfield(input021) → InputBox021
  30. Textfield(input051) → InputBox051
  31. Textfield(input052) → InputBox052
  32. Textfield(input061) → InputBox061
  33. Textfield(input062) → InputBox062
  34. Textfield(input071) → InputBox071
  35. Textfield(input072) → InputBox072
  36. Textfield(input081) → InputBox081
  37. Textfield(input082) → InputBox082
  38. Sequence(Sequence[Polygon[PosQ02 - ((2.5 * disQ), (2.5 * disQ)) + ((k * (dimQ + disQ)), (m * (dimQ + disQ))) + (dimQ * {(0, 0), (0, 1), (1, 1), (1, 0)})], k, 0, 2], m, 0, 2) → polyQ07
  39. Sequence(Sequence[Polygon[PosQ03 - ((2.5 * disQ), (2.5 * disQ)) + ((k * (dimQ + disQ)), (m * (dimQ + disQ))) + (dimQ * {(0, 0), (0, 1), (1, 1), (1, 0)})], k, 0, 0], m, 0, 0) → polyQ08
  40. Textfield(inputQ022) → InputBoxQ022
  41. Textfield(inputQ031) → InputBoxQ031
  42. Textfield(inputQ032) → InputBoxQ032
  43. Textfield(inputQ041) → InputBoxQ041
  44. Textfield(inputQ042) → InputBoxQ042
  45. Textfield(inputQ051) → InputBoxQ051
  46. Textfield(inputQ052) → InputBoxQ052
  47. Textfield(inputQ061) → InputBoxQ061
  48. Textfield(inputQ062) → InputBoxQ062
  49. Textfield(inputQ071) → InputBoxQ071
  50. Textfield(inputQ072) → InputBoxQ072
  51. Textfield(inputQ081) → InputBoxQ081
  52. Textfield(inputQ082) → InputBoxQ082
  53. Textfield(inputQ091) → InputBoxQ091
  54. Textfield(inputQ092) → InputBoxQ092
  55. Textfield(inputQ101) → InputBoxQ101
  56. Textfield(inputQ102) → InputBoxQ102
  57. Textfield(inputQ111) → InputBoxQ111
  58. Textfield(inputQ112) → InputBoxQ112
  59. Textfield(inputQ121) → InputBoxQ121
  60. Textfield(inputQ122) → InputBoxQ122
  61. Textfield(inputQ131) → InputBoxQ131
  62. Textfield(inputQ132) → InputBoxQ132
  63. Textfield(inputQ141) → InputBoxQ141
  64. Textfield(inputQ142) → InputBoxQ142
  65. Textfield(inputQ151) → InputBoxQ151
  66. Textfield(inputQ152) → InputBoxQ152
  67. If(step ≟ 2, correct021, step ≟ 3, anim03 ≟ Length[txtListAnim03], true, step ≟ 5, correct051 ∧ correct052 ∧ correct053 ∧ correctdd051, step ≟ 6, correct061 ∧ correct062, step ≟ 7, correct071 ∧ correct072, step ≟ 8, correct081 ∧ correct082) → clickableBtnNext
  68. Text("\textsf{\large{\bold{\textcolor{black}{A = 36 cm²}}}}", PosQ01 + (dimQ * (3, 3)), false, true, 0, 0) → CapQ01
  69. Segment(Vertex[polyQ01(1), 3] + (disSeg, 0), Vertex[polyQ01(1), 4] + (disSeg, 0)) → seg011
  70. Segment(Vertex[polyQ01(1), 1] + (0, (-disSeg)), Vertex[polyQ01(1), 4] + (0, (-disSeg))) → seg012
  71. Textfield(input053) → InputBox053
  72. Text("\textsf{\bold{\textcolor{black}{A = 9 cm²}}}", PosQ02 + (dimQ * (1.5, 1.5)), false, true, 0, 0) → CapQ02
  73. Text("\textsf{\bold{\textcolor{black}{A = 1 cm²}}}", PosQ03 + (dimQ * (0.5, 0.5)) + (-0.05, 0) + (0, dimQ), false, true, 0, 0) → CapQ03
  74. Text("\textsf{Quadratwurzelziehen}", MP1 - (0, 0.85), false, true, 0, 0) → CapOperation2
  75. Text("\textsf{Quadrieren}", MP2 + (0, 0.85), false, true, 0, 0) → CapOperation1
  76. Segment(Vertex[polyQ06(1, 6), 4] + (disSeg, 0), Vertex[polyQ06(6, 6), 3] + (disSeg, 0)) → seg061
  77. Segment(Vertex[polyQ06(1, 1), 1] + (0, (-disSeg)), Vertex[polyQ06(1, 6), 4] + (0, (-disSeg))) → seg062
  78. Segment(Vertex[polyQ07(1, 3), 4] + (disSeg, 0), Vertex[polyQ07(3, 3), 3] + (disSeg, 0)) → seg071
  79. Segment(Vertex[polyQ07(1, 1), 1] + (0, (-disSeg)), Vertex[polyQ07(1, 3), 4] + (0, (-disSeg))) → seg072
  80. Segment(Vertex[polyQ08(1, 1), 4] + (disSeg, 0), Vertex[polyQ08(1, 1), 3] + (disSeg, 0)) → seg081
  81. Segment(Vertex[polyQ08(1, 1), 1] + (0, (-disSeg)), Vertex[polyQ08(1, 1), 4] + (0, (-disSeg))) → seg082
  82. Text("\bold{\textsf{\begin{array}{c}Quadrieren\\x \cdot x = x²\end{array}}}", MP2 + (0, -0.5), false, true, 0, 1) → txt5
  83. Text("\bold{\textsf{\begin{array}{c}\sqrt{x²} = x\\Quadratwurzelziehen\vphantom{x²}\end{array}}}", MP1 + (0, 0.5), false, true, 0, -1) → txt6
  84. If(step ≟ 2, Corner[txt021, 1] + (0.5, -0.25), step ≟ 5, Corner[txt051, 1] + (4, -0.25), 6 ≤ step ≤ 8, Pos1 + (0.85, 0.25), step ≟ 10, Corner[txt102, 1] + (3.5, 0), (1, 1)) → PosShowSolution