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2025-11-26 03:45
所属专题 Quadratzahlen und Quadratwurzeln
这个范例演示了如何通过几何构造理解小数和进位概念。核心数学概念包括数列、圆和轨迹。作图要点涉及使用GeoGebra命令如Sequence、Circle和Locus来构建图形。适合初中或高中数学学习，用于理解实数和几何关系。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {1, 6, 3, 7, 7, 2, 5, 4, 5, 8}
  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. Textfield(input22) → inputBox22
  8. Textfield(input21) → inputBox21
  9. Textfield(input23) → inputBox23
  10. Textfield(input24) → inputBox24
  11. Textfield(input34) → inputBox34
  12. Textfield(input31) → inputBox31
  13. Textfield(input32) → inputBox32
  14. Textfield(input33) → inputBox33
  15. Polygon(q03LO, q03RO, q03RU, q03LU) → q031, s031_{1}, s031_{2}, s031, s031_{3}
  16. Polygon(q03LO_{1}, q03RO_{1}, q03RU_{1}, q03LU_{1}) → q031_{1}, s031_{4}, s031_{5}, s031_{6}, s031_{7}
  17. CountIf(x ≟ true, {isColor1_1, isColor1_2, isColor1_3, isColor1_4, isColor1_5, isColor1_6, isColor1_7, isColor1_8, isColor1_9, isColor1_10, isColor1_11, isColor1_12, isColor2_1, isColor2_2, isColor2_3, isColor2_4, isColor2_5, isColor2_6, isColor3_1, isColor3_2, isColor3_3, isColor3_4, isColor3_5, isColor3_6, isColor4_1, isColor4_2, isColor4_3, isColor4_4, isColor4_5, isColor4_6, isColor4_7, isColor4_8, isColor4_9, isColor4_10, isColor4_11, isColor4_12}) → sumColored
  18. Circle(pLupM, 0.7) → circleLup
  19. Textfield(input61) → inputBox61
  20. Textfield(input62) → inputBox62
  21. Textfield(input63) → inputBox63
  22. Textfield(input64) → inputBox64
  23. Textfield(input65) → inputBox65
  24. Polygon(pSquare71LO, pSquare71RO, pSquare71RU, pSquare71LU) → qAnim71, a, b, c, d
  25. Textfield(input71) → inputBox71
  26. Textfield(input72) → inputBox72
  27. Textfield(input73) → inputBox73
  28. Textfield(input74) → inputBox74
  29. Textfield(input75) → inputBox75
  30. CountIf(x ≟ true, {isColor5_1, isColor5_2, isColor5_3, isColor5_4, isColor5_5, isColor5_6, isColor5_7, isColor5_8, isColor5_9, isColor5_10, isColor5_11, isColor5_12, isColor6_1, isColor6_2, isColor6_3, isColor6_4, isColor6_5, isColor6_6, isColor7_1, isColor7_2, isColor7_3, isColor7_4, isColor7_5, isColor7_6, isColor8_1, isColor8_2, isColor8_3, isColor8_4, isColor8_5, isColor8_6, isColor8_7, isColor8_8, isColor8_9, isColor8_10, isColor8_11, isColor8_12}) → sumColored2
  31. Textfield(input511) → inputBox511
  32. Textfield(input512) → inputBox512
  33. If(step ≟ 5.1, correct511 ∧ correct512 ∧ step ≟ 5.1, listClickableBtnNext(step)) → clickableBtnNext
  34. Textfield(input30) → inputBox30
  35. Textfield(input20) → inputBox20
  36. Segment(A, B) → seg51
  37. Segment(A_{1}, B_{1}) → seg51_{1}
  38. Segment(A_{2}, B_{2}) → seg51_{2}
  39. Segment(A_{3}, B_{3}) → seg51_{3}
  40. Segment(A_{7}, B_{7}) → seg51_{4}
  41. Segment(A_{6}, B_{6}) → seg51_{5}
  42. Segment(A_{5}, B_{5}) → seg51_{6}
  43. Segment(A_{4}, B_{4}) → seg51_{7}
  44. Textfield(input101) → inputBox101
  45. Textfield(input102) → inputBox102
  46. Circle(pLupM2, 0.7) → circleLup2
  47. Polygon(pHint6LO, pHint6RO, pHint6RU, pHint6LU) → qHint63, c_1, d_1, e_1, f
  48. Polygon(pHint6LO_{1}, pHint6RO_{1}, pHint6RU_{1}, pHint6LU_{1}) → qHint62, c_{2}, d_{2}, e_{2}, f_{1}
  49. Polygon(pHint6LO_{3}, pHint6RO_{3}, pHint6RU_{3}, pHint6LU_{3}) → qHint61, c_{4}, d_{4}, e_{4}, f_{3}
  50. Polygon(pHint6LO_{5}, pHint6RO_{5}, pHint6RU_{5}, pHint6LU_{5}) → qHint64, c_{6}, d_{6}, e_{6}, f_{5}
  51. Polygon(pHint6LO_{7}, pHint6RO_{7}, pHint6RU_{7}, pHint6LU_{7}) → qHint65, c_{8}, d_{8}, e_{8}, f_{7}
  52. Segment(pWarumL, pWarumR) → warum_{6}
  53. Segment(pWarumL_{1}, pWarumR_{1}) → warum_{1}
  54. Segment(pWarumL_{2}, pWarumR_{2}) → warum_{2}
  55. Segment(pWarumL_{3}, pWarumR_{3}) → warum_{3}
  56. Segment(pWarumL_{4}, pWarumR_{4}) → warum_{4}
  57. Segment(pWarumL_{6}, pWarumR_{6}) → warum_{5}
  58. Segment(pWarumL_{7}, pWarumR_{7}) → warum_{12}
  59. Segment(pWarumL_{12}, pWarumR_{12}) → warum_{7}
  60. Segment(pWarumL_{11}, pWarumR_{11}) → warum_{8}
  61. Segment(pWarumL_{10}, pWarumR_{10}) → warum_{9}
  62. Segment(pWarumL_{9}, pWarumR_{9}) → warum_{10}
  63. Segment(pWarumL_{8}, pWarumR_{8}) → warum_{11}
  64. Segment(pWarumL_{21}, pWarumR_{21}) → warum_{16}
  65. Segment(pWarumL_{20}, pWarumR_{20}) → warum_{17}
  66. Segment(pWarumL_{19}, pWarumR_{19}) → warum_{18}
  67. Segment(pWarumL_{15}, pWarumR_{15}) → warum_{22}
  68. Segment(pWarumL_{14}, pWarumR_{14}) → warum_{23}
  69. Segment(pWarumL_{13}, pWarumR_{13}) → warum_{24}