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Rechentrick: Nullen und Nachkommastellen

Rechentrick: Nullen und Nachkommastellen
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2025-11-26 03:45
In collections Quadratzahlen und Quadratwurzeln
This example demonstrates how to understand decimal places and carrying through geometric construction. Key math concepts include sequences, circles, and loci. Construction involves GeoGebra commands like Sequence, Circle, and Locus. Suitable for middle or high school math learning to understand real numbers and geometric relationships.

GeoGebra Commands & Parameters

  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}