自然数之间的平方根范围可视化

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2026-05-18 19:28

所属专题 Quadratzahlen und Quadratwurzeln

该范例用于展示“平方根落在自然数之间”的数值关系：例如比较某个数的平方根与相邻自然数，从而直观判断其大小位置。核心数学概念包括：平方根的定义与单调性、实数范围判断、以及用解析几何/坐标思想把数与区间对应起来。作图与交互要点：利用 GeoGebra 的随机生成与交互流程来产生问题数据（如 NumberListLevel2、NumberLevel2、randomNumbers、randomNumber、level），并通过文本输入与判断逻辑完成校验（Textfield、input21/input22/input3、KeepIf/If、Element、Sequence、Translate、Join、Text）。答案与反馈通过对象集合进行显示（SolutionList3、sol21/sol22、showsolution），并在正确/错误时给出提示与按钮状态控制（validate、btnValida

GeoGebra 命令及参数

Remove(2…143, Sequence[k^(2), k, 1, 12]) → NumberListLevel2
Shuffle(NumberListLevel2) → NumberLevel2, {93, 8, 54, 85, 63, 50, 11, 89, 76, 15, 29, 56, 13, 69, 108, 31, 94, 99, 40, 24, 122, 18, 117, 114, 75, 138, 39, 12, 128, 124, 80, 118, 136, 37, 106, 14, 77, 142, 103, 95, 140, 72, 91, 52, 141, 46, 74, 38, 90, 119, 102, 45, 113, 17, 101, 132, 34, 127, 27, 30, 73, 55, 61, 58, 10, 67, 26, 96, 131, 137, 43, 78, 68, 7, 62, 123, 104, 3, 71, 98, 84, 129, 28, 42, 48, 107, 133, 57, 134, 53, 120, 86, 139, 22, 143, 105, 32, 97, 47, 116, 5, 20, 2, 115, 79, 6, 21, 130, 19, 126, 135, 65, 60, 35, 88, 59, 125, 33, 82, 109, 66, 51, 23, 70, 83, 110, 87, 41, 44, 92, 112, 111}
Shuffle(NumberListLevel3) → NumberLevel3, {2, 3, 6, 11, 5, 10, 9, 4, 1, 8, 7}
If(IsInteger[sqrt(number2)], number2 - 1, floor(sqrt(number2))) → sol21
If(IsInteger[sqrt(number2)], number2 + 1, ceil(sqrt(number2))) → sol22
KeepIf(number31 < sqrt(a) < number32, a, Sequence[k, k, 2, 143]) → SolutionList3
If(level ≟ 2, correct21 ∧ correct22, level ≟ 3, correct3) → correct
Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {4, 9, 10, 7, 2, 1, 10, 9, 7, 9}
Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
Textfield(input) → inputBox
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
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
Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
Translate(imgChilliRot1, Vector[(2 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
Text(txtCapLevel2, PosCalc, false, true, 0, 0) → txtInputLevel2
Text(txtCapLevel3, PosCalc, false, true, 0, 0) → txtInputLevel3
Textfield(input21) → InputBox21
Textfield(input22) → InputBox22
Textfield(input3) → InputBox3
Text(InputBox21) → txtIB21
Text(InputBox22) → txtIB22
If(level ≟ 2, Defined[input21] ∧ IsInteger[input21] ∧ input21 ≥ 0 ∧ (¬isSqrt21) ∧ Defined[input22] ∧ IsInteger[input22] ∧ input22 ≥ 0 ∧ (¬isSqrt22), level ≟ 3, Defined[input3] ∧ IsInteger[input3] ∧ input3 ≥ 0) → clickableBtnValidate
Textfield(inputH21) → InputBoxH21
Textfield(inputH22) → InputBoxH22
Textfield(inputH31) → InputBoxH31
Textfield(inputH32) → InputBoxH32
If(number2 < 4^(2), 1, number2 < 9^(2), 6, number2 < 10^(2), 7, 8, number2 < 5^(2), 2, number2 < 6^(2), 3, number2 < 7^(2), 4, number2 < 8^(2), 5) → firstNumberHint1
Textfield(inputH11) → InputBoxH11
Textfield(inputH12) → InputBoxH12
Textfield(inputH13) → InputBoxH13
Textfield(inputH14) → InputBoxH14
Textfield(inputH15) → InputBoxH15