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勾股定理求直角三角形斜边长度

勾股定理求直角三角形斜边长度
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2024-09-26 21:28
测试改名0角三角函数几何作图
所属专题 Satz des Pythagoras - Einführung
该范例让学习者通过交互输入直角三角形两条直角边的长度，计算并验证斜边（Hypotenuse）的长度，并引导学生使用计算器完成求值。核心数学概念是勾股定理：a²+b²=c²，以及在平面几何中建立边长关系并用公式求未知量。作图要点包括用 Sequence 生成题目所需随机数与计数流程，使用 Point 与 Polygon 生成/构造三角形及其边；用 Angle 设置直角位置与几何关系；通过 Textfield 与 If 实现输入、合法性判断与反馈；并结合 validate、showHint、showsolution、txtHintTypical 等对象显示提示与答案核验。适合7-8年级用于直角三角形计算练习、公式应用与几何建模入门。

GeoGebra 命令及参数

  1. Sequence(Random[10, 1000] / 10, i, 1, 100) → randomNumbersA, {17.1, 19.1, 82.8, 11, 74.3, 20.9, 12.6, 32.6, 22.6, 14.4, 63.9, 30.7, 49.8, 96, 49, 3.6, 30.9, 75.3, 61.2, 50.8, 77.2, 25, 35, 16.8, 16, 72.4, 19.5, 29.4, 87.1, 55.2, 62.1, 1.5, 60.2, 74.7, 43, 68.6, 22.5, 15.9, 98, 93.6, 40.3, 99, 68.2, 87.9, 91.1, 55, 79.3, 12.1, 52.4, 90.5, 87, 20.3, 24.3, 27.1, 52.9, 73, 19.5, 63, 64.1, 78.2, 48.2, 22.6, 82.4, 1.5, 6.1, 47.3, 37.1, 21.3, 38.8, 2.7, 53.2, 17.3, 83.1, 33.6, 15.7, 3.9, 24.1, 73.6, 97.2, 65.9, 98.6, 7.4, 27, 26, 91.9, 29.8, 89.5, 52.5, 7.2, 3.6, 78.9, 13.6, 6.5, 15.3, 56.7, 28.2, 16.9, 69.3, 31.5, 29.3}
  2. Element(randomNumbersA, Mod[questionCount, Length[randomNumbersA]] + 1) → randomNumberA
  3. Sequence(Random[If[floor((randomNumbersA(i) * 0.3)) > 1, (floor((randomNumbersA(i) * 0.3)) * 10), 10], If[ceil((randomNumbersA(i) * 1.7)) < 100, (ceil((randomNumbersA(i) * 1.7)) * 10), 1000]] / 10, i, 1, 100) → randomNumbersB, {27.4, 14.4, 62.7, 11.2, 99.7, 27.9, 8.6, 13.6, 8.4, 15.8, 77.3, 36.1, 37.9, 65, 24.3, 5.7, 38, 54, 54.6, 25.9, 70.1, 8.3, 38.6, 26.2, 23.6, 33.4, 28.7, 19.9, 57, 54.4, 57.9, 1.7, 62.7, 80.1, 59.6, 77.2, 10, 25.6, 95.3, 86.2, 66.4, 66.4, 58, 39.4, 58.1, 73.7, 94.5, 19.6, 82.2, 95.9, 46.1, 22, 21.3, 21.8, 34.2, 43.6, 27.5, 66.1, 74.8, 79.7, 50.7, 35.6, 57.8, 2.2, 6.6, 37.2, 53.6, 13.5, 64.5, 1.8, 30.8, 15.2, 32.7, 50.3, 27, 6.6, 8.8, 98.8, 70.6, 66.5, 59.7, 6.8, 32.3, 34.8, 30.5, 43.8, 94, 81.4, 5.9, 3.4, 40, 21.8, 1.4, 21.6, 29.5, 41.8, 22.2, 49.5, 27.7, 20.8}
  4. Element(randomNumbersB, Mod[questionCount, Length[randomNumbersB]] + 1) → randomNumberB
  5. Textfield(input) → inputBox
  6. If(Length[Text[inputBox]] > 0, Length[KeepIf[¬(temp ∈ TextToUnicode[erlaubteZeichen]), temp, Take[TextToUnicode[Text[inputBox]], Min[Length[Text[inputBox]], 2]]]] ≟ 0, true) → inputValid
  7. Polygon(dreieckStartA, dreieckStartB, dreieckStartC) → dreieckStart, dreieckStartc, dreieckStarta, dreieckStartb
  8. Angle(dreieckStartA, dreieckStartC, dreieckStartB) → dreieckStartGamma
  9. Angle(dreieckStartB, dreieckStartA, dreieckStartC) → dreieckStartAlpha
  10. Angle(dreieckStartC, dreieckStartB, dreieckStartA) → dreieckStartBeta
  11. Point(Circle[dreieckSolutionC, (randomNumberA * dreieckFactor)]) → dreieckSolutionA
  12. Polygon(dreieckSolutionC, dreieckSolutionA, dreieckSolutionB) → dreieck1, dreieckSolutionb, dreieckSolutionc, dreieckSolutiona
  13. Angle(dreieckSolutionB, dreieckSolutionA, dreieckSolutionC) → dreieckSolutionAlpha
  14. Angle(dreieckSolutionA, dreieckSolutionC, dreieckSolutionB) → dreieckSolutionGamma
  15. Angle(dreieckSolutionC, dreieckSolutionB, dreieckSolutionA) → dreieckSolutionBeta
  16. Flatten(Sequence[Shuffle[{"mm", "cm", "dm", "m"}], i, 1, 10]) → randomUnits
  17. Element(randomUnits, Mod[questionCount, Length[randomUnits]] + 1) → randomUnit

AI 绘图提示语参考

画一个直角三角形，两条直角边的长度分别为17.1和27.4单位长度，使用勾股定理计算斜边长度，并在输入框中输入计算结果。根据输入验证结果，如果正确则显示正确提示，否则显示错误提示。
以上提示语为根据原始绘图命令整理而来，仅供参考。