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计算圆的面积：几何作图与公式应用

计算圆的面积：几何作图与公式应用
几何画板及绘图内容加载中，请稍等……
2024-12-19 16:41
所属专题 Kreis Umfang und Flächeninhalt
这个范例演示了如何计算圆的面积，特别是通过几何作图和公式应用来理解圆的面积概念。核心数学概念包括圆的面积公式、半圆、圆的四分之一和八分之一的面积计算。作图要点包括使用GeoGebra命令如Circle、Segment、Intersect等来构造圆和相关图形。适合小学7-8年级学生，用于学习几何面积计算和公式应用。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle(Sequence[Random[1, 20], i, 1, 100]) → randomNosForX, {3, 6, 15, 19, 5, 13, 3, 14, 10, 14, 8, 9, 18, 2, 15, 17, 11, 18, 8, 16, 17, 8, 17, 9, 3, 13, 4, 6, 8, 11, 18, 10, 2, 20, 15, 18, 20, 14, 13, 17, 15, 16, 5, 9, 2, 15, 10, 14, 3, 4, 16, 10, 15, 4, 6, 12, 8, 3, 4, 12, 14, 10, 12, 4, 16, 7, 15, 6, 1, 1, 3, 12, 17, 3, 8, 8, 3, 5, 10, 3, 13, 2, 17, 7, 20, 15, 7, 18, 6, 11, 18, 9, 10, 11, 20, 16, 12, 13, 14, 1}
  4. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  5. Shuffle(Sequence[Random[1, 99], i, 1, 100]) → randomNosForY, {40, 18, 97, 84, 73, 29, 77, 5, 88, 68, 93, 98, 18, 21, 88, 25, 6, 49, 43, 32, 29, 41, 65, 95, 58, 44, 91, 22, 95, 70, 53, 72, 42, 59, 25, 28, 47, 38, 98, 16, 93, 61, 95, 30, 61, 6, 92, 98, 38, 11, 30, 76, 99, 76, 21, 73, 47, 35, 40, 88, 65, 93, 16, 43, 51, 45, 99, 41, 89, 79, 96, 87, 85, 83, 90, 87, 32, 29, 67, 36, 90, 85, 8, 26, 48, 45, 48, 68, 53, 24, 49, 48, 68, 67, 7, 47, 95, 8, 18, 45}
  6. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  7. If(Mod[questionCount, 2] ≟ 0, (num^(2) * pi), (((num) / 2)^(2) * pi)) → umfang
  8. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  9. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  10. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  11. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  12. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  13. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  14. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  15. Circle(M, B) → c
  16. Segment(M, B) → r
  17. Ray(B, M) → g
  18. Intersect(c, g) → C, D
  19. Segment(B, D) → d
  20. RemoveUndefined({floor(input1 / 10), Mod[floor(input1), 10], floor(Mod[round((input1 * 100)), 100] / 10), Mod[round((input1 * 100)), 10]}) → listInput
  21. RemoveUndefined({floor(sol / 10), Mod[floor(sol), 10], floor(Mod[round((sol * 100)), 100] / 10), Mod[round((sol * 100)), 10]}) → listSol
  22. If(Mod[questionCount, 2] ≟ 0, (((num) / 2)^(2) * pi), (num^(2) * pi)) → umfangVertauscht
  23. Mod((input1 * 1000), 10) → hintRunden