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Calculate the Area of a Circle: Geometric Construction and Formula Application

Calculate the Area of a Circle: Geometric Construction and Formula Application
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2024-12-19 16:41
In collections Kreis Umfang und Flächeninhalt
This example demonstrates calculating the area of a circle, especially through geometric construction and formula application to understand the concept of circle area. Key mathematical concepts include the area formula for circles, areas of semicircles, quarters, and eighths. Construction points involve using GeoGebra commands like Circle, Segment, Intersect to construct circles and related figure

GeoGebra Commands & Parameters

  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