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圆环计算

圆环计算
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2024-12-19 16:42
所属专题 Kreis Umfang und Flächeninhalt
本范例演示如何计算圆环中不同扇形（如半圆、四分之一圆、八分之一圆）的面积。涉及的核心数学概念包括圆面积公式及其在特定区域的应用。构造过程中使用了GeoGebra命令如Textfield, Shuffle, Element, If, Polygon, Circle, Segment, Ray, Intersect, RemoveUndefined, Mod, CountIf等，以及对象如颜色、按钮和输入框。适合7-8年级学生使用，用于练习和巩固圆面积计算技能。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle(Sequence[Random[1, 15], i, 1, 100]) → randomNosForX, {8, 7, 14, 9, 8, 5, 6, 12, 9, 9, 9, 14, 6, 7, 12, 15, 11, 1, 8, 5, 3, 15, 2, 7, 14, 3, 14, 2, 9, 11, 11, 15, 14, 10, 12, 3, 12, 10, 9, 11, 8, 15, 7, 14, 3, 5, 12, 6, 14, 2, 1, 6, 13, 14, 10, 3, 14, 8, 5, 2, 7, 12, 3, 9, 9, 15, 9, 15, 8, 10, 13, 15, 8, 14, 1, 10, 6, 7, 13, 5, 13, 13, 14, 8, 9, 14, 9, 7, 13, 6, 1, 2, 7, 10, 9, 8, 8, 13, 7, 10}
  4. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  5. Shuffle(Sequence[Random[1, 99], i, 1, 100]) → randomNosForY, {40, 46, 21, 16, 38, 82, 66, 26, 45, 67, 19, 94, 38, 19, 21, 25, 77, 34, 18, 88, 71, 94, 75, 64, 84, 86, 43, 29, 80, 78, 7, 90, 41, 4, 51, 43, 3, 7, 12, 45, 24, 37, 77, 31, 10, 5, 6, 58, 48, 60, 68, 66, 11, 65, 3, 37, 43, 27, 92, 61, 4, 77, 65, 34, 16, 51, 26, 8, 47, 60, 58, 57, 84, 90, 32, 1, 97, 27, 75, 50, 11, 54, 39, 99, 25, 2, 69, 17, 16, 52, 63, 64, 65, 6, 31, 86, 42, 43, 4, 74}
  6. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  7. Shuffle(Sequence[Random[1, 15], i, 1, 100]) → randomNosForX_1, {7, 2, 3, 14, 9, 11, 3, 6, 11, 14, 12, 7, 12, 3, 1, 12, 12, 13, 5, 6, 6, 3, 15, 10, 8, 1, 6, 9, 15, 12, 13, 3, 8, 2, 2, 9, 14, 2, 11, 7, 5, 13, 13, 7, 6, 11, 12, 12, 6, 2, 3, 6, 9, 4, 10, 3, 8, 2, 5, 1, 4, 2, 8, 10, 11, 7, 10, 5, 9, 10, 2, 15, 1, 3, 2, 3, 12, 3, 15, 5, 3, 9, 6, 9, 11, 4, 7, 8, 1, 6, 10, 7, 13, 4, 1, 8, 6, 1, 5, 12}
  8. Shuffle(Sequence[Random[1, 99], i, 1, 100]) → randomNosForY_1, {14, 24, 7, 45, 81, 53, 23, 94, 77, 41, 88, 31, 93, 83, 31, 37, 90, 65, 75, 32, 16, 24, 46, 4, 85, 9, 51, 23, 12, 72, 53, 35, 38, 2, 67, 14, 33, 49, 43, 72, 94, 10, 84, 70, 78, 2, 46, 20, 4, 82, 70, 53, 64, 37, 89, 64, 69, 73, 50, 10, 82, 13, 50, 79, 37, 61, 14, 20, 70, 53, 23, 94, 99, 99, 23, 83, 77, 69, 25, 76, 18, 73, 39, 53, 35, 67, 72, 11, 27, 19, 71, 75, 49, 89, 77, 6, 5, 78, 68, 19}
  9. Element(randomNosForX_1, Mod[questionCount, 100] + 1) → numX_1
  10. Element(randomNosForY_1, Mod[questionCount, 100] + 1) → numY_1
  11. If(rad1 > rad2, rad1, rad2) → radius1
  12. If(rad1 > rad2, rad2, rad1) → radius2
  13. If(Mod[questionCount, 2] ≟ 0, sol_a ≤ input1 ≤ sol_a, sol_u ≤ input1 ≤ sol_u) → correct
  14. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  15. Circle(M, B) → c
  16. Segment(M, B) → r_{1}
  17. Ray(B, M) → g
  18. Intersect(c, g) → C, D
  19. RemoveUndefined({floor(input1 / 10), Mod[floor(input1), 10], floor(Mod[round((input1 * 100)), 100] / 10), Mod[round((input1 * 100)), 10]}) → listInput
  20. RemoveUndefined({floor(sol_u / 10), Mod[floor(sol_u), 10], floor(Mod[round((sol_u * 100)), 100] / 10), Mod[round((sol_u * 100)), 10]}) → listSol_u
  21. Circle(M, E) → d
  22. Segment(M, E) → r_2
  23. Circle(M, B) → e
  24. Circle(M, E) → f
  25. Mod((input1 * 1000), 10) → hintRunden
  26. RemoveUndefined({floor((sol_a) / 10), Mod[floor(sol_a), 10], floor(Mod[round((sol_a * 100)), 100] / 10), Mod[round((sol_a * 100)), 10]}) → listSol_a
  27. CountIf(x ≠ 0, listInput) → digitsInput
  28. If(Mod[questionCount, 2] ≟ 0, CountIf[x ≠ 0, listSol_a], CountIf[x ≠ 0, listSol_u]) → digitsSol