圆 - 圆心角与所对弧长

圆 - 圆心角与所对弧长
几何画板及绘图内容加载中,请稍等……
2015-04-09 04:36
这个范例演示了圆心角与所对弧长的关系。核心数学概念包括圆、角和弧。通过使用GeoGebra命令如Circle、Angle、ArcDeg等,可以动态地展示圆心角变化时所对弧长的变化。适合初中及以上学生学习圆的相关性质。

GeoGebra 命令及参数

  1. Element(Dimension[Arc1Arc2Radius], 1) → NumberOfEquations
  2. Random(1, NumberOfEquations) → CircleCounter
  3. Element(Arc1Arc2Radius, CircleCounter) → targetCircleCoef
  4. Textfield(h) → inputBox1
  5. Textfield(k) → inputBox2
  6. Textfield(r) → inputBox3
  7. Random(1, 4) → WhichPoint
  8. Element(targetCircleCoef, 1) → Arc1
  9. Element(targetCircleCoef, 2) → Arc2
  10. Element(targetCircleCoef, 3) → radius
  11. Circle(YourCenter, radius) → c
  12. Mod(CircleCounter + 1, NumberOfEquations + 1) → counter
  13. Point(c) → A
  14. Random(1, (360 - Arc1 - Arc2) / 2) → MissingArcBetween1and2
  15. Rotate(A, α°, YourCenter) → C
  16. Angle(A, YourCenter, C) → AngleArc1
  17. ArcDeg(c, A, C) → d, text1
  18. Rotate(C, MissingArcBetween1and2°, YourCenter) → D
  19. Angle(C, YourCenter, D) → AngleArcCD
  20. Rotate(D, Arc2°, YourCenter) → F
  21. Angle(D, YourCenter, F) → AngleArc2
  22. ArcDeg(c, D, F) → e, text3
  23. Segment(YourCenter, A) → a
  24. Segment(YourCenter, C) → b
  25. Rotate(A, (Arc1 / 2)°, YourCenter) → B
  26. Angle(A, YourCenter, B) → ε
  27. Rotate(D, (Arc2 / 2)°, YourCenter) → E
  28. Angle(D, YourCenter, E) → ζ
  29. Circumference(c) → CircCircumf
  30. Area(c) → CircArea
  31. Textfield(YourArea) → inputBox4
  32. Textfield(YourCircumference) → inputBox5
  33. Textfield(YourSectorAOC) → inputBox6
  34. Textfield(YourArcACLength) → inputBox7
  35. Textfield(YourAngleAOC) → inputBox8
  36. Textfield(YourAngleFOD) → inputBox9
  37. Textfield(YourArcACdegree) → inputBox10
  38. Textfield(YourArcFDdegree) → inputBox11
  39. Textfield(YourRadius) → inputBox12
  40. Textfield(YourDiameter) → inputBox13
  41. CircumcircleSector(A, B, C) → f

AI 绘图提示语参考

画一个圆,圆心为点O,半径为r。在圆上选取两点A和C,使得∠AOC为α度,∠AOC所对的弧长为d度。然后在圆上选取点D,使得∠COD为β度,∠COD所对的弧长为e度。最后画出圆的周长和面积,并标注圆心角∠AOC、圆周角∠BAC、圆周角∠FOD、弧AC的度数和弧FD的度数。
以上提示语为根据原始绘图命令整理而来,仅供参考。