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正多边形（带极限）

正多边形（带极限）
几何画板及绘图内容加载中，请稍等……
2019-04-15 07:34
圆多边形极限
本范例演示正多边形的构造及其与圆的关系。核心概念包括正多边形、极限、圆周率等。通过使用GeoGebra命令如Sequence、Element、Circle等，可以动态展示正多边形的边长、内角、半径等属性。适合高中数学教学，帮助学生理解正多边形与圆的几何关系。

GeoGebra 命令及参数

  1. Sequence(Rotate[A + (r, 0), ((k * 2) * π / n), A], k, 0, n) → pointList1
  2. Sequence(Segment[Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → segList
  3. Sequence(Midpoint[Element[segList, k]], k, 1, n) → midPtList
  4. Sequence(Segment[A, Element[midPtList, k]], k, 1, n) → apothemList
  5. Element(apothemList, 1) → radius_2
  6. Circle(A, radius_2) → circle_2
  7. Circumference(circle_2) → circum_2
  8. Segment(A, A + (r, 0)) → radius_1
  9. Sequence(Rotate[radius_1, (360° * k / n), A], k, 1, n) → radiiList
  10. Circle(A, r) → circle_1
  11. Sequence(Sector[circle_1, Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → sectorList
  12. Sequence(((Element[segList, k] * Element[apothemList, k])) / 2, k, 1, n) → apothArea
  13. Sequence(Element[sectorList, k] - Element[apothArea, k], k, 1, n) → segmentArea
  14. Sum(segmentArea, n) → valueSegAreaTotal
  15. Sum(apothArea, n) → areaPolygon
  16. Sequence(Arc[circle_1, Element[pointList1, k], Element[pointList1, k + 1]], k, 1, n) → arclist
  17. Area(circle_1) → areaCircle_1
  18. Circumference(circle_1) → circum_1
  19. If(n < 13, Element[polyList, n - 2], n + Element[polyList, 11]) → showPolyName
  20. Textfield(n) → inputBox1
  21. Area(circle_2) → areaCircle_2
  22. TableText({{"Regular " + showPolyName, TableText[{{"No.Sides", n}, {"Area", areaPolygon}, {"Perimeter", perimeterPoly}}, "c|111_"]}}, "vc_|11") → polyText
  23. TableText({{"Circle_1 A circumscribed", TableText[{{"Radius", r}, {"Area", areaCircle_1}, {"Circumference", circum_1}}, "c|111_"]}}, "vc_|11") → circle_1Text
  24. TableText({{"Shaded Space", TableText[{{"Area", valueSegAreaTotal}, {"% of Circle", (ratioCircleSegment2Circle * 100) + "\%"}}, "c|11_"]}}, "vc_|11|") → shadeText
  25. TableText({{"White Space", TableText[{{"Area", areaPolygon}, {"% of Circle", (100 * ratioPolyArea2Circle_1) + "\%"}}, "c|11_"]}}, "vc_|11|") → whiteText
  26. TableText({{"Circle_2 A circumscribed", TableText[{{"Radius", radius_2}, {"Area", areaCircle_2}, {"Circumference", circum_2}}, "c|111_"]}}, "vc_|11") → circle_2Text
  27. First(radiiList) → radius_f
  28. First(apothemList) → apothem_f
  29. TableText({{"Central Triangle A", TableText[{{"Chord", Element[segList, 1]}, {"Apothem", Element[apothemList, 1]}, {"Area", Element[apothArea, 1]}}, "c|111_"]}}, "vc_|11") → trianText

AI 绘图提示语参考

绘制一个正多边形，边数由输入框决定，同时画出其外接圆和内切圆。展示正多边形的边长、角度、半径，以及与外接圆和内切圆的关系。计算并显示正多边形的面积、周长、外接圆和内切圆的面积和周长。
以上提示语为根据原始绘图命令整理而来，仅供参考。