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面积-周长关系演示

面积-周长关系演示
几何画板及绘图内容加载中，请稍等……
2014-09-23 00:11
多边形函数
①本范例演示多边形的面积与周长关系及变化现象；②涉及核心数学概念包括多边形构造、周长计算、面积计算、函数关系、步进函数、反射变换等；③通过 GeoGebra 命令如 Polygon, Length, Sequence, OrthogonalLine, Join, Midpoint, Perimeter 等实现多边形绘制与测量，并利用 Textfield, Slider 等展示动态变化；④适合高中数学教学，用于理解函数、几何变换与优化问题的关联。

GeoGebra 命令及参数

  1. Polygon(PolyPoints) → MyShape
  2. Textfield(PolyPoints) → inputBox1
  3. Length(PolyPoints) → NumberOfPolygonPoints
  4. Sequence(Distance[Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]], Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]], k, 1, NumberOfPolygonPoints) → DistanceBetweenPolygonPoints
  5. OrthogonalLine(PerimeterStartPoint, yAxis) → a
  6. Sequence(PerimeterStartPoint + (Sum[DistanceBetweenPolygonPoints, k], 0), k, 1, NumberOfPolygonPoints) → PolygonPointsOnTheLine
  7. Sequence(If[x(Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]]) ≠ x(Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]), Slope[Segment[Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]], Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]]], If[y(Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]]) > y(Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]), -1.5707963267948966, 1.5707963267948966]], k, 1, NumberOfPolygonPoints) → SlopeBetweenPolygonPoints
  8. Sequence(If[x(Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]]) ≠ x(Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]), (-atan(Element[SlopeBetweenPolygonPoints, k])), If[y(Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]]) > y(Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]), 1.5708, -1.5708]], k, 1, NumberOfPolygonPoints) → AngleOfRotationOfPolygonSegments
  9. Sequence(Segment[Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]], Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]], k, 1, NumberOfPolygonPoints) → PolygonSegments
  10. Join({{PerimeterStartPoint}, PolygonPointsOnTheLine}) → AllPointsOnTheLine
  11. Sequence(Vector[Element[PolyPoints, k], Element[AllPointsOnTheLine, k]], k, 1, NumberOfPolygonPoints) → TranslationVectors
  12. Sequence(Translate[Element[PolygonSegments, k], Vector[(TranslationFactor * Element[TranslationVectors, k])]], k, 1, NumberOfPolygonPoints) → TranslatePolygonSegments
  13. Sequence(If[x(Element[PolyPoints, 1 + Mod[k - 1, NumberOfPolygonPoints]]) > x(Element[PolyPoints, 1 + Mod[k, NumberOfPolygonPoints]]), 3.141592653589793, 0], k, 1, NumberOfPolygonPoints) → AngleCorrectionFactor
  14. Sequence(Rotate[Element[TranslatePolygonSegments, k], (RotationFactor * (Element[AngleOfRotationOfPolygonSegments, k] + Element[AngleCorrectionFactor, k])), Element[AllPointsOnTheLine, k]], k, 1, NumberOfPolygonPoints) → RotatePolygonSegments
  15. Sequence(Segment[AreaStartPoint + (k, 0), AreaStartPoint + (k, -1)], k, 1, floor(MyShape)) → AreaDivisions
  16. Polygon(AreaStartPoint, AreaStartPoint + (0, -1), AreaStartPoint + (MyShape, -1), AreaStartPoint + (MyShape, 0)) → AreaPolygon, c, d, e, f
  17. Midpoint(AreaStartPoint + (0, -1), AreaStartPoint + (MyShape, -1)) → AreaLabel
  18. Midpoint(Element[AllPointsOnTheLine, 1], Element[AllPointsOnTheLine, NumberOfPolygonPoints + 1]) → PerimeterLabel
  19. Perimeter(MyShape) → PerimeterPolygon

AI 绘图提示语参考

这是一个展示多边形面积与周长关系的几何图形。图形中包含一个可调整的多边形，其顶点由点标记，周长和面积通过计算和显示呈现。图形还包含动态元素，如滑块控制多边形形状，以及标签显示周长和面积值。图形旨在帮助理解面积和周长的变化关系，适用于数学教学。
以上提示语为根据原始绘图命令整理而来，仅供参考。