绕y轴旋转区域

几何画板及绘图内容加载中，请稍等……

2020-01-27 15:24

①本范例演示了平面区域绕y轴旋转形成旋转体的过程；②涉及核心数学概念包括旋转、抛物线、球体、中位线、积分微积分和角度；③作图要点使用了Line, Segment, CurveCartesian, Sequence, Textfield等GeoGebra命令和对象，如aa, bb, n, st, yDir, ss, ff, f, Qss, Pss, PQ, gg, fInRotation, g, gInRotation, st2, lateralSurfAA, lateralSurfBB, st3, region, regionInRotation, st1, lowerCircles, upperCircles等；④适合高中及以上学段学习积分微积分和立体几何，用于理解旋转体体积计算和几何变换。

GeoGebra 命令及参数

Line((0, 0, 0), (0, 1, 0)) → yDir
Segment(Pss, Qss) → PQ
CurveCartesian((t * cos(ss)), ff(t), (t * sin(ss)), t, aa, bb) → fInRotation
CurveCartesian((t * cos(ss)), gg(t), (t * sin(ss)), t, aa, bb) → gInRotation
Sequence(Segment[((aa * cos(k)), gg(aa), (aa * sin(k))), ((aa * cos(k)), ff(aa), (aa * sin(k)))], k, 0, (2 * π), st2) → lateralSurfAA
Sequence(Segment[((bb * cos(k)), gg(bb), (bb * sin(k))), ((bb * cos(k)), ff(bb), (bb * sin(k)))], k, 0, (2 * π), st2) → lateralSurfBB
Sequence(Segment[(t, gg(t), 0), (t, ff(t), 0)], t, aa, bb, st3) → region
Sequence(Segment[((t * cos(ss)), gg(t), (t * sin(ss))), ((t * cos(ss)), ff(t), (t * sin(ss)))], t, aa, bb, st3) → regionInRotation
Sequence(Circle[(0, gg(aa + (k * st)), 0), aa + (k * st), yDir], k, 0, n, st1) → lowerCircles
Sequence(Circle[(0, ff(aa + (k * st)), 0), aa + (k * st), yDir], k, 0, n, st1) → upperCircles
Textfield(ff) → InputBox1
Textfield(gg) → InputBox2