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维维安尼曲线

2009-08-13 22:10:19| 分类：高等数学图形动画 | 标签： |举报 |字号大中小订阅

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球面 x^2+y^2+z^2=a^2 与圆柱面 x^2+y^2=ax 相交的曲线称为

维维安尼曲线（Viviani's curve），

它是以意大利数学家维维安尼 (Vincenzo Viviani) 的名字命名的曲线。

维维安尼曲线 - calculus - 徐小湛的博客

with(plots): R:=1:
zhumian1:=plot3d([R*sin(u)*cos(v), R*sin(u)*sin(v), R*cos(u)], u=0..Pi, v=0..2*Pi, color=yellow):
zhumian2:=plot3d([(R/2)*(1+cos(t)), (R/2)*sin(t), z], z=-1.1..1.1, t=0..2*Pi, color=green):
z:=(x,y)->sqrt(R^2-x^2-y^2): x:=t->(R/2)*(1+cos(t)): y:=t->(R/2)*sin(t):
quxian1:=spacecurve([(R/2)*(1+cos(t)), (R/2)*sin(t), z(x(t),y(t))], t=0..2*Pi, thickness=5,color=red):
quxian2:=spacecurve([(R/2)*(1+cos(t)), (R/2)*sin(t), -z(x(t),y(t))], t=0..2*Pi,thickness=5,color=red):
display(zhumian1, zhumian2,quxian1,quxian2, scaling=constrained,orientation=[40,65],axes=frame);

以下是曲线的上半部分（见同济大学《高等数学》（五版上册），320页，例2）

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