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高等数学课件、函数图形动画、数学软件应用

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猴鞍面

2009-07-13 11:53:01| 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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所有图形见：数学图形目录

猴鞍面 （Monkey saddle）是数学家为猴子量身定做的一种鞍面。

猴鞍面的方程：

注意：猴鞍面不是二次曲面，而是三次曲面。

说明：之所以将这个曲面称为猴鞍面，是因为这是适合猴子坐的一种鞍面。
问题：为什么猴子坐在这个猴鞍面上比它坐在马鞍面上更舒服？

with(plots): a:=3:b:=4:

qumian:=plot3d(x*(x^2-3*y^2),x=-2..2,y=-2..2):

x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):

y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):

z_axis:=plot3d([0,0,u],u=-0..6,v=0..0.01,color=blue):

xyz:=display(x_axis,y_axis,z_axis,thickness=3):

display(qumian,xyz,tickmarks=[4,4,4],title="monkey saddle",axes=none,grid=[40,40],lightmodel=light2);

用隐函数绘制

with(plots):

implicitplot3d(z=x*(x^2-3*y^2),x=-2..2,y=-2..2,z=-1..1);

动画的Maple程序：
with(plots):
K:=60:for i from 1 to K do:
qumian[i]:=implicitplot3d(z=x*(x^2-3*y^2),x=-2..2,y=-2..2,z=-1..1,orientation=[90+6*i,55]) od:
display(seq(qumian[i],i=1..K),insequence=true);

返回：数学图形目录

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