Construct the monkey's saddle given by z = x3 - 3xy2 above the unit circle.

> restart:

> x:=cos(t):

> y:=sin(t):

> z1:=cos(3*t):

> z2:=-1:

> z:=(1-s)*z1+s*z2:

> with(plottools):

> a:=plot3d([x,y,z],s=0..1,t=0..2*Pi,scaling=constrained,grid=[5,100]):

> x:=r*cos(t):

> y:=r*sin(t):

> z:=x^3-3*x*y^2:

> b:=plot3d([x,y,z],r=0..1,t=0..2*Pi,scaling=constrained,grid=[10,100]):

> with(plots):

Warning, the name changecoords has been redefined

> display(b);

>