Nice plots, thanks David!
About the cardiod, I gave it a try and started with this:
var('t')
a = 1
fx = a*cos(t)*(1-cos(t))
fy = a*sin(t)*(1-cos(t))*exp(-0.5*t)
f1 = (fx, fy)
parametric_plot(f1, 0, pi)
which then extended to this:
var('t v')
a = 1
fx = a*cos(t)*(1-cos(t))
fy = a*sin(t)*(1-cos(t))*exp(-0.5*t)*cos(v)
fz = a*sin(t)*(1-cos(t))*exp(-0.5*t)*sin(v)
f = (fx, fy, fz)
parametric_plot3d(f, (t,0,pi), (v,0,2*pi), rgbcolor='red')
Will your wife settle for an apple instead? :)
--
Hector
On Jan 18, 2008 9:06 AM, William Stein <[EMAIL PROTECTED]> wrote:
> On Jan 18, 2008 6:24 AM, David Joyner <[EMAIL PROTECTED]> wrote:
> >
> > Hi:
> >
> > Here are a few examples which I think are interesting.
> >
> > If anyone can figure out a way to plot a cardioid,
> > http://mathworld.wolfram.com/HeartSurface.html,
> > in SAGE, I'd be very interested.
> >
> > - David Joyner
> >
> > #M\"obius strip:
> > sage: u,v = var("u,v")
> > sage: p = parametric_plot3d([cos(u)*(1+v*cos(u/2)),
> > sin(u)*(1+v*cos(u/2)), 0.2*v*sin(u/2)], (u,0, 4*pi), (v,0,
> > 0.3),plot_points=[50,50])
> >
> > #twisted ribbon
> > sage: p = parametric_plot3d([3*sin(u)*cos(v), 3*sin(u)*sin(v),
> > cos(v)], (u,0, 2*pi), (v, 0, pi),plot_points=[50,50])
> >
> > #ellipsoid (automatically rescaled axes make it look spherical)
> > sage: p = parametric_plot3d([3*sin(u)*cos(v), 2*sin(u)*sin(v),
> > cos(u)], (u,0, 2*pi), (v, 0, 2*pi),plot_points=[50,50])
>
> Use the aspect_ratio option:
>
> sage: var('u,v')
> sage: parametric_plot3d([3*sin(u)*cos(v), 2*sin(u)*sin(v), cos(u)],
> (u,0, 2*pi), (v, 0, 2*pi),plot_points=[50,50], aspect_ratio=[1,1,1])
>
> I've attached a Sage worksheet that has all the plots in this email rendered,
> but with a few tweeks to make some of them work right or actually work.
>
> Thanks!
>
> I'll be adding this to the examples section of parametric_plot3d.
>
> -- William
>
> >
> > #cone
> > sage: p = parametric_plot3d([u*cos(v), u*sin(v), u], (u, -1, 1), (v,
> > 0, 2*pi), plot_points=[50,50])
> >
> > #paraboloid
> > sage: p = parametric_plot3d([u*cos(v), u*sin(v), u^2], (u, 0, 1), (v,
> > 0, 2*pi), plot_points=[50,50])
> >
> > #hyperboloid
> > sage: p = plot3d(u^2-v^2, (u, -1, 1), (v, -1, 1), plot_points=[50,50])
> >
> > #weird looking surface - like a M\"obius band but also an O
> > sage: p = parametric_plot3d([sin(u)*cos(u)*log(u^2)*sin(v),
> > (u^2)^(1/6)*(cos(u)^2)^(1/4)*cos(v), sin(v)], (u, -1, 1), (v, -pi,
> > pi), plot_points=[50,50])
> >
> >
> > #a heart, but not a cardioid (for my wife)
> > sage: p1 = parametric_plot3d([sin(u)*cos(u)*log(u^2)*v*(1-v)/2,
> > ((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, 1),
> > (v, 0, 1), plot_points=[90,90])
> > sage: p2 = parametric_plot3d([-sin(u)*cos(u)*log(u^2)*v*(1-v)/2,
> > ((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, 1),
> > (v, 0, 1), plot_points=[90,90])
> > sage: show(p1+p2, frame=False)
> >
> > >
> >
>
>
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washington
> http://wstein.org
>
>
> >
>
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