Surface of revolution

[I.N. Galidakis]

I seem to have forgotten how to create a surface of revolution for a function
y=f(x).

Wiki says:

>plot3d([x,f(x)*sin(y),f(x)*cos(y)],x=0..Pi,y=0..2*Pi);

http://en.wikipedia.org/wiki/Surface_of_revolution

(section "rotating a function")

but the above is the revolution around the x-axis. I need the surface of
revolution to revolve around the y-axis instead. How should I modify the
plot3d's arguments?

Thanks,
--
Ioannis

[Thomas Richard]

On 13 Nov., 04:08, "I.N. Galidakis" <morph...@olympus.mons> wrote:

> >plot3d([x,f(x)*sin(y),f(x)*cos(y)],x=0..Pi,y=0..2*Pi);

> but the above is the revolution around the x-axis. I need the surface of
> revolution to revolve around the y-axis instead. How should I modify the
> plot3d's arguments?

Maple has a specific tool for that task:

with(Student[Calculus1]):
SurfaceOfRevolution(f(x), x=0..Pi, axis=vertical, output=plot);

--
Thomas Richard
Technical Support Maple/MapleSim
Scientific Computers GmbH
http://www.scientific.de

[I.N. Galidakis]

Thomas Richard wrote:
> On 13 Nov., 04:08, "I.N. Galidakis" <morph...@olympus.mons> wrote:
>
>>> plot3d([x,f(x)*sin(y),f(x)*cos(y)],x=0..Pi,y=0..2*Pi);
>> but the above is the revolution around the x-axis. I need the surface of
>> revolution to revolve around the y-axis instead. How should I modify the
>> plot3d's arguments?
>
> Maple has a specific tool for that task:
>
> with(Student[Calculus1]):
> SurfaceOfRevolution(f(x), x=0..Pi, axis=vertical, output=plot);

Thanks Thomas. I am also interested in an explicit description of the resultant
function. Can anyone show me an example, say with f(x)=x^2?

How do I describe the resulting surface in mathematics?
--
Ioannis

[I.N. Galidakis]

Thomas Richard wrote:
> On 13 Nov., 04:08, "I.N. Galidakis" <morph...@olympus.mons> wrote:
>
>>> plot3d([x,f(x)*sin(y),f(x)*cos(y)],x=0..Pi,y=0..2*Pi);
>> but the above is the revolution around the x-axis. I need the surface of
>> revolution to revolve around the y-axis instead. How should I modify the
>> plot3d's arguments?
>
> Maple has a specific tool for that task:
>
> with(Student[Calculus1]):
> SurfaceOfRevolution(f(x), x=0..Pi, axis=vertical, output=plot);

Is there any way to increase the range of the variable x on the xz-plane? If I
use this command, I do indeed get the desired shape, but the variable on the
xz-plane goes from -0.02 to 0.02. I'd like the range to be -1..1. Here's my
function:

> F:=x->1/5*(1-25*x^2)^(1/2)-1+1/4*(225-16*x^2)^(1/2);
> with(Student[Calculus1]):
> SurfaceOfRevolution(F(x), x=0..Pi, axis=vertical, output=plot);

In other words, not enough of the shape is shown laterally. How do I make it
BIGGER?

Thanks,
--
Ioannis

[I.N. Galidakis]

Never mind. I got it. That's the wrong function, above. Many thanks Richard.

If anyone knows of any closed form expressions for the surface of revolution
around the y-axis for the function f(x), please post.
--
Ioannis

[Ray Vickson]

Your F(x) is not real-valued for |x| > 1/5.

R.G. Vickson