Hello,
For a calculus project I must design a vase and graph it using rotations, I
was wondering what pieces of software allow one to graph 3d rotatoins.

Thanks,
Sam

Maple has commands like VolumeOfRevolution and SurfaceOfRevolution in
its Student[Calculus1] package. While their primary purpose is computing
integrals, these commands also support an output=plot option which does
what you want.

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

news:_DZBd.64327$k25.9536@attbi_s53...

# One way to do this without using the Student package is to build a grid
# of points on your vase, called MESH in maple, and display that.

# First make plotting routines available by loading the plots and plottools
# packages

with(plots): with(plottools):

# start with a single curve on the x-y plane (approximated by a list
# of points) say:

rib0:=CURVES([[0,1,0],[1,2,0],[2,2,0],[3,1,0],[4,1,0]]);

# now rotate this repeatedly by say 2*Pi/5 about the x-axis:
# use 2*Pi/n to create n ribs instead of 5

t:=2*Pi/5;
rib1:=rotate(rib0,t,0,0);  # rotate by t about x-axis, 0 about y-axis, 0 about
z-axis
rib2:=rotate(rib0,2*t,0,0);
rib3:=rotate(rib0,3*t,0,0);
rib4:=rotate(rib0,4*t,0,0);

# now you have 5 longitudinal ribs on your vase
# you can display and interactively view them using the display command

display(rib0,rib1,rib2,rib3,rib4,scaling=constrained);

# To make it look more like a vase turn the ribs into a MESH
# A mesh is a list of lists, not a list of curves so we need
# to remove CURVES from each rib.  The op command does this:

vase:=MESH([op(rib0),op(rib1),op(rib2),op(rib3),op(rib4),op(rib0)]);

# note rib0 is used twice so the mesh 'closes'
# now display again:

display(vase,scaling=constrained);

# of course your curve will have more points and you will want
# more ribs.  I'll leave that to you, but you might consider
# using seq to generate a sequence of ribs, and put the result
# in brackets to prepare it for MESH.

# Jim Buddenhagen

 Hi!

How does one coerce Maple 9.5.2 to expand half angle trignometric
expressions like:

cos(o/2)=sqrt((1+cos(o))/2)

I googled everywhere and I can not find a way to do this!

Thank you very much.

Best regards
José Rui

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In article <33vjlbF40sms...@individual.net>, José Rui Faustino de Sousa

Since it is WRONG in some cases (when cos(o/2) is negative, for
example), you should be happy that Maple does not do it automatically.
How about this:

                                 /1  \
                         A := cos|- t|
                                 \2  /
                                              2
                 /1    /1    \        1      \
                 |- exp|- I t| + ------------|
                 |2    \2    /        /1    \|
                 |               2 exp|- I t||
                 \                    \2    //
                           2                      
             1 /   /1    \\    1          1      
             - |exp|- I t||  + - + ---------------
             4 \   \2    //    2                 2
                                     /   /1    \\
                                   4 |exp|- I t||
                                     \   \2    //
                          1          1
                          - cos(t) + -
                          2          2

Yes I am aware of that... But I should have the possibility to choose
that beahvior when is needed.

ANd it should be automatic if o is "assume"ed to have the proper
properties.

The half angle expressions are disperssed in several much longer
equations so I think that will not do.

Thank you very much.

Best regards
José Rui

--
========================================================================
"Theology is never any help; it is searching in a dark cellar at
midnight for a black cat that isn't there." Robert A. Heinlein
========================================================================
mailto://jrfsousaAPW...@esoterica.pt/ Crawler baith. UnCaps me to reply.
Contact information: http://homepage.esoterica.pt/~jrfsousa/contact.html
========================================================================

On Tue, 4 Jan 2005, José Rui Faustino de Sousa wrote:

One way is:

               1/2*(2+2*cos(theta))^(1/2), -1/2*(2+2*cos(theta))^(1/2)

Note, however, that this doesn't work with the sin:

                                    sin(theta)
                                1/2 ----------
                                        theta
                                    cos(-----)
                                          2
Joe

news:87vfabubgw.fsf@k-online.com...

Well, finding identies seems to be a different problem than substituting
them. Usual trig identities are listed in trigsubs, so we can do something
like that, using Carl's idea,

solve(cos(theta)=trigsubs(cos(theta))[3],cos(theta/2));
                              1/2                         1/2
        1/2 (2 + 2 cos(theta))   , -1/2 (2 + 2 cos(theta))

solve(cos(theta)=trigsubs(cos(theta))[4],sin(theta/2));

                              1/2                         1/2
        1/2 (2 - 2 cos(theta))   , -1/2 (2 - 2 cos(theta))

trigsubs(tan(theta/2))[5..6];

                      sin(theta)    1 - cos(theta)
                   [--------------, --------------]
                    cos(theta) + 1    sin(theta)

Returning back to the original question,

that depends on the expressions - whether they contain o/4, for instance,
and what one wants to do with them - convert to o/2 or go all the way up to
o; also, whether one wants to do that only with o/2 angles, or with x/2, y/2
etc.  In the simplest case, when we have only half angles of o, we could
just use subs, or eval, such as

subs(cos(o/2)=sqrt((1+cos(o))/2), expression);

eval(expression, cos(o/2)=sqrt((1+cos(o))/2));

Alec Mihailovs
http://math.tntech.edu/alec/

Hello Maple Experts,

I hope you can help with a problem I'm trying to solve in Maple.  I

I start with....
------------------------------

         2     2     2     2     2     2     2     2     2      2
A := x[1]  x[2]  x[3]  x[4]  x[5]  x[6]  x[7]  x[8]  x[9]  x[10]

B := 1024 x[1] x[2] x[3] x[4] x[5] x[6] x[7] x[8] x[9] x[10]
-------------------------------

Perfect so far.  However, I'd like to generalise the solution to...
-------------------------------

                               m          
                           ,--------'    
                              |  |        
                              |  |       2
                      A :=    |  |   x[i]
                              |  |        
                             i = 1        
Error, unable to execute seq
-------------------------------

After reading the Help pages for seq, I find that the final limit for
seq has to be a literal.

Does anyone else have any ideas?  Thank you for reading this message.

Sam