{VERSION 5 0 "IBM INTEL LINUX" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 58 "Sample Maple Worksheet to create a torus and a sample path" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "f:=cos(beta)*(cos(alpha)+2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "g:=sin(beta)*(cos(alpha)+2);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 14 "h:=sin(alpha);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 90 "plot3d([f,g,h],alpha=0..Pi,beta=0..Pi,scaling=const
rained,style=patchnogrid,shading=ZHUE);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "Next we put a path on th
e torus.  This will be a parametric curve (or parametric curves), depe
nding only on one variable" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 93 "The first path goes around the (great) cricle.  I
n this case, alpha=0 and beta = t*Pi, t=0..1" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "Path1Functions:=
subs(\{alpha=0, beta=t*Pi\},f), subs(\{alpha=0, beta=t*Pi\},g), subs(
\{alpha=0, beta=t*Pi\},h);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
68 "Path1:=spacecurve([Path1Functions, t=0..1],color=black,thickness=5
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "Torus1:=plot3d([f,g,
h],alpha=0..2*Pi,beta=0..2*Pi,scaling=constrained,style=patchnogrid,sh
ading=ZHUE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "display3d(
\{Torus1, Path1\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 126 "An example of a path that needs to be defined \+
in pieces:  In (beta, alpha) we go from (0,0) to (Pi, 0) to (Pi, Pi), \+
to (Pi, 0)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 96 "Path2AF:=subs(\{beta=0,alpha=Pi*t\},f), subs(\{beta
=0,alpha=Pi*t\},g), subs(\{beta=0, alpha=Pi*t\},h);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 99 "Path2BF:=subs(\{beta=Pi*t,alpha=Pi\},f), \+
subs(\{beta=Pi*t,alpha=Pi\},g), subs(\{beta=Pi*t, alpha=Pi\},h);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "Path2CF:=subs(\{beta=Pi,alph
a=Pi*t\},f), subs(\{beta=Pi,alpha=Pi*t\},g), subs(\{beta=Pi, alpha=Pi*
t\},h);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Path2A:=spacecur
ve([Path2AF,t=0..1],color=black, thickness=5):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 62 "Path2B:=spacecurve([Path2BF,t=0..1],color=blac
k, thickness=5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Path2C:
=spacecurve([Path2CF,t=0..1],color=black, thickness=5):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "display3d(\{Torus1, Path2A, Path2B,
 Path2C\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "
21" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }