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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 252 "This worksheet shows how
 Maple may be used to create surfaces of revolution of constant Gauss \+
curvature. The first procedure creates surfaces with constant positive
 curvature while the second procedure creates surfaces with constant n
egative curvature." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(
plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plotconstcurv:=p
roc(c)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "local X,desys,gu,s ;\nif
 1/c>1 then s:=-Pi/2..Pi/2 else s:=-arcsin(1/c)..arcsin(1/c) fi;\nX:=[
c*cos(u)*cos(v),c*cos(u)*sin(v),g]; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 75 "desys:=dsolve(\{diff(g(u),u)=sqrt(1-c^2*sin(u)^2),g(0)=0\},g(u),
type=numeric," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "output=listprocedu
re):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "gu:=subs(desys,g(u)); " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "plot3d(subs(g='gu'(u),X),u=s,v=0..2
*Pi,scaling=constrained,style=patch,\nshading=zhue);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "plotconstcurv(0.85);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 
"plotconstcurv(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotc
onstcurv(1.2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotconst
curv(0.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotconstcurv
(1.7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plotconstcurv2:=p
roc(c,d)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 289 "local X,desys,gu,s,h,k
k,init;\nif d=0 then h:=c*exp(u);\ns:=-2.5..ln(1/c) fi;\nif c>0 and d>
0 then h:=2*sqrt(c*d)*cosh(u);\ns:=arcsinh(-1/(2*sqrt(c*d)))..arcsinh(
1/(2*sqrt(c*d))) fi;\nif c>=0 and d<0 then h:=2*sqrt(-c*d)*sinh(u);\nk
k:=c*d;\nif kk>=-1/4 then s:=0..arccosh(1/(2*sqrt(-c*d)))fi; fi;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "X:=[h*cos(v),h*sin(v),g]; " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "desys:=dsolve(\{diff(g(u),u)=sqrt(1
-diff(h,u)^2),g(0)=0\},g(u),\ntype=numeric,output=listprocedure):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "gu:=subs(desys,g(u)); " }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 99 "plot3d(subs(g='gu'(u),X),u=s,v=0..2*Pi,scali
ng=constrained,style=patch,\nshading=zhue,grid=[15,40]);" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "plotconstcurv2(1,0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "plotconstcurv2(1,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 
"plotconstcurv2(0.5,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "
plotconstcurv2(0.1,-0.4);" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }