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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 
0 109 "desys:=dsolve(\{diff(g(u),u)=sqrt(1-c^2*sin(u)^2),g(0)=0\},g(u)
,\ntype=numeric,method=dna,output=listprocedure):" }}{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=constr
ained,\nstyle=patch,shading=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 "plotconstcurv(1.2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotconstcurv(0.5);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotconstcurv(1.7);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plotconstcurv2:=proc(c,d)" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 289 "local X,desys,gu,s,h,kk,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);\nkk:=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 0 108 "desys:=dsolve(\{diff(g(u),u)=sqrt(1-diff(h,u)^2),g(0
)=0\},g(u),\ntype=numeric,method=dna,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,scaling=con
strained,\nstyle=patch,shading=zhue,grid=[15,40]);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "p
lotconstcurv2(1,0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot
constcurv2(1,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plotcon
stcurv2(0.5,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plotcons
tcurv2(0.1,-0.4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 4 0" 72 }
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