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{SECT 0 {EXCHG {PARA 260 "" 0 "" {TEXT -1 28 "Examples of Minimal Surf
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{PARA 264 "> " 0 "" {MPLTEXT 1 0 12 "with(share):" }}{PARA 265 "> " 0 
"" {MPLTEXT 1 0 29 "readshare(surfaces,geometry):" }}}{EXCHG {PARA 
261 "" 0 "" {TEXT -1 16 "Scherk's surface" }}{PARA 266 "> " 0 "" 
{MPLTEXT 1 0 33 "Scherk:=[x,y,log(cos(x)/cos(y))]:" }}}{EXCHG {PARA 
267 "> " 0 "" {MPLTEXT 1 0 23 "Meancurv(Scherk,[x,y]);" }}}{EXCHG 
{PARA 268 "> " 0 "" {MPLTEXT 1 0 140 "plot3d(Scherk,x=-Pi/2+Pi/100..Pi
/2-Pi/100,y=-Pi/2+Pi/100..Pi/2-Pi/100,scaling=CONSTRAINED,style=PATCH,
axes=BOXED, title=`Scherk's surface`);" }}}{EXCHG {PARA 262 "" 0 "" 
{TEXT -1 17 "Enneper's surface" }}{PARA 269 "> " 0 "" {MPLTEXT 1 0 15 
"assume(u,real):" }}{PARA 270 "> " 0 "" {MPLTEXT 1 0 15 "assume(v,real
):" }}{PARA 271 "> " 0 "" {MPLTEXT 1 0 11 "z := u+I*v:" }}{PARA 272 ">
 " 0 "" {MPLTEXT 1 0 27 "f := Re(expand(z-1/3*z^3)):" }}{PARA 273 "> \+
" 0 "" {MPLTEXT 1 0 31 "g := Re(expand(I*(z+1/3*z^3))):" }}{PARA 274 "
> " 0 "" {MPLTEXT 1 0 21 "h := Re(expand(z^2)):" }}{PARA 275 "> " 0 "
" {MPLTEXT 1 0 19 "Enneper := [f,g,h];" }}}{EXCHG {PARA 276 "> " 0 "" 
{MPLTEXT 1 0 24 "Meancurv(Enneper,[u,v]);" }}}{EXCHG {PARA 277 "> " 0 
"" {MPLTEXT 1 0 109 "plot3d(Enneper,u=-1.5..1.5,v=-1.5..1.5,scaling=CO
NSTRAINED,style=PATCH,axes=BOXED,title=`Enneper's surface`);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 260 70 "Surface with one planner end (fro
m Karcher, Surveys in Geometry, p.24)" }}{PARA 278 "> " 0 "" {MPLTEXT 
1 0 12 "assume(r>0):" }}{PARA 279 "> " 0 "" {MPLTEXT 1 0 15 "assume(t,
real):" }}{PARA 280 "> " 0 "" {MPLTEXT 1 0 25 "z := r*cos(t)+I*r*sin(t
):" }}{PARA 281 "> " 0 "" {MPLTEXT 1 0 7 "k := 3:" }}{PARA 282 "> " 0 
"" {MPLTEXT 1 0 53 "f := Re(expand(1/2*(-evalc(1/z)-z^(2*k+1)/(2*k+1))
)):" }}{PARA 283 "> " 0 "" {MPLTEXT 1 0 53 "g := Re(expand(I/2*(-evalc
(1/z)+z^(2*k+1)/(2*k+1)))):" }}{PARA 284 "> " 0 "" {MPLTEXT 1 0 23 "h \+
:= Re(expand(z^k/k)):" }}{PARA 285 "> " 0 "" {MPLTEXT 1 0 19 "Karcher \+
:= [f,g,h];" }}}{EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 24 "Meancurv(K
archer,[r,t]);" }}}{EXCHG {PARA 287 "> " 0 "" {MPLTEXT 1 0 130 "plot3d
(Karcher,r=0.5..1.2,t=-Pi..Pi,scaling=CONSTRAINED,grid=[10,50],style=P
ATCH,axes=BOXED,title=`Surface with one planner end`);" }}}{EXCHG 
{PARA 258 "" 0 "" {TEXT -1 20 "Helicoid to Catenoid" }}{PARA 259 "" 0 
"" {TEXT -1 45 "     (1 parameter family of minimal surfaces)" }}
{PARA 292 "> " 0 "" {MPLTEXT 1 0 121 "HeliCate := [cos(t)*sinh(v)*sin(
u)+sin(t)*cosh(v)*cos(u),-cos(t)*sinh(v)*cos(u)+sin(t)*cosh(v)*sin(u),
cos(t)*u+sin(t)*v]:" }}}{EXCHG {PARA 293 "> " 0 "" {MPLTEXT 1 0 25 "Me
ancurv(HeliCate,[u,v]);" }}}{EXCHG {PARA 288 "> " 0 "" {MPLTEXT 1 0 
191 "animate3d([cos(t)*sinh(v)*sin(u)+sin(t)*cosh(v)*cos(u),-cos(t)*si
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