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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 619 "restart: with(plots
):with(plottools):\nu:=8*cos(t):\nv:=8*sin(t):\nw:=0:\nr:=0.5:\ndu:=di
ff(u,t): dv:=diff(v,t): d:=sqrt(du^2+dv^2):                         x:
= u + r*f*sin(t/2)*cos(t): \ny:= v + r*f*sin(t/2)*sin(t): \nz:= w + r*
f*cos(t/2): \n\nxb:= u + r*Pi*sin(t/2)*cos(t): \nyb:= v + r*Pi*sin(t/2
)*sin(t):\nzb:= w + r*Pi*cos(t/2): \n\nxj:= u - r*Pi*sin(t/2)*cos(t): \+
\nyj:= v - r*Pi*sin(t/2)*sin(t):\nzj:= w - r*Pi*cos(t/2): \nszalag:=pl
ot3d([x,y,z],f=-Pi..Pi,t=0..2*Pi,\ngrid=[5,41],scaling=CONSTRAINED):\n
vonal:=tubeplot(\{[xb,yb,zb],[xj,yj,zj]\},t=0..2*Pi,radius=0.15,grid=[
41,5],scaling=CONSTRAINED, color=BLACK,  style=PATCHNOGRID):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Eredeti (szok\341sos)  M\366bius-s
zalag:\n" }{MPLTEXT 1 0 58 "display3d(szalag,vonal,style=PATCH, orient
ation=[-55,70]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 173 "vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),\nstyl
e=PATCHNOGRID),`szalag0.wrl`, background_color=COLOR(RGB,0,1,1), shini
ness=0.3, specular_color=COLOR(RGB,1,1,1)):" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 506 "u:=3*cos(Pi*t)+1/(1+10*t^2):\nv:=2
*sin(Pi*t)*(1-t^2)^5:\nw:=-0.5*sin(Pi*t):\nr:=0.5:\ndu:=diff(u,t): dv:
=diff(v,t): d:=sqrt(du^2+dv^2):                         x:= u - r*f*dv
/d: \ny:= v + r*f*du/d: \nz:= w : \nxb:= u - r*dv/d: \nyb:= v + r*du/d
: \nxj:= u + r*dv/d: \nyj:= v - r*du/d:                               \+
  \nszalag:=plot3d([x,y,z],f=-1..1,t=-1..1,\ngrid=[5,41],scaling=CONST
RAINED):\nvonal:=tubeplot(\{[xb,yb,w],[xj,yj,w]\},t=-1..1,radius=0.03,
\ngrid=[41,5],scaling=CONSTRAINED, color=BLACK,  style=PATCHNOGRID):" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "1.szalag: a szok\341sos M\366bi
us-szalag\n" }{MPLTEXT 1 0 45 "display3d(szalag,vonal,orientation=[140
,70]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "v
rml(display3d(szalag,vonal),`szalag1.wrl`, background_color=COLOR(RGB,
0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 368 "x:= u - r*
cos(f)*dv/d: \ny:= v + r*cos(f)*du/d: \nz:= w - r*sin(f):\nxb:= u - r*
dv/d: \nyb:= v + r*du/d: \nxj:= u + r*dv/d: \nyj:= v - r*du/d:        \+
                         \nszalag:=plot3d([x,y,z],f=0..Pi,t=-1..1,\ngr
id=[7,41],scaling=CONSTRAINED):\nvonal:=tubeplot(\{[xb,yb,w],[xj,yj,w]
\},t=-1..1,radius=0.03,\ngrid=[41,5],scaling=CONSTRAINED, color=BLACK,
 style=PATCHNOGRID):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 38 "2. szalag: f\351l-henger keresztmetszet\373\n" }{MPLTEXT 1 0 
45 "display3d(szalag,vonal,orientation=[140,70]);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "vrml(display3d(szalag,vonal
,color=COLOR(RGB,0.6,0.5,0),\nstyle=PATCHNOGRID),`szalag2.wrl`,\nbackg
round_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,
0.5,0.5,0.5));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 407 "r:=0.5*(
1+sin(Pi*t/2)*sqrt(1-t^2)): \nx:= u - r*cos(f)*dv/d: \ny:= v + r*cos(f
)*du/d: \nz:= w - r*sin(f):\nxb:= u - r*dv/d: \nyb:= v + r*du/d: \nxj:
= u + r*dv/d: \nyj:= v - r*du/d:                                    \n
szalag:=plot3d([x,y,z],f=0..Pi,t=-1..1,grid=[7,41],scaling=CONSTRAINED
):\nvonal:=tubeplot(\{[xb,yb,w],[xj,yj,w]\},t=-1..1,radius=0.03,\ngrid
=[41,5],scaling=CONSTRAINED, color=BLACK, style=PATCHNOGRID):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "3. szalag: v\341ltoz\363 sz\351les
s\351g\373" }{MPLTEXT 1 0 46 "\ndisplay3d(szalag,vonal,orientation=[14
0,70]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "
vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),\nstyle=PATCHNO
GRID),`szalag3.wrl`,\nbackground_color=COLOR(RGB,0,1,1), shininess=0.5
, specular_color=COLOR(RGB,0.5,0.5,0.5));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 225 "w:=0 : \nz:= w - r*sin(f):\nszalag:=plot3d([x,y,z]
,f=0..Pi,t=-1..1,\ngrid=[7,41],scaling=CONSTRAINED):\nvonal:=tubeplot(
\{[xb,yb,w],[xj,yj,w]\},t=-1..1,radius=0.03,\ngrid=[41,5],scaling=CONS
TRAINED, color=BLACK, style=PATCHNOGRID):\n" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 39 "4.szalag: a hat\341rvonala egy s\355kban van." }
{MPLTEXT 1 0 46 "\ndisplay3d(szalag,vonal,orientation=[140,70]);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "vrml(displ
ay3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),\nstyle=PATCHNOGRID),`sza
lag4.wrl`,\nbackground_color=COLOR(RGB,0,1,1), shininess=0.5, specular
_color=COLOR(RGB,0.5,0.5,0.5));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 220 "z2:= 1+ r*sin(f):\nszalag2:=plot3d([x,y,z2],f=0..Pi,t=-1..1,g
rid=[7,41],\nscaling=CONSTRAINED):\nvonal2:=tubeplot(\{[xb,yb,1],[xj,y
j,1]\},t=-1..1,radius=0.03, grid=[41,5],scaling=CONSTRAINED, color=BLA
CK, style=PATCHNOGRID):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "5. s
zalag: K\351t, egym\341ssal szembenfekv\365 M\366bis szalag\n" }
{MPLTEXT 1 0 60 "display3d(szalag,vonal,szalag2,vonal2,orientation=[14
0,70]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 194 "vrml(display3d(szalag,vonal,szalag2,vonal2,\ncolor=C
OLOR(RGB,0.6,0.5,0),style=PATCHNOGRID),`szalag5.wrl`,\nbackground_colo
r=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.
5));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "6.szalag: \366sszeragaszt
ott M\366bius szalagok \351s a ragaszt\341s helye\n" }{MPLTEXT 1 0 
122 "szalag:=plot3d([x,y,z],f=0..2*Pi,t=-1..1,grid=[13,41],\nscaling=C
ONSTRAINED):\ndisplay3d(vonal,szalag,orientation=[140,70]);" }}{PARA 
13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 
"vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),\nstyle=PATCHN
OGRID),`szalag6.wrl`,\nbackground_color=COLOR(RGB,0,1,1), shininess=0.
5, specular_color=COLOR(RGB,0.5,0.5,0.5));" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 24 "7.szalag:  Klein-kancs\363\n" }{MPLTEXT 1 0 76 "szalag:=p
lot3d([x,y,z],f=0..2*Pi,t=-1..1,grid=[25,81],\nscaling=CONSTRAINED):" 
}{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "display3d(
szalag,orientation=[-140,70]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 173 "vrml(display3d(szalag,color=COLOR(RGB,0.6,0.5,0),\nstyle=PATC
HNOGRID),`szalag7.wrl`,\nbackground_color=COLOR(RGB,0,1,1), shininess=
0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));" }}}}{MARK "0 0 0" 0 }
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