> restart: with(plots):with(plottools):
> u:=8*cos(t):
> v:=8*sin(t):
> w:=0:
> r:=0.5:
> du:=diff(u,t): dv:=diff(v,t): d:=sqrt(du^2+dv^2):                         x:= u + r*f*sin(t/2)*cos(t): 
> y:= v + r*f*sin(t/2)*sin(t): 
> z:= w + r*f*cos(t/2): 
> 
> xb:= u + r*Pi*sin(t/2)*cos(t): 
> yb:= v + r*Pi*sin(t/2)*sin(t):
> zb:= w + r*Pi*cos(t/2): 
> 
> xj:= u - r*Pi*sin(t/2)*cos(t): 
> yj:= v - r*Pi*sin(t/2)*sin(t):
> zj:= w - r*Pi*cos(t/2): 
> szalag:=plot3d([x,y,z],f=-Pi..Pi,t=0..2*Pi,
> grid=[5,41],scaling=CONSTRAINED):
> vonal:=tubeplot({[xb,yb,zb],[xj,yj,zj]},t=0..2*Pi,radius=0.15,grid=[41,5],scaling=CONSTRAINED, color=BLACK,  style=PATCHNOGRID):
Eredeti (szokásos)  Möbius-szalag:
display3d(szalag,vonal,style=PATCH, orientation=[-55,70]);
> vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag0.wrl`, background_color=COLOR(RGB,0,1,1), shininess=0.3, specular_color=COLOR(RGB,1,1,1)):
> u:=3*cos(Pi*t)+1/(1+10*t^2):
> v:=2*sin(Pi*t)*(1-t^2)^5:
> w:=-0.5*sin(Pi*t):
> r:=0.5:
> du:=diff(u,t): dv:=diff(v,t): d:=sqrt(du^2+dv^2):                         x:= u - r*f*dv/d: 
> y:= v + r*f*du/d: 
> z:= w : 
> xb:= u - r*dv/d: 
> yb:= v + r*du/d: 
> xj:= u + r*dv/d: 
> yj:= v - r*du/d:                                 
> szalag:=plot3d([x,y,z],f=-1..1,t=-1..1,
> grid=[5,41],scaling=CONSTRAINED):
> vonal:=tubeplot({[xb,yb,w],[xj,yj,w]},t=-1..1,radius=0.03,
> grid=[41,5],scaling=CONSTRAINED, color=BLACK,  style=PATCHNOGRID):
1.szalag: a szokásos Möbius-szalag
display3d(szalag,vonal,orientation=[140,70]);
> vrml(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));
> x:= u - r*cos(f)*dv/d: 
> y:= v + r*cos(f)*du/d: 
> z:= w - r*sin(f):
> xb:= u - r*dv/d: 
> yb:= v + r*du/d: 
> xj:= u + r*dv/d: 
> yj:= v - r*du/d:                                 
> szalag:=plot3d([x,y,z],f=0..Pi,t=-1..1,
> grid=[7,41],scaling=CONSTRAINED):
> vonal:=tubeplot({[xb,yb,w],[xj,yj,w]},t=-1..1,radius=0.03,
> grid=[41,5],scaling=CONSTRAINED, color=BLACK, style=PATCHNOGRID):
2. szalag: fél-henger keresztmetszetű
display3d(szalag,vonal,orientation=[140,70]);
> vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag2.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));
> r:=0.5*(1+sin(Pi*t/2)*sqrt(1-t^2)): 
> x:= u - r*cos(f)*dv/d: 
> y:= v + r*cos(f)*du/d: 
> z:= w - r*sin(f):
> xb:= u - r*dv/d: 
> yb:= v + r*du/d: 
> xj:= u + r*dv/d: 
> yj:= v - r*du/d:                                    
> szalag:=plot3d([x,y,z],f=0..Pi,t=-1..1,grid=[7,41],scaling=CONSTRAINED):
> vonal:=tubeplot({[xb,yb,w],[xj,yj,w]},t=-1..1,radius=0.03,
> grid=[41,5],scaling=CONSTRAINED, color=BLACK, style=PATCHNOGRID):
3. szalag: változó szélességű
display3d(szalag,vonal,orientation=[140,70]);
> vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag3.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));
> w:=0 : 
> z:= w - r*sin(f):
> szalag:=plot3d([x,y,z],f=0..Pi,t=-1..1,
> grid=[7,41],scaling=CONSTRAINED):
> vonal:=tubeplot({[xb,yb,w],[xj,yj,w]},t=-1..1,radius=0.03,
> grid=[41,5],scaling=CONSTRAINED, color=BLACK, style=PATCHNOGRID):
> 
4.szalag: a határvonala egy síkban van.
display3d(szalag,vonal,orientation=[140,70]);
> vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag4.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));
> z2:= 1+ r*sin(f):
> szalag2:=plot3d([x,y,z2],f=0..Pi,t=-1..1,grid=[7,41],
> scaling=CONSTRAINED):
> vonal2:=tubeplot({[xb,yb,1],[xj,yj,1]},t=-1..1,radius=0.03, grid=[41,5],scaling=CONSTRAINED, color=BLACK, style=PATCHNOGRID):
> 
5. szalag: Két, egymással szembenfekvő Möbis szalag
display3d(szalag,vonal,szalag2,vonal2,orientation=[140,70]);

> vrml(display3d(szalag,vonal,szalag2,vonal2,
> color=COLOR(RGB,0.6,0.5,0),style=PATCHNOGRID),`szalag5.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));
6.szalag: összeragasztott Möbius szalagok és a ragasztás helye
szalag:=plot3d([x,y,z],f=0..2*Pi,t=-1..1,grid=[13,41],
scaling=CONSTRAINED):
display3d(vonal,szalag,orientation=[140,70]);

> vrml(display3d(szalag,vonal,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag6.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));
7.szalag:  Klein-kancsó
szalag:=plot3d([x,y,z],f=0..2*Pi,t=-1..1,grid=[25,81],
scaling=CONSTRAINED):
> display3d(szalag,orientation=[-140,70]);
> vrml(display3d(szalag,color=COLOR(RGB,0.6,0.5,0),
> style=PATCHNOGRID),`szalag7.wrl`,
> background_color=COLOR(RGB,0,1,1), shininess=0.5, specular_color=COLOR(RGB,0.5,0.5,0.5));