>

restart:

>	with(plots): with(linalg):

Warning, the name changecoords has been redefined

Warning, the protected names norm and trace have been redefined and unprotected

>	assume (u,real); Forteller Maple at u og v er reelle tall (ikke komplekse) assume (v,real);

>	x := (4-v*sin(u/2))*sin(u); Parametriseringen y := (3-v*sin(u/2))*cos(u); z := v*cos(u/2);

>	a := 0; b := 2*Pi; Parameterintervallene for u og v c := -1; d := 1;

>	Flaten := plot3d([x,y,z],u=a..b,v=c..d,grid=[20,4],projection=0.9,scaling=constrained): Plotter flaten

>	Ru := [diff(x,u),diff(y,u),diff(z,u)]; Regner ut partiellderiverte av posisjonsvektoren R Rv := [diff(x,v),diff(y,v),diff(z,v)];

>	N := (a,b) -> crossprod(subs({u=a,v=b}, Rv),subs({u=a,v=b}, Ru)); Regner ut kryssproduktet, dvs. en normalvektor N til flaten

>	R := (a,b) -> [subs({u=a,v=b}, x), subs({u=a,v=b}, y), subs({u=a,v=b}, z)];

>	Npil := (a,b) -> arrow( R(a,b), N(a,b), color=red):

>

n := 30;

>	animasjon := seq( display(Flaten,Npil(2*Pi*i/n,0),scaling=constrained),i=0..n-1):

>	display(animasjon, insequence=true);

>	display(animasjon);

>

n := 30;

>	FlatenAnimert := seq(plot3d([(4-v*sin(u/2*i/n))*(-(1-i/n)* (u-Pi)/2 + (i/n)*sin(u)), (3-v*sin(u/2*i/n))*(i/n)*cos(u), v*cos(u/2*i/n)], u=a..b, v=c..d, grid=[20,4], projection=0.9, scaling=constrained), i=0..n):

>	display(FlatenAnimert,insequence=true);

>