> #sfb mar21, 2002
> with(plots);
> spacecurve([cos(t),sin(t),t/(5*Pi)],t=0..20*Pi,numpoints=1000,scaling=constrained);
> tubeplot([cos(t),sin(t),t/(5*Pi)],t=0..20*Pi,radius=1/10, scaling=constrained);
> tubeplot([cos(t),sin(t),t/(5*Pi)],t=0..20*Pi,radius=1/30,numpoints=1000,scaling=constrained);
> # 16.1 #11 (t,t^2) vs (t^2,t^4) vs (t^3,t^6)
> a:=plot(x^2,x=-1..1,color=black):a;
> b:=seq(plot([t,t^2,t=-1+(i-1)/50..-1+i/50],color=red,thickness=3),i=1..100):
> c:=seq(plot([t^2,t^4,t=-1+(i-1)/50..-1+i/50],color=blue,thickness=3),i=1..100):
> d:=seq(plot([t^3,t^6,t=-1+(i-1)/50..-1+i/50],color=green,thickness=3),i=1..100):
> display(b,insequence=true,view=[-1..1,0..1]);
> display(c,insequence=true,view=[-1..1,0..1]);
> display(d,insequence=true,view=[-1..1,0..1]);
> display(seq(display(b[i],c[i],d[i]),i=1..100),insequence=true);
> # From last time
> with(linalg):with(plottools):
> F:=[x,0];
> A:=fieldplot(F,x=-2..2,y=0..2):A;
> B:=plot([cos(t),sin(t),t=0..Pi],color=blue):B;
> display(A,B,scaling=constrained);
> #C:=plot3d([cos(t),sin(t),s*(-sin(t)*cos(t))],t=0..Pi,s=0..1):C;
> C:=plot3d([cos(t),sin(t),s*(-sin(t)*cos(t))],t=0..Pi,s=0..1):C;
> display3d(A,B,C,scaling=constrained);
> with(plottools);
> T:=transform((x,y)->[x,y,0]):
> display(T(A),T(B),C);
> #
> r:=vector([cos(t),sin(t)]);
> diff(r,t);map(diff,r,t);
> r:=[cos(t),sin(t)];r[1];
> diff(r,t);
> map(diff,r,t);
> F:=vector([x,0]);
> fieldplot(F,x=-3..3,y=-3..3);
> 
> eval(F,{x=r[1],y=r[2]});eval(subs({x=r[1],y=r[2]},F));
> pretty:=subs({x=r[1],y=r[2]},dotprod(F,diff(r,t),orthogonal));
> int(pretty,t=0..2*Pi);
> #machine
> r:=[0,cos(t),sin(t)];a:=0;b:=2*Pi;F:=[-z/sqrt(x^2+z^2),y/sqrt(x^2+z^2),x/sqrt(x^2+z^2)];
> v:=diff(r,t);Ft:=subs({x=r[1],y=r[2],z=r[3]},F);inside:=dotprod(Ft,v,orthogonal);
> Int(inside,t=a..b)=int(inside,t=a..b);
> display(fieldplot(F,x=-2..2,y=-2..2),circle(),scaling=constrained);
>