10-03-10.mws

> i1 := (2/( t^2 + 1 )) + 1;

i1 := 2*1/(t^2+1)+1

> j1 := (2*t)/( t^2 + 1 );

j1 := 2*t/(t^2+1)

> k1 := 0;

k1 := 0

> r1 := [i1,j1, k1];

r1 := [(1-t^2)/(t^2+1), 2*t/(t^2+1), 0]

> with(plots);

> spacecurve(r1,t=0..5, axes=normal, color=red, numpoints=100, labels=[x,y,z]);

[Maple Plot]

> r1d := simplify(diff(r1,t));

r1d := [-4/(t^2+1)^2*t, -2*(-1+t^2)/(t^2+1)^2, 0]

> r1dmag := ((simplify(r1d[1]^2 + r1d[2]^2))^(1/2));

r1dmag := sqrt(4)*sqrt(1/((t^2+1)^2))

> r1dmag2 := (2/( t^2 + 1 ));

r1dmag2 := 2*1/(t^2+1)

> s1 := int(r1dmag2, t);

s1 := 2*arctan(t)

> T1 := tan(s/2);

T1 := tan(1/2*s)

> r1s := subs(t = T1, r1);

r1s := [(1-tan(1/2*s)^2)/(tan(1/2*s)^2+1), 2*tan(1/...

> spacecurve(r1s,s=0..6.24, axes=normal, color=red, numpoints=100, labels=[x,y,z]);

[Maple Plot]

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