Find the radius of osculating sphere of the helix: alpha(t)=(acos(t),asin(t),bt), a,b>0.
Well, the function r(s)=<m(s0)-alpha(s),m(s0)-alpha(s) is the radius of the sphere squared I believe. Then would it just be r^2=(acost,asint,bt), and then r^2=sqrt[(acost)^2+(asint)^2+(bt)^2]=sqrt[a^2(1)+b^2t^2) so r=(a^2+b^2t^2)^(1/4).
Is that correct?
No. For a start, it wouldn't depend on t, since translations on the helix are realised by isometries of
, i.e. for any two points on the helix, there exists an isometry of
bring one to the other presering the helix.