ParametricPlot[{Sin[t], Cos[t] + Log[Tan[t/2]]}, {t, 0, Pi}, AspectRatio -> Automatic]

 Integrate[Sqrt[D[{Sin[t], Cos[t] + Log[Tan[t/2]]}, t] . D[{Sin[t], Cos[t] + Log[Tan[t/2]]}, t]], {t, 0, Pi}]

Integrate :: idiv : 
Sqrt[Cos[t]^2  + (<< 1 >>)^2 ] の積分は {0, π} で収束しません．

∫ _ 0^π √ (Cos[t]^2 + (1/2 Csc[t/2] Sec[t/2] - Sin[t])^2) d t

 curvature[c_][t_] := Det[{D[c[tt], tt], D[c[tt], {tt, 2}]}]/((D[c[tt], tt] . D[c[tt], tt])^(3/2)) /. tt -> t

radiuscurvature[c_][t_] := Abs[1/curvature[c][tt]] /. tt -> t

c[t_] = {Sin[t], Cos[t] + Log[Tan[t/2]]} ; Plot[curvature[c][t], {t, 0, Pi}]

Converted by Mathematica  (February 10, 2004)