Hi, everyone: I am trying to show this: Given C(t) a unit-speed curve, using the usual Frenet-Serre frames T,N,B. Define the normal lines to C(t) to be the lines extending N, i.e, line segments containing N. Then: If all normal lines meet at a common point, C(t) must be part of a circle. Problem is that for curves, unlike for surfaces, tangent plane is not defined , meaning that there is no unique direction, no unique plane containing all derivatives thru a point ; I know N is perpen- dicular to T , by the first F-S equation, together with the fact that <T,T>=1 (by unit speed; k is curvature, assume k =/0): T'=kN <T,T>=1-> 2<T',T>=0 But there is a planeful worth of perpendiculars to T', so I don't know how to tell which plane contains N. I tried to shift the axes so that the normals meet at the origin, but I still cannot see it. I thought I had found a counterexample, by embedding a curve in S^2 , so that the tangent space of the curve is a subspace of the tangent space to S^2. Then I used the fact that the normals to S^2 meet at the origin. I showed this to a friend, who told me only that my counterexample was worth 2 Kourics (S.Park), and I am back to the drawing board. Thanks for any ideas.