Differentiable curves that are not smooth We call a curve admitting a parameterization $t\to z(t)$, $t\in[0,1]$ differentiable if the vector function $z$ is differentiable. We call the curve smooth if it is differentiable and its derivative is non-zero.

What are examples of differentiable curves that are not smooth? What are the geometrical differences between the two types? Are there curves, which are not smooth at a point and still have a unique tangent at that point? Which are some differentiable curves do not have a tangent.
the smoothness that you mean is what we call geometric continuity of a curve , in other words a curve is sad to be geometric continuous if it has at each point a tangent vector and varie continuously along the curve.
I m interseting at such field of geometry,  i will be happy if you give me any open question in .
the smoothness that you mean is what we call geometric continuity of a curve , in other words a curve is sad to be geometric continuous if it has at each point a tangent vector and varie continuously along the curve.
I m interseting at such field of geometry,  i will be happy if you give me any open question in .