On a euclidean plane, what is the minimal area shape S, such that for every unit length curve, a translation and a rotation of S can cover the curve.

What are the bounds of the shape's area if this is a open problem?

When I asked this problem few years ago, someone told me it's open. I don't know if this is still open and I can't find any reference on it.

I don't even know what branch of mathematics it falls under. so I can't even tag this question.