Question

can a simple curve be closed ?

Answer 1

Let us answer your question by splitting it into two :


Simple means it doesn’t intersect itself.Closed means that it ends where it starts (or rather, it has no start or end, but is bounded).

Hence, triangles, rectangles, circles,etc are examples of closed curves.

A closed curve which does not cross itself is called a simple closed curve.
Hence all the examples given above are examples for a simple closed curves.

Note: the shape of "8" is a closed curve, but it intersects at a point, hence it is not simple.

Hope I helped.