When we talk about curves - we actually mean lines.
When one starts thinking about the line a whole world of perspectives, definitions and reflextions opens up.

The register of the Britannica devotes 1 1/2 columns to the term "line" alone.

Now here some ruminations on the line; the line encircled.

Pictures: Some lines have a beginning and an end. Others a beginning ... but no end and other others an end but no beginning.