Very nice.

Create Catenary.

Unwrap to see that actual Length of catenary is slightly less than selected distance, due to the fact that
the catenary is being approximated by nurbs control points.

Place one point on end of curve.

Do circular array of point on catenary curve, with an item count of 3. (or 5 or 7 ...)

Trim the catenary curve with the points, and change the color of the segments.
Select all the catenary segments, and Unwrap them, and see that the distances add up to the same total length.