Fitting / drawing a closed curve of a given length within given dimensions.
I'm trying to fit / draw a given length of a closed curve within given dimensions.
Example: Curve length=941mm, width=3mm, and height=5mm and it must fit within the dimensions x=250mm y=210mm
I was thinking of creating a shape like this (where it starts and ends at the same location and it doesn't crossover / intersect with itself)
Another thought I had was to start off with a circle with the correct length / circumference, width and height and have it re-configured in a way to fit the given dimensions without it intersecting or crossing over (think indenting a rubber band multiple times)
What type mathematical category would this fall under and how can I go about solving / calculating this?