Given a circle with radius length r, what is the maximum length of a curve which starts at the center and can cross any radius at most once? the curve must be contained inside the circle.
I would intuitively assume it is some kind of spiral, but honestly I don't even know if that question makes sense. Any help would be much appreciated.
I doubt there is a limit without further constraints
For example consider a curve like this
and with more petals the blue curve could be made arbitrarily long