I have a player thinking of researching a breakthrough, changing Circle/Ring to only have to be a bounded space of essentially any shape rather than just a circle. What level of breakthrough would this be and what limitations should be considered for this?
On a related note, what ways are there to use magic to travel the circle instead of taking the time/concentration to do it by hand/foot when casting such?
I'd say you can have an individual other shape with a Minor Breakthrough, while carrying those Breakthrough points on to work with any shape would be Major.
As for the time "traversing" the circle while casting, remember that the magus not only needs to "walk" around the area, but also draw the circle, even if over an already existing circle.
To quote the rulebook:
It also seems to clear up the matter of magical means of movement while "walking" the ring. I'd allow any magical means of transport, as long as the magus is still drawing the ring, and as long as the magus is not moving faster than ten paces per round, no matter how he's moving.