I'd start with the triangle at the bottom, put on one side and the second, and then the next triangle, then the two sides, and on- until getting to the top.
I would not do them as separate FG and then sew them together trying to keep the arc and center point correct.
Once the FG arc is done, I'd trim and remove all the paper, then sew the inner and outer parts on to make the square.
I bought "Catch Me If You Can" and have all the fabric, but have not started it yet.