Well, if I had been piecing the arcs from small squares of fabric, I would have had the squares in the corners, but since I just wanted one colour in my arcs, I just didn't bother. At first, I thought that might have been my problem, but since it all fit together so well with the melons, I don't think that's it... plus, my arcs still went together really easily with the inner curve of the funny curvy triangular pieces, I didn't even have to pull the pieces into place, or ease them so that they lined up... they just fit. *sigh*
I think I will re-cut my outside pieces keeping the same curve, but add a couple of inches that I can later trim and square up so they all match.