Originally Posted by PaperPrincess

I agree that you have allow for seam allowance in the size of the patch, but seam allowance does not affect the angle. if you sew a square patch, you wind up with a smaller square, but the angles are still 90 degrees. if you cut a wedge with a 9 degree ruler, sew it to its neighbors, you wind up with a smaller wedge, but it's still 9 degrees (if you sewed perfect seam allowances) and it will still take only 40 perfectly cut and sewn wedges to make the circle.