I made the scalloped back by sewing together two semicircles and turning them inside out. I would have to draw scallops on one of the semicircles. This was a math problem. There are 37 points on the mandala. So I looked up the formula for the length of the side of a 37 sided polygon. The formula was 2 * radius * sin(180/37). (2 * radius = 32 inches.) This was something like 2.71 inches. I understood that if I just measured that distance 37 times (or 18 1/2 times for one semicircle) starting from one end, the accumulated error would cause the scallops to be in the wrong place when I got to the other end. So I cut six pieces of card stock to the (approximately) correct side length, cut a scallop into the ends, and taped them together. That way I could make sure that the spacing was as even as possible without getting overly precise.
Here are the two pieces with right sides together. The scallops are marked on the print (a scrap that escaped being stuffed into a pouf). The marking can be seen best at the lower right edge. It was quick and easy to sew the semicircles together along the marked scallops.
Next I clipped corners and notched the seam the way your grandmother learned to do in high school.
Here is half of the back, turned inside out and pressed. The black satin will be the part of the back that shows. The inside, while not the ugliest print in the world, was a piece of fabric that someone gave me, which I was never going to use for anything. But I kept it anyway, which was wise.
I also kept 24 inches of black velcro just in case I ever had to do something like this. Just kidding, I kept it because I could not bring myself to get rid of 24 inches of black velcro. Smart move. I attached the black velcro to the raw edges of the sewn-together semicircles. Notice that one piece of velcro is on the inside (you can't see it in the picture) and the other piece is on the outside. This is the only way it could possibly work. Now this was a tricky step and I have not described it all that well. The reason is that nobody else is ever going to sew a back onto a giant mandala with 37 points. But just in case anyone wants to do something like this, I made sure that I had enough extra fabric at the straight edges of the semicircles to add the velcro. I sewed a piece of velcro to the straight side along one edge of the velcro and then turned it under and sewed it down along the other edge, such that the center of the circle was exactly at the middle of the velcro strips. That way when the velcro was fastened the shape would be a "perfect" circle.
Next I overlapped the semicircles and sewed them together at each end. I pinned the edges together carefully and sewed them together by stitching a rectangle.
This is where I stand today. I have about seven points sewed down. 30 more to go.
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