Working in the Round
One of the keys to creating a neat looking unit is to lay out and cut the circular shelves as accurately as possible. The ideal tool for drawing a perfect circle would be a compass, but it is doubtful that you will have one capable of drawing such a large radius. The simple solution to this problem is to make your own tool for the job. There are two quick and easy ways to do this. The first is to use a piece of string with loops tied in each end. Attach one loop to a tack or small nail in the center of the circle, then slip a pencil through the other end. Hold the pencil straight up and, with the string taut, draw your circle. You can gain a bit more accuracy by using a piece of wood (a 1x4, or even a yardstick, will do) instead of the string. Drive a small nail through one end, then slip the pencil through a drilled hole on the other. Set the point of the nail at the center, then pivot the board around as the pencil draws a perfect circle.
You may find it quicker to draw full circles on the MDF, then divide and cut it into quarters. Or you may want to cut out one perfect section and use it as a template to lay out the others. Note, however, that you will need two different sizes of pie-shaped sections. The top and bottom shelves, which overlap the sides, will each be exact quarters from the circle. The shelves in between, however, will not fit perfectly, as Ty discovered on the show. Instead, they need to be trimmed along each straight edge by 3/4 inch. In Ty's case, a quick pass on the table saw reduced the shelves to perfect size.
Cutting MDF
MDF can be cut with a circular saw or on a table saw. It is best to use sharp, carbide-tipped blades for the job. To cut the rounded edges, however, you will need a jigsaw (use a sharp, fine-tooth blade). Because it generates so much dust, it is best to cut the material outside or in a garage or workshop. If you must cut it inside the house, do so behind closed doors and be prepared to vacuum the powdery remains from all surfaces in the room. If necessary, you can smooth any rough edges with sandpaper.
When cutting the sides for each section, note that while they should be exactly the same height, one side should be 3/4-inch wider to allow it to overlap in the corner.