I wasn't sure how I would finish the edges of my lonestar circle coasters. I liked the idea of double-fold quilt binding, but it seemed like it might be tricky, especially the curves and the relatively tight diameter. I decided to try it on one coaster, and then decide what to do with the rest.
It turned out exactly like I wanted. I'll show you how I did it.
I used 17" lengths of 2 1/4" bias strips for my 4 1/2" diameter circles. If you're working with a different sized circle the length of your bias strip will be
(Diameter * 3.14) + 3"
This will give you about 3/4" extra length for wiggle room. Please note that you must use bias-cut binding strips. Binding strips cut on the grain will not conform to the curve, and your finished project will not sit flat. Bias is essential!
Mark a 45-degree diagonal line on the wrong side of one end of the bias strip starting at the top right corner. (Pay attention to the diagonal orientation - top right corner to bottom left edge. It won't work if you draw from the bottom right corner.) Press the strip in half.
Begin pinning the strip to the front of the circle. Leave a 4" unpinned tail at the marked end.
Carefully pin the bias strip about 2/3 of the way around the circle. Pin every 3/4" to 1", angling the pins toward the center of the circle. Gather the folded edge as you pin. Be careful not to stretch the cut bias edge.
Go back to the 4" marked tail. Gingerly wrap the tail around the circle edge as if you were going to pin it. Place a pin in the coaster circle where the binding ends (note the yellow flower pin head behind my finger).
Now set the marked binding tail aside and pick up the opposite binding tail. As before, wrap it around the circle edge until you reach the marker pin. Mark the bias strip at the pin (I've made a small tick mark in the photo).
Flip the coaster over, with the trailing binding strip extended and the new mark visible. Trim the strip 2 1/4" from the mark you just made. (If you look very closely you can see my tick mark on the fabric at 2 1/4".)
Press the crease flat at the two ends of the binding strip.
Pin the two ends together right sides together at a 90-degree angle, aligning the edges.
Sew along the marked line.
Time for a reality check. Before you trim anything, fold the bias strip in half to make sure you didn't make a Möbius strip or some other unworkable shape.
But it looks good! So trim the excess, and press the seam flat.
Re-crease the binding strip.
Pin around the remaining 1/3 of the circle, careful to even out any excess or tightness. Now sew around the circle with a 1/4" seam allowance.
Turn and press the binding to the back of the coaster. Finish the back of the binding as you wish. I enjoy finishing by hand!