It is impossible to make a circle (rug) w/o overlapping the ties. The standard spread of a tie will not allow you make a circle w/o either overlap or gaps unless you vary the taper. Figure out what diameter circle you want, then figure out the circumference (3.14 X diameter). Now take this number and divide it by the average width of the ties at the wide end. That will tell you how many ties you will need to make the circle. You will have to alter the length and width as you go toward the center. Hope this helps.
If I totally misunderstood your question, sorry.
You sew too? Impressive!