Everybody seems to have gone to all manner of scientific exposition here. I am sticking to the origianl question and NONE OTHER.
I scanned all the replies and nobody came up with this one, so here goes.
In some obscure book on the HISTORY of mathematics, it was mentioned that the Hebrews didn't really consider fractions as very real. (The Egyptians, on the other hand did some clever things with them. But that didn't rub off on the Israelites.) So, as a sneaky shortcut, the Hebrews used an INSCRIBED HEXAGON to work their cirular requirements. There are 6 radii in such a geometric construction. And a diameter is twice the radius (D = 2 * R). (6/2 =3.) So three diametric lengths of string gets the approximate circumference. It seemed to work in their constructions, as a very pragmatic method of doing things.
I'm also emailing you as you mentioned, but I believe the thread escaped the original question, but not necessarily the intention.