Stitches

How long was golden thread used for embroidery?

A weaver embroidered a cloth with golden thread according to the pattern shown here: http://img152.imageshack.us/img152/8974/cloth.gif The pattern consists of infinitely many yellow circles. Grey circle at the center and six tangent straight lines are NOT a part of the embroidery, they only serve to show how the pattern was constructed. Six large golden circles, and one large grey circle in the center all have diameters equal to 1, and all circles and lines are tangent whenever possible.

Public Comments

1. If diameter of the bigest circle is 1, then diameters of the smaller circles are 1/4, 1/9, 1/16, 1/25, ..., 1/n^2. Total circumference of one set of circles is: π*(1+1/4+1/9+1/16+....) = π*π^2/6 = π^3/6 So, because we have 6 sets of circles, total circumference is: π^3 = 31.00627668...