How long was used gold thread for embroidery?
A weaver cloth embroidered with gold thread using the model presented here: http://img152.imageshack.us/img152/8974/cloth.gif model consists of an infinite number of yellow circles. gray circle in the center and six tangent lines do are not part of the embroidery, they only serve to show how the model was built. Six great circles of gold, and a large gray circle in the center all have a diameter equal to 1, and all the circles and lines are tangents to the extent possible.
If the diameter of the largest circle is 1, then diameters smaller circles are 1 / 4, 1 / 9, 1 / 16, 1 / 25, ..., n ^ 1 / 2. total circumference of all 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, the entire circumference is: π ^ 3 = 31.00627668 ...
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