If you form the
string into a
circle and measure distance from the
centre of the circle to the edge (ie the
radius you can calculate the length of the string using 2.
pi.
R
This leaves the small problem that if we had such a measuring device, the question could be answered by simply measuring the string, an alternative solution must be sought.
Let us make some assumptions:
The string is at least 1cm in length
Any smaller and calling it a piece of string is perhaps a misnomer, fluff would be a better definition.
The string cannot exceed one ton
Manufacturing such a string would be impractical, and would instead of being named string, would be better termed as a tourist attraction.
String is no thinner than 1.5mm
Thinner than this, and we are entering the territory of thread.
Worst case density is 0.7kg/litre
Otherwise the string will be too weak.
So, we know the maximum weight, and the volume:
1000
---- = 1429 litres or 1.429 cubic metres.
0.7
Therefore, maximum length is
Volume 1.429m
------ = -------------
Area pix0.5mmx0.5mm
So the string length lies between 1cm and 11,644.39km which can be expressed as above
Paraphrased from "A Mensa Puzzle Book", Victor Serebriakoss; Treasure Press, Bond House, St John's Square, Wolverhampton (1991)