What can be done with a piece of string?

The visit begins with a marker and a simple piece of string, with which you are invited to draw a straight line and a circumference.

Walking on the street, you can sometimes see road workers about to dig a trench, that first draw up its outline by pulling a string between two stakes. We can also draw a straight line (note the verb draw) by pulling the string with two fingers and trying to follow it with the marker. If, instead, we want to draw a circle, we will roll the string around the marker, and we will make it go round by pinning the string's other end with a finger.

The result in the two cases is very different. While usually the arcs of circle which we can draw (arcs - to draw a full circle one needs more precaution) are quite accurate, the segments of a straight line are usually disappointing.

The reason for this difference in behaviour is in the different function of the string. In the case of the circle, it is a tool. In the case of the straight line, it is a profile. With a profile one draws what is already there. We can draw a straight line because a string pulled by two fingers creates a straight line. The accuracy of the result in this case depends on the precision of the profile, and on the possibility of following it with the marker, and that is precisely what is difficult in our case.

Conversely, when drawing a circle, the string does not take up a circular form to follow the marker. We take advantage of a mathematical property of circumference, that is that all its points have the same distance from its centre. The string, pulled taut between the marker and with the end pinned to the table, ensures this very equidistance.

The same happens if, instead of using a string, we use more appropriate objects, like the ruler and the compass. Precision improves greatly with both, but there is no substantial change: the ruler is a profile, the compass an instrument. And although straight lines made with a ruler are always better than those made with a string (but circles are also rounder), the precision of an instrument will always be, at the same degree of complexity, better than the one of a profile.

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