The rolled-up ribbon

The Workings:

Today’s divertimento is once again devoted to the book One hundred problems in elementary Mathematics, by the Polish mathematician Hugo Steinhaus (1887-1972) (one of the most original books of elementary problems ever published, according to the great Martin Gardner). For the Workings we will recall, as on earlier occasions, the previous post from our Basic Wardrobe. It is the sixth and last of those dedicated to the Scottish Café gatherings, one of whose stars was Steinhaus. In it, we explain how Banach and other chatters spent a good part of the Nazi occupation of Lwów feeding lice for the manufacture of a typhus vaccine. Rarely is it so clear how much the passion for mathematics is capable of absorbing not only the mind, but the whole body of those who dedicate themselves to it: how else to explain that the feeding gang of mathematicians often forgot the miserable situation they were in – with thousands of lice sucking their blood – while they were discussing mathematics. It is, as the introduction to this blog says, a demonstration that mathematics is capable of generating the most rapturous of passions: a kind of creative fever very similar to that of artists, be they painters, composers or poets.

The Fun:

We wind a loop 25 m long and 0.1 mm thick around a cylinder of cardboard, obtaining a cylindrical roll whose diameter is 1 dm.

What is the diameter of the cardboard cylinder?

 

 

 

 

Solution:

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.