Mathematicians find way to put 7 cylinders in contact without using their ends

It has been known for a long time that one can arrange 7 cylinders to be mutually touching. That was written about by Martin Gardner decades ago, and was set as a puzzle.

The result had the cylinders touching at the end of one with the length of the other, so the question arose, can one arrange to have seven cylinders all mutually touching, without using the ends. The easiest way to say this is to ask for seven infinitely long cylinders mutually touching.

This has only recently been settled, hence this paper. It's believed impossible to arrange eight identical infinitely long cylinders to be mutually touching. I suspect the result is in fact known, but I haven't searched diligently for it.

There is an associated puzzle that uses cylinders that are very short - think coins. How many coins can you arrange to be mutually touching?

Consider that a puzzle. I can do 5. If you can do more, there's a mathematical paper in it for you, should you care.

Yes, length to radius is important factor. Here's a discussion on 7 cylinders touching (using their end) ...

http://www.ocf.berkeley.edu/~wwu/riddles/cigarettes.shtml

This is going to sound like trolling, but it's not - I'm honestly curious.

Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby?

EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it. Just wondering if this had an application immediately.

Here's the original solution - http://www.mathpuzzle.com/7cylinders.gif

There are many puzzles, games, and obsessions that require the creation of new mathematics to understand properly, and then which eventually prove to be useful.

Sometimes solving these sorts of problems requires pushing the boundaries of existing techniques, sometimes the techniques required are completely new and are invented specifically for the question at hand.

I'm not sure about this specific instance with regards payment, but sometimes people are paid to play with these sorts of things simply because you don't know what will come from it.

People constantly, constantly ask this question - "What's the point of pure research?" The question has been discussed many, many times over, and there are eloquent and robust defences for pure research to be found in many places. There's no way I could do better than some of the things already out there, so I won't try. However, many of the things you use today and take for granted for first created by people "playing," sometimes in their spare time, sometimes in time paid for by companies (and in some cases individuals) who were willing to let people play and see what came of it.

If we knew what we were doing, it wouldn't be called "Research."