I hereby resolve to read to the end any given post before leaping to try and understand the details.

After scribbling lines and points over both sides of several sheets of paper trying to picture this, I then resorted (as any ex-Mech.Eng. would) to a cardboard box, a pencil, a ruler and a pair of sissors.

I was going along great until I got to the bit about the cylinder. A loo roll center wasn't big enough (Have you ever tried to re-roll a pile of loo paper? Take it from me, don't bother!).

So, out to the garage, a hacksaw to a discarded carpet roll tube that has been sitting on the rafters (cos I thought it might be useful) and a 1 foot section later. A few judicious snips on the cardboard box allowed me to roughly center this over one axis (a corner of the box to us laymen). A quick re-labelling, lay the whole thing on its side. And the realisation dawns and finally it makes sense.

Those things that you mathematicians call curves, are (in this case) what any engineer would call straight lines. Now the description makes sense :^).

Then I read the last paragraph and "Ah! Now there's a good reason for not doing it".

Seriously though, thankyou for the excellent explanation!