To both of troy and wwh:

These are truly amazing tales, both of them.

Specifically to wwh:

You speak of mathematics in such a terrific way that I wish you'd been all of my math teachers. I think I may have come one day to have worked calculations.

At least--at the very least--I do read what you write with interest although I'm not quite tempted enough to sit down with a pencil and paper and try what you naturally do myself. Many of the threads I read here I just pass over as being not-so-terribly interesting--but your mathematical observations I always pause over with real interest. You're a very good writer.