After a series of corrections to the pattern, here is the latest version of my
paper pith-helmet. This is a beta version, that I'm putting up so that other people can have a play.
The zip-file contains 7 gifs. I have a large head, and this is too big without padding, so you might want to scale them down a bit. This should also help if you want to print this on US letter-sized paper, as this was designed to be printed on A4 at full size. The stiffer the paper the better, in fact if you can print to thin card, it'd probably be ideal; however I've done all my work on this to date with regular A4 80GSM. The 100mm scale printed on figure 3 will help you to calibrate the pattern to your printer; I will eventually produce a PDF for this, which should eliminate much of the stuffing around.
Don't bother to cut away the space between the segments at firstThe idea is that you print all 7 at the same scale, cut them out and glue them together in the center by gluing the "hubs" one on top of the other. The cross-hairs on the hubs will help you align the various different sections. Don't bother to cut away the space between the segments at first, just cut around each section; the illustration on the right should give you an idea of what I mean, although this is a later pattern and will look a little different.
Once the glue has dried, go around and tape the outer segments together. Then cut away the remaining space between segments, and tape them together, one at a time. I recommend that for taping this curving surface, you put the pattern over your knee.
With the finished article, I will put a hat-band around the outside (over the numbers), probably line it with space-filler foam, and paint it. I haven't got that far yet though.
These pictures, although of an earlier, rougher prototype, illustrate the general effect.