h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It shouldn't be much of a loss to lose the link Schreck. Can't spot anything else needing attention in your subbed copy.


Pimms

Hey Pimms, I don't know if this part (from 'Evolving the Features') is quite correct:

. Tucks can be made (cutting a slit, and overlapping material to increase curvature), or

. Darts added (again cutting a slit, but widening it into a gap that needs filling with layers of papier-mâché, to decrease curvature).

Isn't it so that tucks decrease (make less) curvature and darts increase (make more) curvature? Or am I wrong here?

No, I had to figure it out, but my phrasing is correct. Curvature of a circle is equal to the inverse of the radius. Smaller circles bend more sharply, and hence have higher curvature. Curvature is the amount by which a geometric object deviates from being flat.

The way I envisage it is if you take a flat circle and cut a slit to the centre then overlap some of the area you will make a cone - overlapping material makes it less flat - ie increases curvature.

Contrariwise if you take a cone, cut from base to point and flatten it (decreasing curvature) you'll need to add material to fill the gap created.

Another way of looking at it is to imagine your mask is a hemisphere and you make cuts and overlap material - the extreme point you end up with is a smaller thicker (probably a ball) of paper. Going the opposite way making cuts and spreading the hemisphere out you'll achieve a practically flat sheet with many gaps to fill in with darts.
A small ball has a higher rate of curvature to a large one, a very large sphere has a surface which is practically flat (approaching zero curvature).

Does this make clearer the way I was thinking when I described the process?

Yes it does - problem was that 'curvature' hadn't the meaning that I expected. Thanks for clarification.