Good afternoon,
 
Many thanks to Andrew Pettit, Gordon Uber and John B. for their very rapid responses to my questions. Once I got started using their suggestions, I trawled a few web sites and found this one, which had more information than any mere mortal would ever want to know about geometric shapes. It's worth having a look at for some of the fancy plane circles. I get the impression that most are relatively easily computed using standard mathematical software, and could provide some very attractive shapes for sundials.
 
 
Some of the solid shapes on the same web site are truly amazing. Would be interesting to figure out how to make some of them (without using a CNC machine). The "corkscrew surface" http://mathworld.wolfram.com/CorkscrewSurface.html is just crying out to be converted into a sundial using shadows from itself.
 
Be warned, that it is easy to spend a lot of time looking at this site! But it's fun.
 
BTW: the name I was after is an "annular sector" as suggested by Andrew Pettit. And of course, Gordon Uber was correct in pointing out that I am actually referring to "discs" rather than "circles".

Cheers, John
 
John Pickard
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