I am trying to reason about chainmail geometry, and I am not getting very far.

Chainmail: http://realbeer.com/jjpalmer/HowtoChain.html

It looks like there's two common patterns: where each ring intersects
with four others and where each ring intersects with six others.

If fall back to just two overlapping rigid rings, and if the minor
radius of the ring's torus is half of the major radius of the ring's
torus, I think the two rings would have to orient at right angles to
each other.

If, on the other hand, the minor radius was zero, the rings could lay
flat and the center-to-center distance could equal the major radius.

But let's say we used 14 gauge wire to make chainmail. The diameter of
the wire (our torus minor diameter) would be about 1.6mm. And, just to
have a value to work with, let's say our torus major diameter would be
25mm.

So what would the center-to-center distance be for our two kinds of
chainmail? It seems like this should be straightforward, but I keep
drawing a blank. (I probably need to spend some time with a pencil and
paper...). For a first approximation, I'm pretending that the wire
doesn't bend after it's been bent into a circle. (Not true, obviously,
but too many variables would make working this out be even more
difficult.)

Anyone here feel like walking me through this? (Er... please feel free
to take this to the chat forum if you don't feel like using J to
express the concepts?)

Thanks,

-- 
Raul
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