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Inscribed Regular Polygons in Unit Circle

A while ago I posted this problem.

I wonder if there is a generalisation for such areas, with conditions such as

a) n, (n+k)-sided regular polygons

b) u, v-sided regular polygons

c) >2 regular polygons

The only trivial fact that I realize now is:

for two u, v-sided polygons and WLOG \(v>u\)

the v-sided polygon will cover \(\gcd\left(u, v\right)\) vertices of the u-sided polygon.

If v is a multiple of u then the u-sided polygon need not be considered.

But this is a very, very specific case :(

Any ideas?

Note by Lolly Lau
3 months ago

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