On a problem of Croft on optimally nested regular polygons
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- Dilworth, S.J. & Mane, S.R. J. Geom. (2010) 99: 43. doi:10.1007/s00022-011-0065-3
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We present a solution for the largest regular m-gon contained in a regular n-gon. We find that the answer depends critically on the coprimality of m and n. We show that the optimal polygons are concentric if and only if gcd(m, n) > 1. Our principal result is a complete solution for the case where m and n share a common divisor. For the case of coprime m and n, we present partial results and a conjecture for the general solution. Our findings subsume some special cases which have previously been published on this problem.