Optimally nested regularN-gons

Various sequences of polygons are described and the radii are determined when each successive member of the sequence is the largest next member of the sequence containing its predecessor, or else the smallest next member of the sequence containing its predecessor. In particular, a correct solution of the problem of finding the area of the circle that is the limit of the largest regularn-gon fitting inside a regular (n?1)-gon, starting from an equilateral triangle of unit area, is found to be 0.0753105.