[rtuzfhzb] Square in octagon in square

Draw a larger square around a smaller square.  What is an aesthetically pleasing margin?

Fit an octagon exactly between the larger and smaller so that 4 sides of the octagon are coincident with sides of the larger square and the corners of the smaller square are on midpoints of the other 4 sides of the octagon.

The ratio of areas between the larger and smaller squares is then 2:1; or linear dimensions sqrt(2):1.