Let An be the area enclosed by the nth orbit in a hydrogen atom.  The graph of ln(An/A1) against ln(n): (Here A1 is the first orbit.)

It cant be a circle, since the orbits are in elliptical shape as described by sommerfield. The mathematical reason is we get the equationy=2(logn2)x, if x=0 the line passes throgh the origin. The equation is y=mx+C form.