Suppose we are observing a rotating frame from an inertial frame, free from gravity, and try to measure the circumference of a circle drawn in the rotating frame. Since our measuring rod would be contracted if we measure the circumference but it would not if we are measuring the diameter, according to Einstein we would conclude that the circumference to diameter ratio will be greater than $\pi$, since we would measure circumference greater.
But shouldn't the circumference itself contract so that we would get the same ratio pi in both the rotating as well as stationary case, where the circle is drawn in the inertial frame itself?
