Some logical implications of the two Einstein assumptions used in his analysis of geometry on a relativistically rotating disc

We show that. with the help of the two well known Einstein assumptions used by him in the treatment of geometry on relativistically rotating disc, and elementary logical analysis only, two different and opposite models of rotating discs can be constructed: In one of them the disc, set rotating from the stationary state, changes neither its radius nor circumference, as measured from stationary inertial frame; while in the other both the radius and the circumference contract by the same Lorentz factor. We also show that one can construct discs whose contraction factors vary continuously from unity (no contraction) to the full Lorentz factor