::: The "problem" is not the definition of the constant itself; it's the definition of unit circle. To the ancients, diameter was basic. It's easy to see why. A jar with unit diameter takes up that much room on the shelf. More recently, radius has come to be thought of basic. This serves the needs of the analytic geometer but otherwise doesn't make much sense. But even the analysts realized that the definition of the constant was far too well established to replace with circumference/radius. So one full turn of the modern unit circle is 2π and that is that.