The approximation argument is flawed: the squares on approximating curves may have sides decreasing to 0, in which case the limiting "square" degenerates to a point. In fact, Stromquist's theorem covers a much wider class of curves than C^1, but not all continuous curves.

## This is flawed

The approximation argument is flawed: the squares on approximating curves may have sides decreasing to 0, in which case the limiting "square" degenerates to a point. In fact, Stromquist's theorem covers a much wider class of curves than C^1, but not all continuous curves.