  The phenomenon, known as "supersmoothness" was first observed for bivariate
splines and attributed to the polynomial nature of splines. Using only standard
tools from multivatiate calculus, we show that if we continuously glue two
smooth functions along a curve with a "corner", the resulting continuous
function must be differentiable at the corner, as if to compensate for the
singularity of the curve. Moreover, locally, this property, we call
supersmoothness, characterizes non-smooth curves. We also generalize this
phenomenon to higher order derivatives. In particular, this shows that
supersmoothness has little to do with properties of polynomials.
