Hilbert Curve

Andreas Loos


The Hilbert Curve is an example of a continuous non differentiable curve completely filling the space and an early example for a fractal. It provides an example for a proof that cube contains exactly as many points as the reals. The latter was in history a major result that lead to new a definition of the notion of dimension; more in [1].


  • Andreas Loos and Günter Ziegler.
    Panorama der Mathematik.
    Springer Spektrum, 2016.

Dr. Andreas Loos   +

University: FU Berlin