Space-Filling Curves

• History
  • Discovered by Peano in 1890
  • Graphically simpler example found by Hilbert, 1891.
  • Other examples due to E.H. Moore, Lebesgue, Osgood, Sierpinski, and Knopp.
• Definition: A space-filling curve is a continuous function from an interval into real n-dimensional space whose image contains an n-dimensional disk (n at least 2).
• Example: Hilbert's curve