Space-Filling Curves & Generalizing the Peano Curve

The theory of space-filling curves will be developed. The two original space-filling curves, those of Peano and Hillbert, will be dissected and analyzed, with an emphasis on geometric constructions and demonstration of analytic properties. The Peano curve will be extended to every odd base, with an analogous geometric construction to the original. New proofs will be shown in order to conclude that these ``extended" Peano Curves are indeed space-filling curves, mapping surjectively and continuously from the unit interval to the unit square. Two fairly recent applications of space-filling curves in computer science will also be touched on.Bachelor of Scienc