Finding Keys to the Peano Curves

Paul Humke, Khang Vo Huynh

Abstract:

The purpose of this paper is to give a fairly complete analysis of
Peano’s space filling curve. We begin with a synopsis of the history of the curve,
but then begin an analysis using the geometric methods that Hilbert developed.
We show that this inherent geometry can be viewed as governed by the action
of the Klein Four Group and continue to give a rather full arithmetization of the
Peano Curve.