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.
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Humke, P.D., Huynh, K.V. Finding keys to the Peano curve. Acta Math. Hungar. 167, 255–277 (2022). https://doi.org/10.1007/s10474-022-01242-1
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DOI: https://doi.org/10.1007/s10474-022-01242-1