Finding keys to the Peano curve (Q2166119)

The paper contains a complete analysis of construction of the Peano curve, that is, a continuous map from the unit interval \(I=[0,1]\) onto the unit square \(I^2\). The authors start with historical notes on the Peano curve. Next, they present the geometric method of construction of the Peano curve that was given by \textit{D. Hilbert} [Math. Ann. 38, 459--460 (1891; JFM 23.0422.01)], see also [\textit{E. H. Moore}, Trans. Am. Math. Soc. 1, 72--90 (1900; JFM 31.0564.03)], or [\textit{S. Flaten} et al., Am. Math. Mon. 128, No. 2, 99--114 (2021; Zbl 1458.26005)]. Finally, the authors observe that Hilbert's construction can be described by the action of the Klein Four group. This approach can be thought of as a kind of arithmetization of the Peano curve.