A construction of a Peano curve

Year, pages: 2016, 583 - 584

[PEANO, G.: Sur une courbe, qui remplit toute une aire plane, Math. Ann. 36 (1890), 157--160] invented a surjective continuous mapping $f$ of the unit interval $I=[0,1]$ onto $I\times I$. A well-known geometric construction was given by [HILBERT, D.: Über die stetige Abbildung einer Linie auf ein Flächenstück, Math. Ann. 38 (1891), 459--460]. In general, Peano curves are constructed as limit of a series of piecewise linear functions. Here, we present another type of proof. A detailed survey on Peano curves is given in [WUNDERLICH, W.: Über Peano-Kurven, Elem. Math. 28 (1973), 1--10].

Harzheim, E. 2016. A construction of a Peano curve. In Mathematica Slovaca, vol. 66, no.3, pp. 583-584. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0161

Harzheim, E. (2016). A construction of a Peano curve. Mathematica Slovaca, 66(3), 583-584. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0161