About the Serpinsky-Knopp curve
Metric Geometry
2020-08-26 v1 Computational Geometry
Abstract
The Serpinsky-Knopp curve is characterized as the only curve (up to isometry) that maps a unit segment onto a triangle of a unit area, so for any pair of points in the segment, the square of the distance between their images does not exceed four times the distance between them.
Cite
@article{arxiv.2003.01390,
title = {About the Serpinsky-Knopp curve},
author = {Evgeny Shchepin},
journal= {arXiv preprint arXiv:2003.01390},
year = {2020}
}
Comments
An abridged version of this article is accepted for publication in Russian Mathematical Surveys