This article is cited in 2 papers

Lower Bounds for the Square-to-Linear Ratio for Plane Peano Curves

E. V. Shchepin^a, E. Yu. Mychka<sup>b

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University

Abstract: It is proved that, for any map of the unit interval onto the unit square, there exist two points in the interval such that the squared Euclidean distance between their images exceeds the distance between them on the interval at least by a factor of $3.625$. The additional condition that the images of the interval endpoints belong to opposite sides of the square increases this factor to more than $4$.

Keywords: Peano curves, square-to-linear ratio.

UDC: 517.518

Received: 10.03.2021

DOI: 10.4213/mzm13069

 English version: Mathematical Notes, 2021, 110:2, 267–272

Bibliographic databases:

• 
• 
• 
•