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Matematicheskie Zametki, 2021, Volume 110, Issue 2, Pages 289–296
DOI: https://doi.org/10.4213/mzm13069 (Mi mzm13069) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

E. V. Shchepina, E. Yu. Mychkab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
Full-text PDF (421 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13069
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.
Received: 10.03.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 2, Pages 267–272
DOI: https://doi.org/10.1134/S0001434621070282
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: E. V. Shchepin, E. Yu. Mychka, “Lower Bounds for the Square-to-Linear Ratio for Plane Peano Curves”, Mat. Zametki, 110:2 (2021), 289–296; Math. Notes, 110:2 (2021), 267–272
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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