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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 55–67 (Mi tm3336)  
This article is cited in 3 scientific papers (total in 3 papers)

One-side Peano curves of fractal genus 9

K. E. Bauman

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (196 kB) Citations (3)
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Abstract: This paper completes the analysis (begun by E. V. Shchepin and the author in 2008) of regular Peano curves of genus 9 in search of a curve with the minimum square-to-linear ratio. One-side regular Peano curves of genus 9 are considered, and, among these curves, a class of minimal curves with a square-to-linear ratio of 523 is singled out. A new language to describe curves is introduced which significantly simplifies the coding of these curves.
Received in April 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 47–59
DOI: https://doi.org/10.1134/S0081543811080037
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: K. E. Bauman, “One-side Peano curves of fractal genus 9”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 55–67; Proc. Steklov Inst. Math., 275 (2011), 47–59
Citation in format AMSBIB
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\by K.~E.~Bauman
\paper One-side Peano curves of fractal genus~$9$
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 55--67
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3336}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 275
\pages 47--59
\crossref{https://doi.org/10.1134/S0081543811080037}
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Linking options:
  • https://www.mathnet.ru/eng/tm3336
  • https://www.mathnet.ru/eng/tm/v275/p55
    • This publication is cited in the following 3 articles:
    1. Yuri Malykhin, Evgeny Shchepin, “Search of fractal space-filling curves with minimal dilation”, Discrete Comput. Geom., 70 (2023), 189–213  mathnet  crossref
    2. Yu. V. Malykhin, E. V. Shchepin, “Minimal self-similar Peano curve of genus 5×5”, Dokl. Math., 101:2 (2020), 135–138  mathnet  crossref  crossref  zmath  isi  elib
    3. K. E. Bauman, “Lower estimate of the square-to-linear ratio for regular Peano curves”, Discrete Math. Appl., 24:3 (2014), 123–128  mathnet  crossref  crossref  mathscinet  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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