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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 329, Pages 88–91 (Mi znsl298)  
This article is cited in 8 scientific papers (total in 8 papers)

Equilateral simplices in normed 4-space

V. V. Makeev

Saint-Petersburg State University
Full-text PDF (134 kB) Citations (8)
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Abstract: Let $E$ be a 4-dimensional real normed space, $x\ge3/4$ a positive number, and $P\subset E$ a 3-plane. It is proved that there exist 4 equidistant points $A_1$, $A_2$, $A_3$, $A_4\in P$ and a point $A_5\in E$ such that $\|A_5A_i\|=x\cdot\|A_1A_2\|$ for $i=1,2,3,4$. In particular, $E$ contains an equilateral simplex.
Received: 25.12.2005
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 140, Issue 4, Pages 548–550
DOI: https://doi.org/10.1007/s10958-007-0436-3
Bibliographic databases:
UDC: 514.179
Language: Russian
Citation: V. V. Makeev, “Equilateral simplices in normed 4-space”, Geometry and topology. Part 9, Zap. Nauchn. Sem. POMI, 329, POMI, St. Petersburg, 2005, 88–91; J. Math. Sci. (N. Y.), 140:4 (2007), 548–550
Citation in format AMSBIB
\Bibitem{Mak05}
\by V.~V.~Makeev
\paper Equilateral simplices in normed 4-space
\inbook Geometry and topology. Part~9
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 329
\pages 88--91
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl298}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2215334}
\zmath{https://zbmath.org/?q=an:1151.52305}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 140
\issue 4
\pages 548--550
\crossref{https://doi.org/10.1007/s10958-007-0436-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845756803}
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  • https://www.mathnet.ru/eng/znsl/v329/p88
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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