RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2015, Volume 97, Issue 2, Pages 231–248 (Mi mz10330)  

This article is cited in 1 scientific paper (total in 1 paper)

Family of Equal-Sized $n$-Dimensional Polyhedra Satisfying Cavalieri's Principle

F. M. Malyshev

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We prove the equality of the $(n-1)$-dimensional volumes of the cross-sections by parallel hyperplanes of a large family of $n$-dimensional convex polyhedra with nonnegative integer coordinates of their vertices, including the unit cube and the rectangular simplex with “legs” of lengths $1,2,…,n$. The cross-sections are perpendicular to the main diagonal of the cube. The first proof is carried out by a gradual reconstruction of the polyhedra, while the second one employs a direct calculation of the volumes by representing the polyhedra as the algebraic sum of convex cones.

Keywords: $n$-dimensional polyhedron, Cavalieri's principle, multiset, abelian group, pyramid, cone, cube.

DOI: https://doi.org/10.4213/mzm10330

Full text: PDF file (641 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2015, 97:2, 213–229

Bibliographic databases:

Document Type: Article
UDC: 514.172.45
Received: 13.06.2013

Citation: F. M. Malyshev, “Family of Equal-Sized $n$-Dimensional Polyhedra Satisfying Cavalieri's Principle”, Mat. Zametki, 97:2 (2015), 231–248; Math. Notes, 97:2 (2015), 213–229

Citation in format AMSBIB
\Bibitem{Mal15}
\by F.~M.~Malyshev
\paper Family of Equal-Sized $n$-Dimensional Polyhedra Satisfying Cavalieri's Principle
\jour Mat. Zametki
\yr 2015
\vol 97
\issue 2
\pages 231--248
\mathnet{http://mi.mathnet.ru/mz10330}
\crossref{https://doi.org/10.4213/mzm10330}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3370509}
\zmath{https://zbmath.org/?q=an:06459069}
\elib{http://elibrary.ru/item.asp?id=23421510}
\transl
\jour Math. Notes
\yr 2015
\vol 97
\issue 2
\pages 213--229
\crossref{https://doi.org/10.1134/S000143461501023X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000350557000023}
\elib{http://elibrary.ru/item.asp?id=24949364}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84941650843}


Linking options:
  • http://mi.mathnet.ru/eng/mz10330
  • https://doi.org/10.4213/mzm10330
  • http://mi.mathnet.ru/eng/mz/v97/i2/p231

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Nevskii, A. Yu. Ukhalov, “On $n$-dimensional simplices satisfying inclusions $S\subset[0,1]^n\subset nS$”, Autom. Control Comp. Sci., 52:7 (2018), 667–679  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:262
    Full text:17
    References:36
    First page:35

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019