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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 403, Pages 142–157 (Mi znsl5254)  
This article is cited in 2 scientific papers (total in 2 papers)

On equidissection of balanced polygons

D. Rudenko

University of Cambridge, Cambridge, UK
Full-text PDF (240 kB) Citations (2)
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Abstract: In this paper we show that a lattice balanced polygon of odd area cannot be cut into an odd number of triangles of equal areas. The first result of this type was obtained by Paul Monsky in 1970. He proved that a square cannot be cut into an odd number of triangles of equal areas. In 2000, Sherman Stein conjectured that the same holds for any balanced polygon.
We also show connections between the equidissection problem and tropical geometry.
Key words and phrases: equidissections, balanced polygons, Monsky theorem.
Received: 11.09.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 190, Issue 3, Pages 486–495
DOI: https://doi.org/10.1007/s10958-013-1265-1
Bibliographic databases:
Document Type: Article
UDC: 519.1+514.17
Language: English
Citation: D. Rudenko, “On equidissection of balanced polygons”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 142–157; J. Math. Sci. (N. Y.), 190:3 (2013), 486–495
Citation in format AMSBIB
\Bibitem{Rud12}
\by D.~Rudenko
\paper On equidissection of balanced polygons
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXI
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 403
\pages 142--157
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029586}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 190
\issue 3
\pages 486--495
\crossref{https://doi.org/10.1007/s10958-013-1265-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880605306}
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  • https://www.mathnet.ru/eng/znsl/v403/p142
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:38
     
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