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Matematicheskie Zametki, 2005, Volume 77, Issue 1, Pages 117–120
DOI: https://doi.org/10.4213/mzm2474 (Mi mzm2474) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A short proof of the twelve-point theorem

D. Repovša, M. B. Skopenkovb, M. Cencelja

a University of Ljubljana
b M. V. Lomonosov Moscow State University
Full-text PDF (193 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm2474
Abstract: We present a short elementary proof of the following twelve-point theorem. Let $M$ be a convex polygon with vertices at lattice points, containing a single lattice point in its interior. Denote by $m$ (respectively, $m^*$) the number of lattice points in the boundary of $M$ (respectively, in the boundary of the dual polygon). Then $m+m^*=12$.
Received: 29.06.2004
English version:
Mathematical Notes, 2005, Volume 77, Issue 1, Pages 108–111
DOI: https://doi.org/10.1007/s11006-005-0010-6
Bibliographic databases:
UDC: 514
Language: Russian
Citation: D. Repovš, M. B. Skopenkov, M. Cencelj, “A short proof of the twelve-point theorem”, Mat. Zametki, 77:1 (2005), 117–120; Math. Notes, 77:1 (2005), 108–111
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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