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Diskretnyi Analiz i Issledovanie Operatsii, 2008, Volume 15, Issue 3, Pages 65–73 (Mi da535)  
This article is cited in 5 scientific papers (total in 5 papers)

Ranking small regular polygons by area and by perimeter

Ch. Audeta, P. Hansenbc, F. Messined

a GERAD and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal
b GERAD and Département des Méthodes Quantitatives de Gestion, École des Hautes Études Commerciales de Montréal
c École des Hautes Études Commerciales de Montréal
d Enseeiht-Irit
Full-text PDF (251 kB) Citations (5)
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Abstract: From the pentagon onwards, for each odd number $n$ the area of the regular convex polygon with $n$ sides and unit diameter is greater than the area of the similar polygon with $n+1$ sides. Moreover, from the heptagon onwards, the difference in areas decreases when $n$ increases. Similar properties hold for the perimeter. A new proof of the Reinhardt's result is obtained. Tabl. 1, illustr. 1, bibl. 18.
Keywords: polygon, diameter, area, perimeter.
Received: 10.10.2007
Revised: 03.03.2008
English version:
Journal of Applied and Industrial Mathematics, 2009, Volume 3, Issue 1, Pages 21–27
DOI: https://doi.org/10.1134/S1990478909010037
Bibliographic databases:
UDC: 519.178
Language: Russian
Citation: Ch. Audet, P. Hansen, F. Messine, “Ranking small regular polygons by area and by perimeter”, Diskretn. Anal. Issled. Oper., 15:3 (2008), 65–73; J. Appl. Industr. Math., 3:1 (2009), 21–27
Citation in format AMSBIB
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\by Ch.~Audet, P.~Hansen, F.~Messine
\paper Ranking small regular polygons by area and by perimeter
\jour Diskretn. Anal. Issled. Oper.
\yr 2008
\vol 15
\issue 3
\pages 65--73
\mathnet{http://mi.mathnet.ru/da535}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2542326}
\zmath{https://zbmath.org/?q=an:1249.52005}
\transl
\jour J. Appl. Industr. Math.
\yr 2009
\vol 3
\issue 1
\pages 21--27
\crossref{https://doi.org/10.1134/S1990478909010037}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-63349106596}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
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    Full-text PDF :168
    References:33
    First page:4
     
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