Geodesic
Ranking small regular polygons by area and by perimeter
Diskretnyj analiz i issledovanie operacij, Tome 15 (2008) no. 3, pp. 65-73

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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.
Mots-clés : polygon
Keywords: diameter, area, perimeter. 
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Ch. Audet; P. Hansen; F. Messine. Ranking small regular polygons by area and by perimeter. Diskretnyj analiz i issledovanie operacij, Tome 15 (2008) no. 3, pp. 65-73. http://geodesic.mathdoc.fr/item/DA_2008_15_3_a6/