Group for Research in Decision Analysis

G-2005-92

Ranking Small Regular Polygons by Area and by Perimeter

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From the pentagon onwards, the area of the regular convex polygon with n sides and unit diameter is greater for each odd number n than for the next even number n + 1. Moreover, from the heptagon onwards, the difference in areas decreases when n increases. Similar properties hold for the perimeter. A new proof of a result of Reinhardt follows.

, 12 pages

This cahier was revised in November 2006