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.
Published December 2005 , 12 pages
This cahier was revised in November 2006