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Ranking small regular polygons by area and by perimeter |
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| Authors: | Ch Audet P Hansen F Messine |
| Institution: | 1. GERAD and Département de Mathématiques et de Génie Industriel, école Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal, Québec, H3C 3A7, Canada 2. GERAD and Département des Méthodes Quantitatives de Gestion, HEC Montréal, 3000 Chemin de la c?te Sainte Catherine, Montréal, H3T 2A7, Canada 4. école des Hautes études Commerciales, C.P. 6079, Succ. Centre-ville, Montréal, Québec, H3C 3A7, Canada 3. ENSEEIHT-IRIT, UMR-CNRS 5828, 2 rue Camichel, 31000, Toulouse, France |
| Abstract: | 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 as n increases. Similar properties hold for the perimeter. A new proof of a result by K. Reinhardt follows. |
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