See Graham, R. L. (1975). The largest small hexagon. *Journal of Combinatorial Theory, Series A*, *18*(2), 165-170. The problem of determining the largest area a plane *hexagon* of unit diameter can have, raised some 20 years ago by H. Lenz, is settled. It is shown that such a *hexagon* is unique and has an area exceeding that of a regular *hexagon* of unit diameter by about 4 ... available here: https://ac.els-cdn.com/0097316575900047/1-s2.0-0097316575900047-main.pdf?_ti... Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Fri, Sep 21, 2018 at 4:01 PM, Allan Wechsler <acwacw@gmail.com> wrote:
For a fixed N, suppose we want to make a polygonal pasture with N sides, with the largest possible area given a fixed perimeter. Is the unique optimum always a regular N-gon? I am looking for a figure of merit that tells how regular a polygon is, and perimeter/area seems promising. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun