quasi
Posts:
11,311
Registered:
7/15/05


Re: A tensided polygon has the following property ...
Posted:
Jun 11, 2014 1:00 AM


quasi wrote: > >For each integer n >= 3, let f(n) be the greatest integer m >such that there exists an mgon in the plane whose boundary >can be covered by n lines. > >Some instant observations: > >(1) f(n) >= n, for all n. > >(2) f is nondecreasing. > >An easy observation: > >(3) f(n) >= 2n, for all n >= 5. > >Some tentative data: > > f(3)=3 > f(4)=4 > f(5)=10 > f(6)=12 > f(7)=18 > f(8)=21 > f(9)=32 > f(10)=36 > f(11)=48 > >Corrections and/or extensions to the above are welcome. > >A few conjectures: > >(1) f is strictly increasing. > >(2) f <= C(n,2), for all n. > >(3) As n > oo, f/C(n,2) > 1.
Correcting a few otypos ...
A few conjectures:
(1) f is strictly increasing.
(2) f(n) <= C(n,2), for all n.
(3) As n > oo, f(n)/C(n,2) > 1.
quasi

