Renyi's parking problem: http://mathworld.wolfram.com/RenyisParkingConstants.html On Dec 2, 2012, at 8:05 PM, Dan Asimov <dasimov@earthlink.net> wrote:
1) For small L > 0, Let I(L) be a random maximal collection of disjoint closed intervals each of length L and lying in [0,1] in R.
Let |I(L)| denote the total length of all the intervals of I(L).
It seems clear that there exists some constant C(1) such that, with probability 1, the limit of |I(L)| as L -> 0 = C.
Question: Find C. -----------------
One 2D version of this is:
2) For small L > 0 let D(L) denote a random maximal collection of disjoint closed geometric disks each of diameter L and lying in [0,1]^2 in R^2.
Likewise, as L -> 0 what is the limit C(2) of the total area of the disks of D(L) ? -----------------
n) The nD version: In [0,1]^n, what is C(n) for any n ? -----------------
(If you don't like edge effects, these questions can be asked for the cubical n-torus R^n / Z^n instead of [0,1]^n, with the same answer C(n).)
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun