Divide L into L/e pieces to maximize product of the pieces
A stick of length L is to be broken into n equal-length parts.
The value of n that maximizes the product of the parts' lengths (i.e. (L/n)n)
is either ⌊L/e⌋ or ⌊L/e⌋+1.
(L/n)n
L = e e2 10 e3
⌊L/e⌋ = 1 2 3 7
n (e/n)n (e2/n)n (10/n)n (e3/n)n
--- ------- ------- -------- -------
1 2.71828* 7.38906 10.0000 20.08554
2 1.84726 13.64954 25.0000 100.85720
3 0.74391 14.94181* 37.0370 300.11422
4 0.21327 11.64437 39.0625* 635.76090
5 0.04749 7.04847 32.0000 1,046.08556
6 0.00865 3.48840 21.4335 1,407.32101
7 0.00133 1.46028 12.1427 1,601.39268*
8 0.00018 0.52965 5.9605 1,578.87471
9 0.00002 0.16948 2.5812 1,373.30951
10 0.00000 0.04852 1.0000 1,068.64746
11 0.00000 0.01256 0.3505 752.31265
12 0.00000 0.00297 0.1122 483.53331
